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Multi-criteria timber allocation models for the analysis of sustainable forest management decisions Marinescu, Marian V. 2004

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MULTI-CRITERIA TIMBER A L L O C A T I O N MODELS FOR THE A N A L Y S I S OF SUSTAINABLE FOREST M A N A G E M E N T DECISIONS by MARIAN V. MARINESCU B.Sc. Forestry, Transilvania University, Brasov, R O M A N I A , 1987  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (Forestry) We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH C O L U M B I A August 2004  ©Marian V . Marinescu, 2004  Abstract  The problem addressed in this dissertation is that of optimally allocating timber to different processing facilities, while meeting the multi-criteria conditions of sustainable forest management and integrating the medium-term and operational decisions. A Multi-criteria Timber Allocation Model using goal programming was developed to include various criteria and indicators for sustainable forest management. The allocation procedure was demonstrated using five allocation criteria: profit, employment, wildlife, recreation, and visual. In a case analysis, two multi-criteria allocation scenarios, generated with different sets of goal weights, were compared against a profit-based scenario. The results demonstrated the capability of the Multi-criteria Timber Allocation Model to deal with sustainability criteria in a practical and flexible manner. A D E A Timber Allocation Model was developed using Data Envelopment Analysis, a method of calculating technical efficiencies of different operations. The model was demonstrated using two allocation criteria: profit and employment. The allocation results were compared to those of random, profit-based, and employment-based allocations and suggested that the model balanced the two allocation criteria without the need for their prioritization. However, adding other allocation criteria was complicated by procedural concerns. A two-level Hierarchical Timber Allocation Model was developed to integrate the medium-term and operational decisions, while accounting for the sustainability criteria. At the medium-term level, the Multi-criteria Timber Allocation Model was implemented to optimally allocate stewardship units to different forest products companies. At the operational level, the FTP Analyzer®, a sawmilling optimization model, was implemented for each company to optimally process the allocated timber. A n iterative algorithm was developed and demonstrated, in which the two planning levels reached mutually beneficial solutions. The model was demonstrated with an array of policy questions and revealed potential effects on both manufacturing processes and sustainability criteria. Future research was recommended to allow other criteria and indicators for sustainable forest management to be included in the D E A Timber Allocation Model. The Hierarchical Timber Allocation Model could also benefit from the addition of a strategic planning level, which could address the long-term, forest ecosystem management decisions and provide the medium-term level with available harvesting areas.  Table of Contents  Abstract  ii  Table of Contents  iii  List of Figures  v  List of Tables  ix  Acknowledgments  x  Chapter 1. Introduction  1  1.1. 1.2. 1.3.  Thesis Obj ecti ves Thesis Benefits Thesis Outline  Chapter 2. Background and Literature Review 2.1.  Linear Programming Models  2.2. 2.3. 2.4. 2.5. 2.6.  Criteria and Indicators for Sustainable Forest Management Goal Programming Models Data Envelopment Analysis Models Hierarchical Planning Models Summary  Chapter 3. The Development of a Multi-criteria Timber Allocation Model for the Analysis of Sustainable Forest Management Decisions  3 4 4 5 5 7 8 11 14 18  20  3.1.  Introduction  20  3.2.  Goal Programming  22  3.3.  The Multi-Criteria Timber Allocation Model  25  3.4.  Case Study  34  3.5.  Results  38  3.6.  Discussion  45  3.7.  Summary  50  Chapter 4. The Development of a Timber Allocation Model Using Data Envelopment Analysis  53  4.1.  Introduction  53  4.2.  Data Envelopment Analysis  54  4.3.  The DEA Timber Allocation Model  58  4.4.  Case Study  64  4.5.  Results  66  4.6.  Discussion  69  4.7.  Using Weights in the DEA Timber Allocation Model  72  4.8.  Summary  73  Chapter 5. Linking the Forest to the Product: The Development of a Hierarchical Timber Allocation Model 75 5.1. 5.2.  Introduction Theoretical Background  5.3. 5.4. 5.5.  Methods Policy Analyses Conclusion  75 78 82 98 149  Chapter 6. Thesis Summary and Conclusions  150  Bibliography  153  Appendix 1 - The Sawmilling Data  160  Appendix 2 - The Multi-criteria Timber Allocation Model Data  164  Appendix 3 - The DEA Timber Allocation Model Data  173  Appendix 4 - The Hierarchical Timber Allocation Model Data  178  Appendix 5 - The Policy Analysis Data  188  iv  List of Figures  Figure 3.1 - The map of the two landscape units  34  Figure 3.2 - The area of non-dominated solutions and the trade-off area for the visual criterion  38  Figure 3.3 - The area of non-dominated solutions and the trade-off area for the wildlife criterion  39  Figure 3.4 - The area of non-dominated solutions and the trade-off area for the recreation criterion  40  Figure 3.5 - The area of non-dominated solutions and the trade-off area for the employment criterion  41  Figure 3.6 - The comparison between the profit values  42  Figure 3.7 - The comparison between the employment values  43  Figure 3.8 - The comparison between the recreation, visual, and wildlife criteria values  44  Figure 3.9 - The comparison between the recreation, visual, and wildlife criteria values (partial-cutting techniques)  45  Figure 3.10- The map of the allocated stewardship units in the Base Case  48  Figure 3.11- The map of the allocated stewardship units in the Profit M A X scenario  48  Figure 4.1 - The efficient frontier generated by the CCR model  56  Figure 4.2 - The efficient frontier generated by the BCC model  57  Figure 4.3 - The structure of the DEA Timber Allocation Model  58  Figure 4.4 - The input and the output parameters into the DEA sub-model  60  Figure 4.5 - Profit (per thousand cubic meters) comparison  67  Figure 4.6 - Employment (per thousand cubic meters) comparison  68  Figure 4.7 - Volume comparison  69  Figure 4.8 - Profit (per thousand cubic meters) comparison - DEA (One Input and Three Inputs)  70  Figure 4.9 - Employment (per thousand cubic meters) comparison - DEA (One Input and Three Inputs)  71  Figure 4.10 - Volume comparison - DEA (One Input and Three Inputs)  71  Figure 4.11- Profit and the employment criteria when different weights were used  73  Figure 5.1 - The structure of a multi-level hierarchical system  78  Figure 5.2 - Example of the rolling horizon principle  79  Figure 5.3 - The structure of the Hierarchical Timber Allocation model  82  Figure 5.4 - The inter-level negotiating algorithm between the medium-term and operational level  87  Figure 5.5 - The comparison between the profit results of the Multi-criteria Timber Allocation and the Hierarchical Timber Allocation models  91  Figure 5.6 - The convergence of the profit values toward the optimal solution - the Equal Weights scenario. 93 Figure 5.7 - The convergence of the profit values toward the optimal solution - the Profit M A X scenario Figure 5.8 - The stem class distributions of timber allocated to Company 1 in Iteration 0 to 3  94 95  Figure 5.9 - The stem class distributions of timber allocated to Company 2 in Iteration 0 to 3  96  Figure 5.10 - The stem class distributions of timber allocated to Company 3 in Iteration 0 to 3  97  v  Figure 5.11 - The map of the allocated stewardship units in the Equal Weights scenario (unconstrained).... 101 Figure 5.12 - The map of the allocated stewardship units in the Equal Weights scenario, under the Wildlife Corridor policy Figure 5.13 - The impact of the Wildlife Corridor policy on the Equal Weights scenario - criteria  101 102  Figure 5.14 - The impact of the Wildlife Corridor policy on the Equal Weights scenario - volume differences of small end diameter  103  Figure 5.15- The impact of the Wildlife Corridor policy on the Equal Weights scenario - differences in the harvested areas and the profits Figure 5.16 - The map of the allocated stewardship units in the Profit M A X scenario (unconstrained)  104 106  Figure 5.17 - The map of the allocated stewardship units in the Profit M A X scenario under the Wildlife Corridor policy Figure 5.18- The impact of the Wildlife Corridor policy on the Profit M A X scenario - criteria  106 107  Figure 5.19 - The impact of the Wildlife Corridor policy on the Profit M A X scenario - volume differences of small end diameter  108  Figure 5.20 - The impact of the Wildlife Corridor policy on the Profit M A X scenario - differences in the harvested areas and the profits  109  Figure 5.21 - The comparison between the results of the Equal Weights and the Profit M A X scenarios under the Wildlife Corridor policy  110  Figure 5.22 - The map of the allocated stewardship units in the Equal Weights scenario under the Accessibility policy Figure 5.23 - The impact of the Accessibility policy on the Equal Weights scenario - criteria  112 113  Figure 5.24 - The impact of the Accessibility policy on the Equal Weights scenario - volume differences of small end diameter  114  Figure 5.25 - The impact of the Accessibility policy on the Equal Weights scenario - differences in the harvested areas and the profits  115  Figure 5.26 - The map of the allocated stewardship units in the Accessibility policy - The Profit M A X scenario Figure 5.27 - The impact of the Accessibility policy on the Profit M A X scenario - criteria  116 117  Figure 5.28 - The impact of the Accessibility policy on the Profit M A X scenario - volume differences of small end diameter  118  Figure 5.29 - The impact of the Accessibility policy on the Profit M A X scenario - differences in the harvested areas and the profits  119  Figure 5.30 - The comparison between the results of the Equal Weights and the Profit M A X scenarios under the Accessibility policy Figure 5.31 - The impact of the U.S./Canada Trade policy on the Equal Weights scenario - criteria  120 123  Figure 5.32 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 1 in the Equal Weights scenario  124  vi  Figure 5.33 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 2 in the Equal Weights scenario  125  Figure 5.34 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 3 in the Equal Weights scenario  126  Figure 5.35 - The impact of the U.S./Canada Trade policy on the Equal Weights scenario - volume differences of small end diameter  127  Figure 5.36 - The impact of the U.S./Canada Trade policy on the Equal Weights scenario - differences in the harvested areas and the profits  128  Figure 5.37 - The impact of the U.S./Canada Trade policy on the Profit M A X scenario - criteria  129  Figure 5.38 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 1 in the Profit M A X scenario  130  Figure 5.39 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 2 in the Profit M A X scenario  130  Figure 5.40 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 3 in the Profit M A X scenario  131  Figure 5.41 - The impact of the U.S./Canada Trade policy on the Profit M A X scenario - volume differences of small end diameter  :  132  Figure 5.42 - The impact of the U.S./Canada Trade policy on the Profit M A X scenario - differences in the harvested areas and the profits  133  Figure 5.43 - The comparison between the results of the Equal Weights and the Profit M A X scenarios under the U.S./Canada Trade policy Figure 5.44 - The cumulative effect of all policies in the Equal Weights scenario - criteria  134 135  Figure 5.45 - The cumulative effect of all policies in the Equal Weights scenario - volume differences of small end diameter  136  Figure 5.46 - The cumulative effect of all policies in the Equal Weights scenario - differences in the harvested areas and the profits Figure 5.47 - The cumulative effect of all policies in the Profit M A X scenario - criteria  137 138  Figure 5.48 - The cumulative effect of all policies in the Profit M A X scenario - volume differences of small end diameter  139  Figure 5.49 - The cumulative effect of all policies in the Profit M A X scenario - differences in the harvested areas and the profits  140  Figure 5.50 - The comparison between the results of the Equal Weights and the Profit M A X scenarios under the cumulative effects of policies  141  Figure 5.51 - The effect of the policies on the profit criterion  142  Figure 5.52 - The effect of the policies on the employment criterion  143  Figure 5.53 - The effect of the policies on the recreation criterion  144  Figure 5.54 - The effect of the policies on the wildlife criterion  145  vii  Figure 5.55 - The effect of the policies on the visual criterion  146  Figure 5.56 - The effect of the policies on the reserve area  147  Figure 5.57 - The effect of the policies on the volume harvested with partial-cutting techniques  148  Figure 6.1 - The Multi-criteria Timber Allocation model - The input-output data form  164  Figure 6.2 - The Multi-criteria Timber Allocation Model - The main form  165  Figure 6.3 - The Hierarchical Timber Allocation model - The interactive form  180  Figure 6.4 - The Hierarchical Timber Allocation model - The FTP Analyzer® consoles  181  viii  L i s t of Tables  Table 3.1 - An example of the wildlife, visual, and recreation indicator values  30  Table 3.2 - The employment levels of the three forest products companies  30  Table 3.3 - An example of the stand and stock data  31  Table 3.4 - The maximum volume capacities of the three companies  35  Table 3.5 - The Maximum treatment intensities for the three companies  35  Table 3.6 - The target values for the profit, employment, wildlife, visual and recreation goals  36  Table 3.7 - Scenarios used in the estimation of the non-dominated solution set  37  Table 4.1 - An example of cruise data  59  Table 4.2 - An example of the data input into the DEA sub-model  61  Table 4.3 - An example of efficiency scores  62  Table 4.4 - The technical parameters of the three companies  65  Table 5.1- Comparison between the criteria achievement values - The Multi-criteria Timber Allocation model vs. The Hierarchical Timber Allocation model  92  Table 6.1 - The operational parameters of Company 1  160  Table 6.2 - The operational parameters of Company 2  161  Table 6.3 - The operational parameters of Company 3  162  Table 6.4 - The product mix and the market structure of Company 1  162  Table 6.5 - The product mix and the market structure of Company 2  163  Table 6.6 - The product mix and the market structure of Company 3  163  Table 6.7 - The Multi-criteria Timber Allocation model - The results in the Equal Weights Scenario  166  Table 6.8 - The Multi-criteria Timber Allocation model - The results in the Profit M A X Scenario  169  Table 6.9 - The DEA Timber Allocation model - The input data  173  Table 6.10 - The DEA Timber Allocation model - The efficiency scores  176  Table 6.11- The DEA Timber Allocation model - The allocation results  177  Table 6.12- The Hierarchical Timber Allocation model - The results in the Equal Weights Scenario  182  Table 6.13 - The Hierarchical Timber Allocation model - The results in the Profit M A X Scenario  185  Table 6.14 - The results of the Wildlife Corridor policy  188  Table 6.15 - The results of the Accessibility policy  188  Table 6.16 - The results of the U.S./Canada Trade policy  189  Table 6.17- The results of the cumulative case  189  Acknowledgements  I would like to thank my supervisor, Dr. Thomas Maness for his unconditional support. Also, heartfelt thanks to my committee members: Dr. Taraneh Sowlati, Dr. John Nelson, Dr. Rob Kozak, and Dr. David Cohen. Your help has been priceless and timely. My thesis has benefited from the valuable ideas of Dr. Mark Boyland and Olaf Schwab. I am also grateful to Dr. Cindy Prescott and Dr. John McLean who supported me during very difficult times. There are no words to describe how grateful I am to my family. To my wife Daniela, who has supported me patiently, goes all my love. To my daughter Anca and my son Victor Lucas I apologize for the neglect. I will make it up to you! Many hugs and kisses I give to the many grandmas and grandpas who helped my family while I was at the office. I love you mama, Vica, and Mitica! I am also grateful to my father for his constant encouragements and for introducing me to the world of wood processing. I could not forget Katie Maness, Andre Schuetz, Duane and Dallas Foley for their expertise and assistance with my computer related problems. I would also like to thank my colleagues and friends for being there for me: Helen Rasmussen, Christina Staudhammer, Ross Farrell, Hauke Chrestin, Lin Ye, Diana Hastings, Margaret Graham, Donna Hartson, Mihai Pavel, Catalin Ristea, Eduard Maigut, Ian Elliot, Dorcas and Bill Rimer, Doina and Fanel Hritcu, Dana and Dinu Constantinescu, Violeta Toma, Iulia and Catalin Litman, and many others.  In the memory of my dear grandmother Vera Brodovinschi (Busi), the most courageous person whom I had the privilege of knowing.  CHAPTER 1. INTRODUCTION  In the last few years, the concept of forest sustainability has evolved from sustained yield to sustainable ecosystem (Hof 1993). Sustained yield is the amount of wood that a forest can continually produce at a given intensity of management (Helms 1998). The concept of sustained yield was enlarged to account for the production of other outputs, such as water, recreation, wildlife habitat. Sustainable forest management implies managing the forest for more than its outputs; it refers to the way a forest is managed to maintain and enhance the long-term health of forest ecosystems for current and future generations (Montreal Process 1995). Today, forestry researchers, managers, and analysts are dealing with increasingly complex problems in the area of sustainable forest management because its definition implies that long- and short-term forest management plans in a given forest ecosystem must ensure a stable economy and a non-declining relationship between all its ecological features. To be able to apply the concept of sustainable forest management as clearly and simply as possible, it is necessary to describe it in terms of guiding principles, criteria, and indicators. Consequently, forest management problems have increasingly become multicriteria in nature. Moreover, forest management practitioners have witnessed a shift in the purpose of decision support systems from providing readily applicable solutions, to facilitating a thorough understanding of these complex forest management problems. Timber allocation models have a central role in forest management because of their ability to link different decisions affecting forest ecosystem management problems. These decisions can include, among others: wildlife management, silvicultural prescriptions, harvest scheduling, and forest products manufacturing. In the context of sustained yield, timber allocation models have ensured that the wood resources provided by forests maximized the profits or the timber volumes allocated to wood manufacturing facilities. In these models, sustainability issues were treated as constraints limiting the amount of timber available for harvest. In the context of sustainable forest management, however, the importance of timber allocation models becomes greater. At the strategic and the tactical planning levels, timber allocation models ensure that management actions preserve as much as possible the original state of the forest ecosystem, while finding the optimal use of timber to achieve economic goals. Timber allocation models developed in this dissertation will attempt to bridge former approaches, aimed at sustained yield, to emerging approaches aimed at sustainable forest management. Stated in simple terms, the timber/log allocation problem is "given a certain heterogeneous supply of logs, how should this raw material be allocated among the available utilization facilities?" (Pearse and Sydneysmith, 1966). The ability of timber allocation models to integrate decisions specific to different planning levels has allowed researchers to analyze the effects of management policies on these activities. However, the development of timber allocation models for sustainable forest management requires special features in order to address the following issues:  1  The first issue is that the shift toward sustainable forest management requires timber allocation models to deal with a variety of sustainability criteria, such as visual quality, wildlife habitat, riparian management areas, recreation, and many others. Until recently, most of these models have dealt with the goal of maximizing the profits generated by allocating the timber to different uses (e.g. log production facilities, sawmills, pulp and paper mills, etc.), or maximizing the volume of allocated timber. Although an increasing number of multi-criteria timber allocation models have been developed, they either failed to complete the integration of forest to product decisions, or did not properly account for the sustainability criteria. The second issue is the investigation of the criteria and the indicators for sustainable forest management. In the last ten years, increased efforts in Canada and worldwide have been focused on developing and assessing different criteria and indicators for sustainable forest management. Although progress has been made at the national and regional level, the resulting criteria and indicators are still highly general and difficult to implement in practice. Including these criteria and indicators in the development of multi-criteria timber allocation models could result in major benefits. These models could generate valuable trade-off analyses, which could provide a better understanding of the sustainability of forest management actions. In addition, the operability and the relevance of these criteria and indicators could be further validated. The last and most challenging issue in developing the allocation models results from attempting to deal with decisions relating to different planning levels. When criteria and indicators for sustainable forest management are included, these models tend to become large and difficult to manage. In addition, because they span large time horizons, their results tend to become highly aggregated and, therefore, inaccurate. By separating the decisions belonging to different planning levels and by designing a system of links between them could decrease the complexity of the resulting models and provide more accurate and relevant results. This thesis addresses the problem of optimally allocating timber to different processing facilities, while meeting the multi-criteria conditions of sustainable forest management and integrating the medium-term and operational decisions. Three methods were examined: goal programming, data envelopment analysis, and hierarchical planning. Based on these methods, three multi-criteria timber allocation models were developed and demonstrated in a series of case analyses. These cases involved forest areas and hypothetical sawmills located in the Kootenay-Columbia Region of British Columbia, Canada. The results generated by these models constituted a base for comparison and discussion. Their implementation was addressed, but only to demonstrate the use of the models in the analysis of sustainable forest management decisions. 1  Three sets of results were common to all cases. The first set attempted to reflect the sustained yield approach to sustainability and was generated by profit maximization Sawmills were modeled after existing operations. They were considered hypothetical because of the sensitivity of their production/product data.  2  models. The second set of results suggested a transition from sustained yield to sustainable forest management approach and was produced by multi-criteria models in which the profit criterion was given a higher priority that the other allocation criteria. The third set of results presented an example of a multi-criteria allocation approach aimed at sustainable forest management, in which all the allocation criteria were given equal priority. In the process of generating results, the allocation criteria entered in the models were assumed to reflect the public views and concerns about the sustainability of forest ecosystem management in the study area. However, since the number of criteria and indicators for sustainable forest management is considerably larger than the number of criteria used in this thesis, their role was solely of demonstrating the methodological advances of the models, not of defining the sustainability of forest management activities depicted in the case analyses. It is therefore important to note that the inclusion in the models of other criteria and indicators for sustainable forest management may produce different results than those presented in this thesis.  1.1.  Thesis Objectives  The objectives of this thesis are: 1. To analyze the capability of goal programming (GP) to deal with the multi-criteria timber allocation problem by considering criteria and indicators for sustainable forest management, regardless of their number, nature, and unit of measurement. This objective was met by developing a Multi-criteria Timber Allocation model based on goal programming. The model uses the flexibility of GP to include allocation criteria, such as profit, employment, wildlife habitat, visual quality, and recreation. In addition, due to a system of goal weights, the model is capable of generating various scenarios and trade-off analyses. 2. To test the potential of data envelopment analysis (DEA) to assist with the multicriteria timber allocation problem without the need to prioritize/weigh the allocation criteria. This objective was met by developing a D E A Timber Allocation model that includes two allocation criteria: profit and employment. 3. To examine the ability of the hierarchical planning (HP) method to address the multicriteria timber allocation problem by integrating the medium-term and the operational decisions, while accounting for the sustainability criteria. This objective was met by developing a two-level Hierarchical Timber Allocation model that separates the medium-term and operational decisions, while retaining the necessary level of detail at each of the planning levels. In addition, the iterative procedure devised in this model ensures the compatibility of the decisions made at each level and, ultimately, the integration of forest to product decisions.  3  1.2.  Thesis Benefits  The most important benefit of this thesis is that employing each of the methods in the development of the multi-criteria timber allocation models expands the knowledge about the complexities involved in the multi-criteria timber allocation decisions. In addition, through trade-off analyses between different allocations criteria, a better understanding of the effects of different sustainability policies on both the forest ecosystem and the timber processing operations can be provided. The practical benefits of this research revolve around more accurate forest valuation analyses that include timber and non-timber values and improved assessments of forest estate to assigning cutting permits. In addition, the capability of these models to generate various scenarios that reflect the views and interests of many stakeholders, affected by the multi-criteria timber allocation decisions, provides means to resolve resource use and management conflicts, through negotiations and resource sharing/trading.  1.3.  Thesis Outline  In Chapter 2, a short background and literature review about the methods used in the development of the models is provided. Chapter 3 describes the Multi-criteria Timber Allocation model developed with a goal programming framework. Chapter 4 presents the development of a Tactical Timber Allocation model using data envelopment analysis. In Chapter 5, the Multi-criteria Timber Allocation model is used as a sub-model in the newly developed Hierarchical Timber Allocation model. In order to demonstrate the hierarchical model, a series of forest management policies aimed at sustainability are analyzed. Chapter 6 draws some conclusions about the methods analyzed in the dissertation and discusses future research.  4  CHAPTER 2. BACKGROUND AND LITERATURE REVIEW  For many years, analysts have recognized the merit of timber/log allocation models in integrating the forest management and wood processing decisions. Whether concerning volume-based or area-based allocation of logs or tracts of forest, these models have been perfected to include large and complex forest management issues. The early models were mainly concerned with forest regulation, harvest scheduling, and less with allocating timber to different facilities or uses. Timber allocation models came later as extensions to these problems. In these models, profit was the unique allocation criterion and linear/mixed integer programming was the preferred modeling method. Recently, multi-criteria, or multi-objective decision-making, has achieved increased recognition, because of its capability to address the allocation decisions in a more holistic context, including consideration of the social and moral values (Tarp and Helles 1995). Multi-criteria decision-making has become a prerequisite in forest management problems dealing with sustainability and multiple use issues (Mendoza 1988). One of the greatest consequences was the shift from the traditional decision-making, which neglected the human factor (the "black box" approach), to a more interactive and flexible process. As a result, the choice of methods for the multi-criteria allocation decisions needed to be supple and to allow for individual learning about the specific decision situations. Therefore, visual interaction, exploring and generating decision alternatives became tools in the development of individual strategies (Angehrn 1991). The experience accumulated over the years in developing multi-criteria applications (de Steiguer et al. 2003) and the current investigations regarding the criteria and indicators for sustainable forest management could play an essential role in the development of new multi-criteria allocation models. Through valuable scenario and trade-off analyses, these models could shed new light into the relationships between different sustainable forest management decisions. This chapter will introduce some applications of the methods used in this thesis, with emphasis on forestry and wood processing. First, the earlier studies, dealing with linear programming (LP) allocation models, will be presented. Second, the criteria and indicators for sustainable forest management will be introduced. Last, applications of goal programming (GP), data envelopment analysis (DEA), and hierarchical planning (HP) will be presented.  2.1.  Linear Programming Models  Linear programming (LP) is a single objective optimization method that optimizes a linear objective function subject to a linear set of constraints. A n LP model has three basic components: a single identifiable objective, input constraints, and alternative independent activities. For example, the objective could be that of maximizing the profits generated by 5  producing and selling lumber products from a series of logs of different grades and dimensions. The constraints could impose some technological parameters regarding the physical transformation of logs into lumber and could set limits on the amount of raw materials and hours of operations. LP models have been used in a wide range of applications, including the log/timber allocation. A typical LP log/timber allocation model optimizes the value generated by the volumes/forest stands when allocated to different uses, subject to a series of linear resource constraints (Burger and Jamnick 1995). There are cases in which, in order to allocate whole batches of logs or entire forest stands to different uses, spatial and ownership constraints are required. In these cases, integer/binary variables are included and the model becomes a mixed/integer linear programming model. For example, some timber allocation models included constraints dealing with spatial location of different silvicultural and harvesting treatments, such as green-up and adjacency constraints. Other constraints restricted the sharing of timber in a forest stand between different uses or ownerships. Regardless of their formulations, LP timber allocation models provide great practical and theoretical benefits. These models are used and well understood by most of forest management analysts, who are able to generate and analyze the results quickly and thoroughly. L P models provide multifaceted post-optimality analyses that can be further investigated and integrated with other optimization techniques. Last, LP models integrate a large number of processes/activities that can provide valuable impact analyses. When used stand-alone, the integrative capability of LP models is not fully utilized and their size becomes quickly prohibitive. When used as sub-models in decomposed or hierarchical planning models, their integrative role becomes essential and their size manageable. Most of the early LP timber allocation models were stand-alone and were initiated by matching anticipated log demands with groups of forest holdings. Donelly (1965) developed an LP model for plywood manufacturing that extended from the available wood supply to sales forecasts for a range of plywood products. Pearse and Sydneysmith (1966) constructed a log allocation model among several utilization processes (lumber, veneer, plywood, wood chips, and hog fuel) based on an LP model that maximized the total profit. Wolfe and Bates (1968) developed an LP model to allocate different sorts of wood to the production of paper grades. Thompson and Richards (1969) allocated logs to different cutting policies by minimizing wood procurement costs and comparing them for all acceptable mixes of resources and cutting policies. Lonner (1968) and Carlsson (1968) developed an area-based model to plan the allocation of forest tracts to different facilities over a five-year time horizon. The next generation of models presented some integrative features. Pnevmaticos (1974) integrated stem conversion (bucking) and log allocation to different conversion facilities into a single model. Westerkamp (1978) used a linear programming model to determine an optimal log allocation schedule for a hypothetical, vertically integrated firm located in Western Washington. Similarly, Barros and Weintraub (1982) combined an LP model and an information system to plan the production of a vertically integrated forest firm. The  6  model consisted of a large formulation, which included activities, such as: managing timberlands, buying or selling logs, and supplying timber to the processing plants. The use of Danzig-Wolfe decomposition and Lagrange multipliers (Danzig and Wolfe 1961) opened new possibilities in the application of operations research for the integrated forest products industry. Mendoza (1980) formulated an integrated wood resource allocation model as a two-stage decision process. The first stage consisted of determining the optimal bucking policy and the second stage determined the optimal allocation policy for the logs and finished products. The stem conversion and log allocation models were connected in an iterative process that stopped when an optimal solution was found. The shift from simple integrated models to more sophisticated, forest to product optimization models, took place when Hay and Dahl (1984) introduced the notion of "Forest to Product Flows" using linear and dynamic programming algorithms in two intertwined models (RAS and ARBITER). The design allowed strategic and midterm planning of timberland harvests, flows to mills, and production of products. Using the decomposition technique, Maness and Adams (1991) linked log sawing and bucking into a combined optimization model (Sawmill Production Control Model SPCM). The optimal solution provided both bucking policies and cutting patterns for each type of log. Donald et al. (2001) interfaced the combined log bucking and sawing model with a value added manufacturing model by introducing material variables from the latter model into the market constraints of the former. Maness and Norton (2002) combined sawing and bucking with a multi-period LP log allocation model. A l l the above allocation models had one common feature: they allocated the logs/timber to different processes/uses based solely on profit. Although some of the more complex models addressed the multiple-use characteristics of forest management, usually in the constraints, they did not allow for trade-off analyses or for the control of the allocation criteria. These models were designed for and benefited the operational level planning. Their extension to tactical and strategic level planning quickly becomes impractical, because at these levels a multitude of allocation criteria, such as criteria and indicators for sustainable forest management, need to be considered in the objectives.  2.2.  Criteria and Indicators for Sustainable Forest Management  Although specific to every social, geographical, and political entity, the criteria and indicators for sustainable forest management have one common feature: they are a reflection of the people's values in connection with public forests (O'Brien 2003) These values have been divided between two conflicting goals: development and conservation (Lanly 1995). Over the past ten years, many countries and organizations have tried to reconcile these opposing views. The success of these actions relied heavily on how different interest groups understood the notion of sustainability and its implications for protection and production. 7  In 1992, the Canadian Council of Forest Ministers (CCFM) committed, within the National Forest Strategy, to developing a set of criteria and indicators for sustainable management of Canadian forests. In 1997, the Council agreed to a set of 6 criteria and 83 indicators. Following the United Nations Conference on Environment and Development (1992), the Montreal Process (1995) endorsed 7 national level criteria and 67 indicators for sustainable management of temperate and boreal forests. Although the development of criteria and indicators at the national level constituted an important step toward a better understanding of sustainable forest management issues, they were highly general and difficult to implement. According to Bunnell (1997), these indicators needed to be reviewed in order to meet operational requirements. Subsequent to the development of the Canadian National Criteria and Indicators initiative, provincial, territorial, and regional organizations have developed their own sets of criteria and indicators directed toward implementation into forest management plans. For example, a large group of researchers from the University of British Columbia adapted the C C F M criteria for use in the management of Arrow Timber Supply Area, British Columbia (Robinson 2002). The outcome consisted of 9 criteria and 25 indicators, which could be implemented in the management plans of forest products companies in the area. Maness (2002) further evaluated these criteria and indicators based on their accessibility, measurability, operability, and relevancy. He suggested a new set of criteria and indicators, which could assist woodland managers in their strategic and tactical planning. In addition, he suggested that the application of the indicators to an operational planning model could provide further guidance to forest managers to meet the sustainability criteria. Maness acknowledged that because of the ongoing addition of new criteria, the study was only a starting point. Maness and Farrell (2004) developed a multi-criteria allocation model capable of analyzing different forest management scenarios using visual quality, wildlife habitat, and other sustainable forest management indicators. Among other findings, this study demonstrated that, when made operational, criteria and indicators for sustainable forest management became essential in analyzing different forest management policies. This potential could be utilized in the development of multi-criteria timber allocation models, which could be used to integrate and study the relationships between the sustainable forest management and operational decisions.  2.3.  Goal Programming Models  Goal programming (Charnes and Cooper 1962) is an established multi-criteria decision making method. Its mathematical formulation associates the objectives (goals) of the problem with their respective targets and includes them in the constraints. The objective function minimizes the weighted deviations of each goal from its respective target. According to Romero and Rehman (1989), and Tarp and Helles (1995), goal programming  8  (GP) has been the most commonly used multi-criteria decision making technique in forest management. Unlike single objective methods (e.g. linear programming), which find a unique solution, goal programming models find a range of solutions called non-inferior or non-dominated through the set of weights attached to the goals (Cohon 1978). These solutions are used in trade-off analyses, which assist the managers in choosing the best possible decision. Goal weighting is a major strength of goal programming because the weights reflect the importance that the decision maker attaches to each goal. It is simultaneously a weakness, because there is no simple way of pre-specifying the weights so that GP yields the most acceptable solution.  2  Field (1973) first applied the goal programming method to forest management problems. He provided a hypothetical example of a small woodlot management. A GP model allocated forestland to different uses in order to maximize the income from log selling, wood harvesting, outdoor activities, and to minimize the operational costs. Field proposed the employment of the GP model for two other situations: a pulp mill procurement strategy and a public land use conflict management. His study addressed various procedures for assigning priorities and weights to different goals. The study made a strong case for the use of goal prograrnming in allocation problems dealing with conflicting goals, in which linear programming proved impractical. Field et al. (1980) recognized the difficulties in setting the managerial goals and weights in an application of goal prograrnming to the timber harvest-scheduling problem. The goals considered were the maximization of timber volume, net present value, and the minimization of net present cost. The authors suggested a complementary use of linear and goal programming, in which a series of runs on the two models was performed. The most valuable result of the combined GP/LP procedure was that the GP solutions were guaranteed to be non-inferior, a common occurrence when using GP with managerial targets (i.e. practical, as opposed to optimal). Arp and Lavigne (1982) developed a GP application for multiple-use planning of forestlands, with variable planning horizons. A case study that demonstrated the GP procedure dealt with five land uses: dispersed and developed recreation, hunting, timber harvesting, and wildlife. Results showed the trade-offs between different goals and the effect of multiple time horizons on the land use allocations. In the area of wildlife habitat management, Ludwin and Chamberlain (1989) used GP to assist managers in converting areas of different habitat types. They recognized the limitations of the linear programming method in allocations dealing with many contradictory goals. By employing a GP procedure, however, the authors were able to allocate the available habitat area with minimum deviations from the goals. Their application to wildlife management was limited by a lack of information and restrictive habitat constraints.  2  A non-inferior or non dominated solution to a multi-objective problem is that solution in which none of the objectives can be improved without adversely affecting at least one of the other objectives.  Suter and Calloway (1994) applied goal programming to secondary wood manufacturing. The model scheduled the production of furniture rough parts with the following goals: part quota, budget, work-in-progress, schedule, and lumber availability. The application of GP in rough mill planning proved beneficial, especially when incommensurable goals were included (e.g. goal of completing a job on schedule). In another land-use management problem (Van Kooten 1995), a GP model was used to examine the impacts of the stakeholder process for allocating public forest land on Vancouver Island, B C , Canada. The author analyzed the allocation of land amongst alternative uses and determined the impacts on employment, government revenues, and the ability to meet annual allowable cut requirements. The goals were generated by a group of specialists and assumed to reflect the public expectations. The goals were then ranked based on two public surveys. Four allocation scenarios showed that, despite attaching high values to non-timber uses (e.g. tourism jobs, recreation), the net social benefits were substantially reduced under the current land use practices. In an effort to empower local communities and the private sector, the Government of Mozambique decided to manage forest resources as a joint venture. Consequently, Nhantumbo et al. (2001) employed a GP model for the management of miombo woodlands, the main natural forest resource in Mozambique. The model had seven goals: the protection of national parks, fuel wood harvesting, industrial wood harvesting, tourism, firewood consumption, pole consumption, and the demand for wild fruit and animals. The authors acknowledged that for such a large and complex model, data collection and goal prioritization were the most challenging tasks. The integration of biodiversity into forest management has been a widely accepted idea. Bertomeu and Romero (2001) claimed that managing biodiversity involved also the management of the forest landscape age structure. The authors proposed a GP model with binary variables to maximize the edge contrast between adjacent harvesting units. They characterized biodiversity based on four goals: old stands, all age representation, age balance, and the edge effect. Although tentative, this study showed how the spatial characterization of biodiversity could be made operational using a GP framework within a forest management plan. De Oliveira et al. (2002) developed a GP model for the allocation of farm areas in Brazil to different uses: timber harvesting, tealeaves, pasture, tourism, and flora biodiversity. The authors first ran the model one objective at a time in order to compare the optimal values with the targets imposed by the stakeholders. They employed the GP model using different weights in order to compare the conflicting goals and analyze the trade-offs between them. Important conclusions were drawn regarding the conflict between the timber harvesting and flora biodiversity. The majority of the GP applications presented here dealt with decisions made at the tactical and strategic planning levels and had no consideration of the interconnections between these decisions and the operational activities. Although some applications included harvesting activities, they did not consider manufacturing processes and did not complete 10  the forest to product integration. Some applications included indicators for biodiversity, wildlife, and recreation criteria, but did not consider the criteria and indicators for sustainable forest management.  2.4.  Data Envelopment Analysis Models  Unlike linear and goal programming methods, Data Envelopment Analysis (DEA) (Charnes et al. 1978) has received modest implementation in forestry. D E A is a method of assessing the efficiency of operations called decision-making units (DMUs), such as forest management divisions, sawmills, value added facilities. The efficiency of each unit is calculated based on the relationship between the observed sets of inputs and outputs that can include timber volumes, hours of operation, employment, profit, etc. D E A models generate efficiency scores for each of the DMUs involved in a study. These scores indicate the level of inefficiency of the inefficient DMUs in relation to the efficient ones. Consequently, procedures could be devised to re-allocate resources (the inputs) in order to improve the efficiency of those units with lower scores. Timber allocation models could take advantage of the efficiency scores generated by D E A models because this method does not require any prioritization or weighting of different criteria (the inputs and the outputs). However, the addition of criteria is not arbitrary, due to the strict requirements regarding the homogeneity of the decision-making units and the input-output data structure (Dyson, R.G. et al. 2001). The homogeneity condition requires that the DMUs are similar in their activities and products and they operate in similar environments. In addition, the inputs and the outputs need to be common to all the DMUs. Consequently, the inclusion of criteria and indicators for sustainable forest management may be difficult. Kao and Yang (1991) first used D E A to rank and then to analyze the efficiencies of thirteen forest districts of the National forests of Taiwan. The D E A model used multiple inputs (budget, initial stocking, labour, and land area) and multiple outputs (yearly timber harvests, subsequent stocking, and yearly recreational visits per hectare). The study opened the door to more analyses into the causes of different inefficiencies. In 1992, Kao and Yang used their previous study to find ways of reorganizing the forest districts and to improve their efficiency. Unfortunately, the efficiency comparison stopped short of considering the subsequent manufacturing potential. LeBel (1996) used D E A to analyze the efficiency of logging contractors in the US. The study took place in a complex temporal and economic context. The inputs consisted of capital, consumables, and labour and the only output was the volume of logs harvested by contractors. The author used data collected between 1988 and 1994 to assess the efficiencies of logging companies in different years, when various events in the life of these companies occurred (market changes, recession). In addition, another degree of complexity was added to the problem: the size of the logging companies.  11  Shiba (1997) used D E A to calculate the efficiency of 28 Forest Owner Associations in the Mie Prefecture of Japan. The author acknowledged the multi-objective features of forest management problems by using different input/output structures. A large number of inputs were considered, such as total number of staff, total number of private forest owners over 50 ha, total investment funds, number of harvesting machines, number of sawmills, total timber sales, total lumber production, total reforestation areas, and many others. The outputs consisted of total revenue, total profit, and total employment. The case analyses identified which of the inputs or outputs had a dominant effect on the efficiencies. The results suggested that the sawmilling and harvesting activities had an important effect on efficiency and it should always be included in the studies. Viitala and Hanninen (1998) and later Joro and Viitala (1999) used D E A to compare the efficiencies of 19 Forestry Boards . Particularly interesting in these studies was the complex process of selecting the best input and output parameters. Both environmental and organizational factors were used to assess the efficiencies of the Forestry Boards. However, due to a potentially large number of outputs involved in these applications, the analyses were performed separately for the following activities: forest road construction, forest ditching, management planning, training, forestry laws, and administration. For each activity, a series of inputs and outputs were defined, such as planned length of forest ditches, length of supervised ditching, length of inspected ditching, area under forest management plans, area under wood-lot plan, number of owners offered personalized training, owners attending group training, number of internal personnel trained, and many others. The two studies emphasized the complexity of evaluating the efficiencies of public forest organizations and recommended ways of reducing by 20% the cost of their forestry activities. Yin (1998, 1999, and 2000) measured the efficiency of 102 linerboard producers in North America. The studies suggested ways of improving the efficiency of the most inefficient operations by targeting different input factors, such as fiber supply, operating labour, and supervision. Fotiou (2000) compared the efficiencies of 17 sawmills in Greece. Capital (measured by installed power) and labour (measured by yearly employment) were the inputs and total production was the output of this model. The analysis also assessed the effect of logistics on efficiency. The author first calculated the efficiency scores of all 17 sawmills and then separated them into two groups according to the markets from which they purchased raw materials (i.e. local and foreign). A statistical analysis on the efficiency scores of the two groups was performed in order to assess whether logistics had a significant effect on the efficiencies of those operations. The analysis showed a significant tendency of sawmills with large purchasing networks to perform more efficiently than the others did. Nyrud and Baardsen (2002) analyzed the efficiency and productivity of the Norwegian sawmilling industry between 1974 and 1991. They focused their attention on two major 3  Forestry Boards are the most important public forestry organizations in Finland charged with the preparation of forest management plans, forest road planning and construction, and with the implementation of forestry policies and laws.  12  aspects: the efficiency of sawmills over time and their productivity growth. The results showed that 30% of sawmills were efficient and that the inefficient ones maintained their inefficiency over time. In addition, the analysis revealed that the average productivity growth was very low. Nyrud and Bergseng (2002) extended the above analysis to account for the size of Norwegian sawmills and its effect on their efficiencies. Bogetoft et al. (2003) analyzed the efficiency of district offices in the Danish Forest Extension Service (DFES) and assessed the effects of potential mergers. The DFES consisted of 14 district offices, representing 7,200 forest owners and managing 16% of total forest area in Denmark. The authors used a D E A model with three inputs (salary, administrative costs, and site production) and three outputs (annual economic surplus, annual surplus generated to members, and annual sale of seedlings). The analysis revealed great differences in efficiency across offices and identified 15 potential mergers. The conclusion was that the current effort to merge offices might be counterproductive. Instead, the authors proposed that different offices should increase their technical efficiencies by means of cooperation, dissemination of managerial expertise, and change in scale. Hailu and Veeman (2003) analyzed the efficiencies of six Canadian boreal logging industries (provinces) between 1977 and 1995. They used a D E A model with two inputs: capital and labour, and one output: profit from value-added operations. The study revealed substantial differences in efficiency within the boreal logging industry. In addition, the results showed that forest characteristics, such as forest density and proportion of hardwood production, had positive effects on efficiencies. Todoroki and Carson (2003) used D E A to identify the most efficient logs for producing certain lumber products. The D E A model had one input: the processing time of converting the logs into lumber products, and three outputs: the volume of clear-wood lumber (i.e. lumber with no defects), the volume of lumber other than clear wood, and the volume of residues produced from logs. The efficiency scores generated by this model were related to the profitability measures calculated for the same logs and lumber products. Based on this relationship, the study explored the identification of those tree characteristics that could be altered genetically in order o increase the efficiency of producing specific lumber products. Kao (2000) developed the only D E A application dealing with resource reallocation in forestry. Using previous studies (1991 and 1992), the author reallocated budgets to improve the overall efficiencies of forest districts. The reallocation took place after assessing the efficiency scores for each forest district and finding an optimal allocation of budgets within each district. Kao modified the traditional D E A model to include budget allocation variables. To account for an equitable reallocation, these variables were bounded and different scenarios were generated using different bound ranges. In a case analysis, the model was able to reallocate budgets resulting in increased forest district efficiencies. Thus far, the use of D E A in forestry has been almost entirely concerned with assessing the efficiencies of forestry organizations and little with resource reallocation. Although the applications presented above constitute valuable theoretical references, none has been applied to or assisted with the development of multi-criteria timber allocation models. This 13  is unfortunate because the capability of D E A models to assess technical efficiencies and generate scores could potentially be utilized in multi-criteria timber allocation models. In developing these models, D E A model could match timber resources to the requirements of different manufacturing facilities (e.g. sawmills).  2.5.  Hierarchical Planning Models  Despite the fact that all real systems are continuous, without any separation between the decision problems, periods, and time horizons, classifying decisions in a hierarchical manner leads to better understanding of the decision making process and the implementation of solutions (Silver and Petersen 1985). Hierarchical planning is a method of disaggregating a large decision problem according to the principles imposed by real or hypothetical hierarchical planning levels. In practice, the hierarchical planning levels are chosen to reflect some disaggregation principles, such as the goals and time horizons of certain management problems (strategic, tactical, and operational), the geographical location (world, continent, country, province), the competencies of particular managerial categories (central office managers, branch managers, production supervisors), and others. After the planning levels have been established, the decision problem is broken down into sub-problems and assigned to different levels. In order to become operational, a certain level of data aggregation needs to be achieved at each level and data interactions between levels need to be designed (Mesarovic et al. 1970). Due to the complexity of forest ecosystems, hierarchical planning (HP) has received an increased attention from forestry and land-use managers. In modeling timber allocations, the complexity arises from dealing simultaneously, in large models, with decisions spreading over time horizons with different lengths and addressing different goals (strategic, tactical, operational). This results in difficult implementation, computational burden, and data inaccuracy. Hof and Baltic (1991) used HP to analyze the production capabilities of the US National Forest System. The model consisted of a regional and a national level. At the regional level, an LP model (FORPLAN) was used to generate production alternatives for each of the 120 forest planning units considered in the study. The national level used a mixed integer linear program with binary variables that minimized the total cost of production alternatives. Iterating between the two levels was not feasible because the F O R P L A N models were not able to operate simultaneously. Instead, each forest-planning unit provided the national level model with a set of planning alternatives, which served as choice variable options. The case analyses revealed infeasibilities in the current policy of constant supply for all projected resources. The study was lacking because the regional level models were unable to interact dynamically with the national level.  14  Nelson et al. (1991) developed and evaluated procedures for integrating short-term, areabased plans with long-term, strata-based harvest schedules. The long-term goal was to establish strategic harvest targets over a 150-year time horizon and was performed with a linear programming model. The targets were then used as guidelines for the generation of 30-year, area-based plans using a Monte-Carlo integer programming technique. The areabased plans were entered in an integrated, long-term integer linear programming model that considered the harvesting units and the road projects as binary variables. The resulting integrated plans generated net revenue and volume levels within 10% of the strategic goals imposed by the strata-based model. Weintraub and Cholaky (1991) used HP methodology for large scale forest planning. Two planning levels were considered in this study: strategic and tactical. At the strategic level, the forest was divided into zones and variables for area and land management activities were aggregated based on a set of similarity rules. The LP model used at this level maximized the net present value associated with allocating each zone either to timber or wilderness management. At the tactical level, the land use allocations generated by the strategic level model were disaggregated and detailed management alternatives were defined. The model used was an LP model that maximized the profits associated with each zone. Due to possible aggregation errors at the strategic level, the HP procedure allowed for correcting iterations between the levels in order to guarantee consistency between the strategic and tactical plans. However, the correcting procedure did not guarantee the convergence toward optimal solutions. Davis and Barrett (1992) presented a pilot project called California Forest Information and Analysis System (FIAS). The scope of this project was to quantify wildlife habitats for implementation in land use and timber harvesting plans at the landscape level. FIAS consisted of a hierarchy of programs/models, each with its own set of input/output data and goals. These models were interconnected so that data flow between them was consistent with the goals of each model. The most important models/programs were the GIS database containing the wildlife habitat relationship data, the wildlife habitat maps, the US Forest Service timber inventory, the tree growth and yield simulators, and the strategic planning system for the analysis of land use and harvesting plans. The output of FIAS consisted of 50-year projections of wildlife habitat and harvest scheduling. In addition, maps of landowner land use plans were also generated to show where specific activities took place on the ground (e.g. harvesting, wildlife management). Hof et al. (1992) developed an iterative procedure between two hierarchical levels of a forest planning model. The objective was to minimize the cost of meeting forest-wide targets for multiple outputs (timber, forage, sediment, forest cover). The two planning levels consisted of a central forest control model and a set of district-level forest models. The role of the central forest control model was to assign output targets to each of the district forests in order to minimize the total cost. With these targets, the forest level models were run again and sent back to the center reduced costs for each of the outputs. With this information, the central forest control model generated a new set of targets. The procedure was based on the work of Heal (1969) and caused the objective function of the central forest control model to decrease monotonically until it reached a minimum. The authors 15  tested the procedure on a problem comprised of four district forests and four sets of outputs. The results demonstrated the usefulness of the multi-level planning in problems where decomposition was unpractical or impossible to perform. The authors emphasized the use of this procedure in the development of hierarchical allocation models, in which iterations between planning levels are required. Ogweno (1994) applied hierarchical planning to the log production-planning problem. The model consisted of a medium-term tactical model, a short-term tactical model, and an operational scheduling model. The first two levels were both tactical due to their temporal characteristics: up to 30 years time span for the medium-term tactical level and up to 1 year for the short-term tactical level. The medium-term tactical model addressed issues of sustainability, regulatory requirements, and preliminary scheduling of log production over a medium-term horizon. The short-term tactical model disaggregated the medium-term plan into detailed production plans. The operational model solved for optimal scheduling and allocation of harvesting systems to production units, and also developed detailed log mix production and allocation plans. A series of assumptions were made. First, the internal transfer prices for logs and other materials were assumed equivalent to market prices, which might be relevant for a sole log producer, but unrealistic for an integrated company producing many primary and secondary wood products. Second, the external purchasing of material was not considered. Lastly, issues related to log re-manufacturing were not considered, which diminished the integrative aspect of the model. The author acknowledged the need for future research into the integration of manufacturing (operational) processes in order to obtain a complete forest to product framework. Colberg (1996) applied an HP model in a case analysis at Mead Coated Board, a division comprising a paper mill, two sawmills, and half a million acres of forestland. The longterm (strategic) level of the model consisted of a woodlands planning capability that managed the regional fiber balance and provided data about fiber availability to the medium-term (tactical) level. This level consisted of a stand-specific harvesting scheduling system able to prepare one and five-year treatment and harvesting plans. The operational level contained supply, cost data for every known source of fiber, and addressed wood procurement issues. The goal was to minimize the costs of wood delivered to the wood processing facilities. The model was useful for calculating the company's fiber resource availability, but it fell short of considering the interaction with the manufacturing facilities. Although it did not complete the forest to product flow, the model demonstrated that hierarchical planning could thoroughly deal with problems pertaining to the forest products industry. Paredes (1996) proposed a two level HP model. The model was based on an iterative, duality-based framework that coordinated the multiple-use planning of forest resources. Timber and non-timber values could be included in the model. Price-guide methods at the upper level initiated the first allocation. Shadow prices and output levels from the lower level fed back into the upper level, where a new set of adjusted prices was generated. The upper level model stopped the iterative process when a feasible solution was reached. The greatest accomplishment was that the HP model addressed the allocation process  16  dynamically. Unfortunately, the study suffered because the multi-objective features were not explicitly addressed and the model was not demonstrated in a case analysis. Weintraub et al. (1997) presented two aggregation procedures that could complement hierarchical planning approaches. The first procedure, called a posteriori, used cluster analysis techniques to determine which columns in the large L P model (i.e. long-term level model) were to be aggregated. The second procedure, called a priori, cluster analysis techniques were implemented to aggregate similar stands before the actual building of the LP model. The two procedures were demonstrated in a series of case analyses and suggested solutions with smaller errors due to aggregation than manual or silvicultural aggregation techniques. Unfortunately, procedures for testing and reducing of these errors were not investigated. Feunekes and Cogswell (1997) applied an HP model to generate spatially feasible harvest schedules that met long-term sustainability criteria. The model consisted of two levels: strategic (non-spatial) and operational (spatial). At the strategic level, "WOODSTOCK", a forest modeling system, generated LP matrices and produced solutions for the long-term portion of the scheduling problem. At this level, issues of spatiality were not addressed. The lower level model, " S T A N L E Y " , allocated forest stands to harvest blocks subject to adjacency, maximum opening size, and wood flow constraints. Three case studies demonstrated that the model delivered good results, regardless of the spatial scales of the problems. The HP framework, however, was not dynamic; the upper level model imposed strict constraints on the spatial availability of the lower level model. Dewhurst et al. (1997) developed a two level HP model to address the sustainability issues of the Menominee Tribal Forest in Wisconsin, USA. The model consisted of a strategic level (150 years) and a tactical level (25 years). At the strategic level, a goal programming model selected a mix of treatments which, when applied to age classes of different strata at different periods, satisfied the multi-criteria goals (i.e. maintain a sustainable balance of age classes, maintain a high value and productivity of forest species, maintain a sustainable flow of wood). At the tactical level, an integer goal programming model distributed the activities scheduled for the first planning period across the landscape units. The model functioned by extracting the first period (25 years) treatment specifications from the strategic planning results. The two levels were connected through a feedback mechanism, which allowed the tactical level model to suggest treatments to the strategic level model. The overall model could be re-run to assess the effects of the suggested treatments on the strategic plan and to determine the corresponding adjustments. Cea and Jofre (2000) developed an HP model for forestry planning decisions at the strategic and tactical level. The strategic level dealt with the management of pine stands over a time horizon of 45 years. The model used at this level was a mixed integer programming model, which maximized the components of the net present value: harvesting, transportation, silvicultural regimes, and processing. The authors also introduced a set of investment decisions to allow the possibility of expanding, building, or closing processing facilities to which the timber was sold. The tactical level dealt with the construction of roads, transportation costs, income from timber sales, and stand harvest 17  costs. The model used at this level was a mixed integer programming model, which maximized the profit generated from timber sales. The model was solved with an algorithm based on a modified simulated annealing technique. A cluster analysis algorithm aggregated the so-called "macro-stands" in the tactical level model and connected it with the strategic level. This action was essential in attaining consistent solutions for both the strategic and tactical level decisions. Church et al. (2000) reiterated the need for tactical level models within the hierarchical planning structure of the US Forest Service for reconciliation between the strategic level and the operational level planning. Two Bridging Analysis Model (BAM) approaches based, respectively, on linear and goal programming frameworks were developed to make the strategic solutions feasible when interpreted at a greater level of spatial resolution. The difference between the two approaches was that, in the first, the areas prescribed for treatments remained the same as in the strategic solution, whereas, in the second, the activity totals generated at the strategic level acted as targets rather than exact activity levels. The authors acknowledged the usefulness of using a goal programming methodology in the second approach; however, they also proposed further expansion to incorporate other goals, such as protection of biodiversity and fuels management. A n increasing number of hierarchical planning applications have been developed in forestry in the last few years. Although addressing different goals and using different modeling methods, they portrayed HP as a holistic and integrative approach. Therefore, the HP method could benefit the timber allocation decisions, especially those aimed at sustainable forest management.  2.6.  Summary  This chapter showed the evolution of allocation models in forestry from simple, individual problems dealing with profit maximization to complex, multi-criteria, integrative problems. But before any attempt is made to build such models, criteria and indicators for sustainable forest management require increased attention. In this regard, the publications about criteria and indicators presented in this chapter consisted of those directly related to the models described in this thesis. There is ongoing research to make more of these criteria and indicators operational. Goal programming applications embodied a representative sample of the work done in multi-criteria decision making in forestry. Their contribution to the area of sustainable forest management has been valuable in areas ranging from land-use planning to wildlife habitat selection. Unfortunately, no goal programming applications were identified in the areas of timber allocation and forest to product optimization. The method could benefit the development of multi-criteria timber allocation model because of its capability to deal with a wide range of sustainability criteria.  18  Data envelopment analysis (DEA) has the potential to alleviate some of the procedural problems of goal programming, such as assigning weights to managerial goals. Most of the applications presented in this chapter used D E A to estimate the efficiency of decisionmaking units and only one was used for resource re-allocation. No applications were found in which this method was used for multi-criteria timber allocation. The method could be used to generate efficiency scores that could be included into multi-criteria timber allocation models. This chapter also presented numerous applications of hierarchical planning in forestry, which portrayed hierarchical planning as a holistic method that could greatly benefit sustainable forest management decisions. Although, in the last few years, the number of HP applications in forestry has increased, there are large, unexplored areas that could benefit from implementing this method. Multi-criteria timber allocation is definitely one of these areas. The method could help with the separation of different allocation decisions at each level of management, while accounting for the sustainability criteria. The applications presented in this chapter constitute a solid theoretical foundation for the research undertaken in this thesis. The multi-criteria timber allocation models developed in this thesis used the knowledge gained from these applications in order to address the difficulties associated with multi-criteria timber allocation problems, such as goal prioritization, forest to product integration, hierarchical separation of decisions, and others.  19  CHAPTER 3. THE DEVELOPMENT OF A MULTI-CRITERIA TIMBER ALLOCATION MODEL FOR THE ANALYSIS OF SUSTAINABLE FOREST MANAGEMENT DECISIONS  3.1.  Introduction  In the Province of British Columbia, Canada, the practice of forest management has changed dramatically. The decreasing quantity and quality of timber resources, coupled with increasing pressure toward forest ecosystem conservation, have influenced governments and forest products companies to focus on forest practices certification and sustainable forest management. Achieving these objectives, however, has proven to be a difficult and complex undertaking. Although progress has been made, there is still debate about the definition of sustainability and the applicability of certification (Floyd et al. 2001). In addition, there is still confusion about what the measures of sustainability are and whether the sustainability indicators can be made operational (Bunnell 1997). The research presented in this chapter took place in the Kootenay-Columbia Region, located in the southeastern part of British Columbia, Canada. Currently, the Government of British Columbia leases large areas of forest, called charts, to the forest products companies. Each year, they request cutting permits to harvest timber in their own chart areas. The allocation of timber considers only the profit generated from lumber products sales. In this area, the latest studies to identify criteria and indicators for sustainable forest management (Robinson 2002, Maness 2002) and to evaluate their use in sustainable forest management (SFM) plans (Maness and Farrell 2004) have provided encouraging results. These studies have opened the door to new and innovative methods of assessing the impact of forest management practices on the sustainability of forest ecosystems. Timber allocation models have always assisted managers in analyzing the effects of their management actions both on the forest ecosystems and on the processing operations to which the timber was allocated. The capability of timber allocation models to integrate the forest to product decisions has been well documented. The works of Mendoza (1980), Hay and Dahl (1984), Maness and Adams (1991), Maness and Norton (2002), are just a few examples of models that have integrated timber allocation with processing activities. These models, however, dealt with just one goal, that of maximizing the profits generated by converting the allocated timber into lumber products. A n important part of developing sound sustainable forest management plans consists of analyzing the trade-offs between different sustainability criteria that occur when forest areas are allocated to different uses. In order to assist with these analyses, timber allocation models are required to become multi-criteria. Goal programming (GP) has been the preferred multi-criteria method used to address forest sustainability issues and a wealth of multi-criteria allocation models using goal programming exists in the scientific literature. 20  The studies presented by Arp and Lavigne (1982), Ludwin and Chamberlain (1989), Van Kooten (1995), Bertomeu and Romero (2001) demonstrated the applicability of multicriteria allocation models in land-use planning and wildlife habitat selection. Unfortunately, these models did not integrate the forest to product decisions in their formulations. The requirement that the multi-criteria timber allocation models aimed at sustainability integrate the whole spectrum of forest to product decisions is essential, because the relationships between the sustainable forest management activities and downstream operations (harvesting, sawmilling, value-added manufacturing) are difficult and, in some cases, impossible to assess. For example, sustainable forest management actions could force sawmills to close down or to restructure their production in order to account for new timber supply configurations. In turn, value-added facilities would need to change their production and marketing parameters. Communities could also feel the ecological, economic, and social consequences of sustainable forest management activities, through the loss of full time jobs and ultimately poorer standards of living. Multi-criteria timber allocation models can be used to assess these outcomes. Changes at both the operational and the medium-term level can be analyzed and implemented. For example, wood processing facilities, sawmills, and regional businesses can devise new products and technologies that reduce the negative effects of the forest management practices and consequently can access markets for products manufactured from sustainably managed forests. In addition, new forest management practices can be devised to account for priorities set by the local communities. Unfortunately, the latest successes in identifying and evaluating the criteria and indicators for sustainable forest management have been offset by the lack of models that could integrate them into the forest to product decisions. There is a need for multi-criteria timber allocation models capable of generating trade-off analyses between different sustainability criteria and of integrating sustainable forest management decisions with those of downstream operations. This chapter presents the development of a Multi-criteria Timber Allocation model using a goal programming formulation. This is a multi-period model designed to allocate forests tracts to different forest products companies over a 5-10 year time horizon (medium-term planning). In addition, the model allows any number of periods of different lengths. Due to the flexibility of goal programming, the criteria and indicators for sustainable forest management can be directly entered as objectives (goals) in the model. The allocation procedure developed in the Multi-criteria Timber Allocation model was demonstrated in a case study concerning two landscape units in the Kootenay-Columbia Region of British Columbia, in which forest tracts were allocated to three hypothetical forest products companies. The Multi-criteria Timber Allocation model was employed in order to account for the social, ecological, and economic sustainability criteria and to integrate the sustainable forest management with the operational decisions. A Geographical Information System (GIS) database for the two landscape units provides the majority of input data, including the criteria and indicators. The stewardship units (SUs) 21  are the basic units (forest tracts) that are allocated by the model. They are created by merging adjacent polygons with similar attributes, such as: recreational, visual quality, wildlife and species class (Maness and Farrell 2004). Sustainability criteria considered in this model are social, ecological, and economic. The following five indicators are entered in the model: profit, employment, wildlife (ungulate winter range), visual quality objective (VQO), and recreation (hiking). The profit indicator values for each stewardship unit are calculated with the use of a sawmilling optimization model (FTP Analyzer®) for each of the forest products companies involved in the allocation. The employment indicator values are calculated based on employment data taken from the Timber Supply Review of the area under study. The GIS database provides the wildlife, visual, and recreation indicators for each stewardship unit. These indicators consist of values between zero and one, which indicate the existence or lack of the features described by each indicator. The goal programming method was selected for the development of the Multi-criteria Timber Allocation model because it is used by the majority of forestry analysts, it is flexible and easier to develop, and provides many and valuable insights into the multicriteria decision problems (Tarp and Helles 1995). Based on the linear programming structure, its deterministic attributes fit well with the medium-term time horizon (5-10 years). Assuming that the model does not include numerous spatial constraints (usually associated with timber harvest scheduling), it is computationally appropriate to use GP in medium-term planning. In addition, GP is able to model the multiple objectives and the physical elements of the timber allocation in a reasonably realistic manner. Moreover, the method facilitates the integration with other linear programming based models. In this chapter, a short description of the goal programming method precedes the presentation of the Multi-criteria Timber Allocation model. A case analysis is used to demonstrate the model. The chapter concludes with a summary of the findings and some remarks about the practical and theoretical benefits of the model.  3.2.  Goal Programming  A linear goal programming (GP) model has the following formulation (Charnes and Cooper 1962): P  Min  {wf • d* + w • d } t  t  (1)  i=l Subject to:  cx t  Ax<b  + d = G for each goal i i  i  (2) (3) 22  >0  x,dtA  (4)  Where: f+ j i ' i  : Vectors defining slack and surplus deviational variables.  +  : Vectors defining weights of slack and surplus variables.  a  ;  -  X  : Vector defining the variables of interest.  c-  : Vector defining the contribution of each unit of variable x to achieving i.  A  : Vector defining the relationship between variables X and resources b.  b  : Vector defining resources available.  In this formulation, in addition to the set of constraints (3), which define the feasible region, there exists an equality constraint (2) for each specified goal target G . These constraints consist of slack and surplus deviational variables (c?, and dP), which indicate the positive or negative departure of the goal achievement from each of the goal targets. The objective function (1) in the GP formulation minimizes the weighted sum of slack and surplus deviational variables. ;  +  The set of goal constraints (2) does not restrict the feasible region; therefore, if the constraint set (3) is feasible, so is the overall GP problem. The weights Vf, and w, are used to prioritize and/or rank the goals and to make all the weighted deviations commensurate with their respective goals. Unfortunately, there is no simple way of prespecifying the weights so that GP model yields the most acceptable solution. The task of assigning values to weights can be, to some extent, simplified by using relative weights.  Vwt-dt  Min ^  + w7-d7  (5)  i=l By substituting the objective function (1) with (5), each weight is divided by its corresponding goal target and the weight will express the relative importance of deviating by a certain percent from the respective goal. The main advantage of using this feature is that the weights are all expressed in the same unit of measurement and are easier to understand and implement. To simplify the choice of weights even further, it is best to reduce the objective function to those variables that are consistent with the problem at hand. For example, if the negative deviation of a certain goal (e.g. profit) from its target needs to be minimized and the 23  positive deviation is welcomed (i.e. more profit is desired), then only the negative deviation and its associated weight need to remain in the objective. Caution needs to be exercised, so that appropriate target values are assigned to the remaining variables. Assigning target values that are too low in the case of negative deviations or too high in the case of positive deviations could result in infeasible solutions. There are two categories of values that can be used as target levels: an anticipated need for particular goals or their achievable, realistic potential (Rustagi 1985). Often, it is difficult, if not impossible, to anticipate the need for a particular goal (e.g. wildlife habitat). Instead, optimizing one objective at a time and using the optimal value as the target for each goal is the most utilized method of assigning target values (Mendoza 1985). The optimization of each objective guarantees the feasibility of the GP model. The goal programming method does not restrict the goals (criteria) in terms of numbers, units of measurement, and relationships with other goals. This capability is important when incommensurable goals (e.g. 0-1 values, scores) are included in the GP models alongside commensurate goals (e.g. volume, profit, employment). The linear goal prograrnming model presented in expressions (1) to (4) contains continuous variables. In situations where all or some of these variables are required to attain integer values, the model becomes a mixed/integer GP model. This model is used when, as in this study, whole entities (i.e. stewardship units) need to be allocated and including binary (0-1) variables in the model becomes essential. However, the use of integer variables usually increases the computational load of the model. Although many analysts support the idea that the number of integer variables is directly responsible for the increase in computational time, the model formulation is also important. It is advisable to achieve a balance between the number of integer variables and the constraints associated with them (Williams 1991). Unlike linear programming models, goal programming models do not generate unique solutions, but rather non-dominated solutions. Therefore, the user must evaluate a number of scenarios before finding a suitable solution for the multi-criteria decision problem. One of the commonly used procedures involves first estimating the non-dominated solution set and then identifying those scenarios that are most appropriate to the problem at hand. To construct the non-dominated set, extreme weights are applied to different goals and scenarios are generated until the set is revealed. Because of the inherent drawback of assigning weights to different goals, some analysts could become discouraged from using GP models because of procedural complexities and computational burden. This is an unfounded reaction, because all of the other multi-criteria methods suffer from the same complication. Rustagi (1985) stated: "goal programming may not have any special advantage over other techniques, but it clearly does not have any disadvantage either. There is nothing wrong with the goal prograrnming technique and it provides a viable alternative for handling linear multi-objective problems".  24  3.3.  The Multi-Criteria Timber Allocation Model  The model developed in this chapter is a multi-period, multi-criteria timber allocation model using the following mixed integer GP formulation: Wn  Wp  Wrs  Wn  G  G  G  G  p  E  v  Wm G  R  w  Subject to: Y.Vofh-P ) ijkt  + p-=G  ijkt  Z(yo^ 'E ) ijkt h  (7)  p  iJkt  +  E-=G  (8)  E  Z(yolykt • ijkt) + Z(*«; ijkt j  -Vj) + V- = G  Z{Volf ijkt  • Rj) + R~ = G  V  h  • Ryt) + X(Re j  Sj  Z • ijkt  W ) + ZiReSj j  -TotVoff  -M-binSy  • Wj)  + Y.i fkt) kt Vol  +  W~ = G  iJ  Y (VoI°f ) ikt i  j  *'  X (Voff  kt  • Vol ) ijkt  f  M  for each/  < Max V  it  o  re  a  c  h  for each j  for each;  +Resj= TotVoff  kt  (11)  W  -Tot Voff - M • bin Re Sj + Resj > -M  J  (10)  R  ijkt  Y (binS ) + binRes =\ i  (9)  v  for each i,t  V"  O ) 2  (13) ( ) 1 4  (15)  (16)  jk 25  for each j  (17)  0 < binSy; binRes • < 1 integer binary variables  (18)  Tot Volf = 100%  A l l variables are positive Variables:  r  : Negative deviations of the profit, employment, visual, recreation, and wildlife goals from their targets. The positive deviations are welcomed; therefore, they are not included in the model.  ,ET ,ir ,BT ,w  % Volijkt  : Percent of volume of stewardship unit (SU) j allocated to company i and harvested with treatment t in period k.  Resj  : Percent of volume of SU j allocated to reserve throughout the entire time horizon.  binS.  : Binary variable indicating i f SU j was allocated to company  binRes j  : Binary variable indicating i f SU j was allocated to reserve Percentage of volume in SU j allocated.  TotVoff Parameters:  Gp, Gg,Gy, Gft,Gjy  w  p  G  p  ijkt  w  E  G  E  w  w  v  G  v  R  w  G  G  R  w  w  : Profit, employment, visual, recreation, and wildlife goal targets. The goals are calculated by running the model with one goal at a time (i.e. generating allocations that will maximize each goal, one at a time). : Relative weights associated with the profit, employment, visual, recreation, and wildlife goal targets. The weights could be interpreted as the relative importance of deviating by one percentage point from the respective goals. Weights are entered in the model by the user in order to prioritize different goals and usually take values from 1 to 100. : Profit generated by allocating SU j to company / in period k and harvested with treatment t. Profit values are generated by the FTP Analyzer®, by running the model for each company and SU, in each period. For partial-cuts, the profit values are 26  reduced according to the volume intensity of the partial-cut treatment. £. J  : Employment generated by allocating SU j to company i in period k and harvested with treatment /. Employment values are calculated depending on the company, the area, the volume, the distance to sawmill, and the slope of each SU. For partial-cuts, the employment values are reduced according to the volume intensity of the partial-cut treatment.  V -,R-,WJ  J  J  '• Visual, recreation, and wildlife indicator values for SU j when allocated to reserve. These values are entered in the model from the GIS database for the area under study and are scores between 0 and 1.  Vi kf>^i.'ki^ikt  ' Visual, recreation, and wildlife indicator values for SU j when allocated to company i in period k and harvested with treatment t. The indicator values are entered in the model by the user and are scores between 0 and 1. These values depend on the harvesting method used by each company in each S U and period. Generally, for clear-cuts, these values are zero, meaning that no visual, recreation and wildlife features could exist in stewardship units harvested with clear-cutting treatments. For partial-cuts however, these indicator values can retain part of the initial score (i.e. taken from the GIS database) depending on the volume intensity of the treatment applied by each company to each SU, in each period.  Vol--u  '• Volume of timber in SU j available for allocation to company / in period k and harvested with treatment t. These values are calculated based on the tree information in the GIS database. For partial-cuts, the volumes are reduced according to the volume intensity of the partial-cut treatment.  t  Max Vj  '• Maximum volume capacity (m ) of company j in period t.  M  '• Large number. This number should be greater than TotVolf" in order to force SU j to be allocated to just one company.  3  t  The objective (6) of this model is to find an optimal allocation of stewardship units to companies that will minimize the sum of weighted negative deviations of profit, employment, recreation, visual, and wildlife goals from their targets.  27  Constraints (7) to (11) set the targets for each of the goals and connect the allocation variables Voly]/ to the deviational variables in the objective function. 0  Constraints (12) and (13), in combination with constraint (14), connect the binary variables to the stewardship units to which they refer and guarantee that one stewardship unit is allocated to either one company or to reserve. Constraint (15) requires that the sum of volumes allocated to either sawmilling or reserve does not exceed the maximum volume available in each SU j. Constraint (16) sets the maximum volume capacity (m ) of company i in period t. 3  Constraint (17) is an upper bound on the volume available for allocation in each SU. In this formulation, it forces all the volume in each SU to be allocated. Constraint (18) sets the values of the integer variables to zero or one (binary). 3.3.1. The FTP Analyzer® The FTP Analyzer® is a combined linear-dynamic programming optimization model that optimizes sawmilling activities of each company involved in the study. The objective of the model is to find the optimum set of bucking policies, cutting patterns, and production parameters that maximizes the profit generated from manufacturing lumber products. For each sawmill, the inputs into the model are the raw materials, the cut programs, the lumber products and markets, and the plant configuration. There are three categories of raw material data: quota timber, purchased timber, and purchased log distribution. Quota timber represents the amount of timber that the government allows a company to harvest in a certain period. In the case of quota and purchased timber, the input data consists of cruise files for each stewardship unit allocated to the company. Cruise files contain measurements, such as diameter at breast height (DBH) and total height, taken from sampled trees in each stewardship unit. The raw material entered in the model can be expressed also in stem volume distribution format. 4  The model also requires input data about the cut programs for the conversion of stems into lumber. This data is comprised of machine speeds, productivities, and costs for each machine center, such as bucking lines, sawing lines, planers, and others. In addition, lumber products and markets need to be entered for each sawmill. Each product is defined in terms of its gross and net dimensions, the position in the log, the species, the grade, and the selling price. The plant configuration data contains the capacities of each machine center.  4  The model was developed by WoodFlow Systems Corp., Vancouver, BC, Canada. The mathematical formulation can be found in Maness and Adams (1991).  28  By running the model for each company/sawmill, the stems in each stewardship unit are optimally processed into lumber according to each company's production and market parameters. After each run, a report manager compiles the results. Reports are generated for each machine center, product, and for the overall facility. Profit values generated by this model consider a multitude of costs, such as transportation costs, stumpage/purchasing costs, and production costs associated with each machine center. 3.3.2. Data The study area is located in the Kootenay-Columbia Region of British Columbia and consists of two landscape units (LU) with a total area of 45.8 thousand hectares and a total volume of spruce-pine-fir (SPF) timber of 7.75 million m . The area includes a system of permanent roads, fish steams, lakes, wildlife areas and corridors, hiking trails and points of tourist attraction. Consequently, the forest management in this area is complicated by these numerous uses. 3  The Geographic Information System (GIS) database for the study area (Maness, T.C. and Farrell, R. 2004) provided the majority of parameter values entered in the Multi-criteria Timber Allocation model. The basic unit was the stewardship unit (SU), which was created by aggregating adjacent polygons with similar attributes, such as: recreational features, visual quality, and species class. Occasional contrasts in these features required the creation of smaller sized units, which usually lie on landscape unit boundaries. The rationale for the creation of stewardship units was that the polygons were too small in size and their large number made them impractical for use in a medium-term model. In addition, the use of harvesting blocks was not possible because they were usually known only when an area was available for harvest. The creation of SUs was done manually, by carefully studying the GIS data. Four hundred and sixty three stewardship units were compiled, ranging from 0.02 hectares to 1,114 hectares (the average SU was 180 hectares). The GIS data was imported into a M S Access database, where a series of queries were performed in order to determine the criteria and indicators attributes for each SU.  29  Recreation  Visual  Wildlife  Coeficient  Coeficient  Coeficient  1 2  0 0  0.6 0.8  0 1  4  0  0.6 0.6  0 0  0  1  0  0 0 1  0.6 0.6 0 1  0 1 0 1  0.8 0.6 0.8 0.8  S U No.  3  0  5 6  0.8 -  0 0  7  0.8  1  8  0 1  9 10 11 12 13 14 15 16 17  0  1  0.6  1 0 0  18 19  1  0 1 1 1  0 1 0 1 1 0  0.8 0.8 0.6  Table 3.1 - An example of the recreation, visual, and wildlife indicator values in the GIS database. NOTE: These values are incommensurable.  The values for recreation (hiking), visual (VQO ), and wildlife (ungulate winter range) indicators (Rj, Vj, Wj) were taken from the GIS-Access database and reflect the current, unaltered condition of each stewardship unit with regards to each indicator. Table 3.1 shows an example of the data for these indicators. Recreation indicators are comprised of values of one when the SU contains hiking trails and zero otherwise. Visual indicators are comprised of values between zero, for no VQO, and one for the preservation objective. The intermediary visual indicator values are 0.8 for retention, 0.6 for partial retention, 0.4 for modification, and 0.2 for maximum modification objectives. The rationale for these values is that they could relate the V Q O to the treatment intensities proposed in each SU. Wildlife indicators are also comprised of values of one if the SUs are within a winter ungulate range and zero otherwise. 5  Employment Sources: Harvesting/Administration Transportation Road Silviculture Processing  COMPANY 1 High Medium Low (pers-years/1000 m3)  EMPLOYMENT COMPANY 2 Medium Low High (pers-years/1000 m3)  0.71 0.11 0.33 0.03 0.69  0.15 0.07 0.02 0.06 0.46  0.59 0.08 0.28 0.03 0.64  0.47 0.06 0.23 0.03 0.59  0.12 0.07 0.02 0.05 0.43  0.09 0.06 0.02 0.04 0.39  High  COMPANY 3 | Medium Low (pers-years/1000 m3)  0.50 0.17 0.08 0.03 1.49  0.46 0.15 0.07 0.03 1.26  0.41 0.14 0.06 0.03 1.02  Table 3.2 - The employment levels of the three forest products companies considered in the study (from the Timber Supply Review).  VQO (Visual Quality Objective) is a resource management objective that reflects the desired level of visual quality based on the physical characteristics and social concerns for an area. They are the results of visual quality assessments.  30  Employment values (Ey/a) were taken from the socio-economic analysis of the Timber Supply Review (BC Ministry of Forests 2000). Employment values in Table 3.2 indicate the average number of full-time jobs per year and cubic meters of harvested timber for each company. In order to differentiate the employment generated by each SU, a set of classes was developed specific to the average terrain slope (<10 %, 10-30 %, >30 %), the distance to sawmill (<10 km, 10-30 km, >30 km), the volume (<10,000 m , 10,000-20,000 m , >20,000 m ) and the area (<50 ha, 50-100 ha, >100 ha) of the stewardship units considered in the analysis. B y matching these classes with the appropriate employment levels for each activity, the total employment values were calculated for each SU and company. 3  3  3  Stewardship Unit#  Height (m)  Species  DBH (cm)  Number of Trees  1  26.1 25.0 25.1 25.5 25.1 27.4 15.5 25.1 15.5 25.1 15.5 25.1 15.5 25.1 25.1  Pine Fir Pine Pine Pine Pine Pine Spruce Pine Pine Pine Pine Pine Fir Fir  20 45 15 40 35 30 30 30 25 35 20 15 15 60 55  475.34 97.05 180.65 42.33 80.56 131.38 22.22 182.77 27.58 45.44 143.39 706.61 154.88 36.11 36.14  Table 3.3 - An example of the stand and stock data in the GIS database.  The FTP Analyzer® generated the profit values (Pykt)- The model was run for each stewardship unit according to the production settings, the product mixes, and the markets of each company. The timber data was taken from the stand and stock tables contained in the GIS database for each SU. Table 3.3 shows an example of the stand and stock table indicating the values for species, height, diameter at breast height (DBH), and number of trees per hectare in the stewardship unit 1. The stand and stock data was then inputted as raw material data in the FTP Analyzer model. One thousand three hundred and eighty nine runs were performed (i.e. 463 SUs x three companies). In order to decrease the computational time, the FTP Analyzer® was run on a separate computer for each company and the profit values were stored in a central database. The targets for profit, employment, visual, recreation, and wildlife goals (Gp, GE, Gy, GR, Gw) were generated by the Multi-criteria Timber Allocation model by running the model to maximize each goal separately. The rationale for this procedure was that assigning optimal goal targets guaranteed that the Multi-criteria Timber Allocation model generated feasible solutions. This procedure was employed before the actual run of the model and set the appropriate goal targets. 31  The visual, recreation, and wildlife indicator values V^u Rykt, Wykt were entered for each stewardship unit and represented how much of the indicator values remained in the SU after a certain harvesting treatment technique was applied to it. These values were assumed indirectly proportional to the treatment intensities: the larger the harvesting intensities, the smaller the residual values. For example, in the case of clear-cut harvesting (i.e. 100% intensity), the indicator values are zero, or very small. However, deducing how much of each indicator value is retained after applying partial-cutting techniques is difficult to estimate. Depending on the indicator, even the least invasive partial-cutting techniques (i.e. low intensity partial-cut) could cause the indicator values to drop to zero. For example, the wildlife inhabiting a stewardship unit could be so sensitive to human interaction that even the lowest intensity partial-cuts could eradicate its habitat. Despite the difficulty of estimating these indicator values, the rationale behind their inclusion in the model was that the resulting timber allocations could generate valuable analyses of different partial-cutting techniques, otherwise impossible to produce. In order to make these values easier to estimate and apply, the computer model allows the inclusion of different relationships between these values and treatment intensities. For example, users could assign a certain indicator value when the treatment intensity is within a certain interval, or could set it to zero if the intensity is above a threshold. In this study, the visual, recreation, and wildlife criteria values were considered indirectly proportional with the volume intensity (Intensityki) of the harvesting treatment t applied by company i to SU j in period k, according to the following expressions: y  ijkt= j^-  V  v  ijkt= ji -  R  R  yykt)  Intensit  l  yijkt)  Intensit  W =Wj{\-Intensity ) m  m  As a result, all of these criteria values were zero for the clear-cutting treatments (i.e. 100% volume intensity), while the criteria values were greater than zero for those stewardship units with visual, recreation and wildlife features. 3.3.3. Data Handling To enhance the flexibility, the Multi-criteria Timber Allocation model was developed on an M S Access 2002 platform. The model is able to run cases with any number of goals, stewardship units, companies, and periods. Forms were designed to facilitate the input of data in tables and the presentation of results . A form using a slider for each goal was created to facilitate a simple and accurate input of the goal weights. On the same form, the goal results were presented in a graphical format. The user could therefore visualize where 6  6  An example of the input-output data form is provided in Figure 6.1 in Appendix 2.  32  the solution was located in relation to the non-dominated solution set . A connection with the GIS database provided the automation of data input and the visualization of different allocation scenarios on the map. The LP solver used in the model was X A , by Sunset Technologies. A number of queries generated the Row/Column/Coefficient (RCC) data format required by this solver. Other queries were also developed to decode and present the results. The data automation and model loading were performed with Visual Basic for Applications (VBA) code within the MS Access™ environment. The model was run on an Intel® Pentium 2.2 GHz, 1.99 G B R A M , dual processor PC. 3.3.4. Model Assumptions and Limitations Due to the use of linear goal programming, the relationships among variables were all assumed linear. Some operational costs, such as costs of dispersed operations and stand tending costs were not considered. The relationships between the wildlife, recreation, and visual indicators values and the volume intensities of different treatments were assumed linear. A non-linear relationship would have a direct effect on the timber volumes allocated to clear-cut and partial-cut treatments. The volume of timber was assumed uniformly distributed across the stewardship units. When parts of the stewardship units were allocated, the resulting timber volume was assumed to be equally divided among all log classes. Data taken from the GIS database was assumed to reflect the real forest characteristics of each stewardship unit. In this model, only spruce, pine, and fir species (SPF) were considered. The Multi-criteria Timber Allocation model has some limitations. First, due to time horizon (medium-term planning), scope (timber allocation to different companies), and size (medium size) of the model, the spatial layout of different treatment activities was not considered. Implementation of spatial constraints will result in increased computational time. Second, the model dealt concomitantly with forest management (medium-term planning) and wood processing (operational) issues, which will result in implementation problems. Last, the model implemented a static allocation procedure, meaning that the profit values calculated for each stewardship unit and company were assumed constant after the mix of stewardship units was allocated to companies. However, profit values could change depending on different factors, such as the timber composition of the stewardship units in the mix and the operational constraints imposed by the sawmilling operations (bottlenecks, etc.). This limitation will cause inaccurate allocations.  7  The form is presented in Figure 6.2 in Appendix 2.  33  3.4.  Case S t u d y  In the study area, three hypothetical companies (Company 1, 2, and 3) share the timber located in the two landscape units, each managing one sawmill in the region. These companies present large differences in production parameters, products, markets, and sizes . Company 2 manages a high speed, low cost stud mill and it employs the least number of people. The other two companies manage sawmills with similar production parameters. However, there are some differences between these two companies regarding their machine centers, product structures, and ages. Company 1 has an older, less diverse and less automated operation than the other companies did. By contrast, Company 3 produces a large number and types of products destined for a variety of markets (domestic, US, Japanese). 8  Map of study area  Legend  Figure 3.1 - The map o f the two landscape units considered i n the study, indicating the chart areas for Company 1, 2, and 3.  Figure 3.1 indicates that the three forest products companies currently operate in their own timber supply areas (charts). To harvest timber, each company must apply for a permit in its own chart. The profit generated from lumber sales is the only criterion considered in the allocation of stewardship units to each company. In contrast with this method of allocation, the Multi-criteria Timber Allocation model accounts for the following sustainability criteria: profit, employment, wildlife, recreation, and visual. Moreover, companies have access to timber located outside their charts.  For sawmilling parameters please refer to Tables 6.1 to 6.6 i n Appendix 1. Note: Lumber prices were taken from Random Lengths ( M a y 2001).  34  3.4.1. The Base Case The Base Case modeled the current allocation policy and required that the companies selected from their own chart those stewardship units that produced the most profit. To model this policy, the Multi-criteria Timber Allocation model was modified to maximize just one allocation criterion: the profit generated by each company from processing the allocated timber. A separate run of the model was required for each company. In each run, the model selected the stewardship units belonging to a company's chart until the maximum volume capacity in each period was reached (Table 3.4).  Period 1 Period 2  Company 1  Maximum Capacity Company 2  Company 3  (thous. cubic meters)  (thous. cubic meters)  (thous. cubic meters)  350 1,400  200 800  250 1,000  Table 3.4 - The maximum volume capacities of the three companies.  In order to provide a realistic balance between the volume of timber in the two landscape units (7.75 million m ) and the total volume capacity of the companies (4 million m ), the time horizon chosen for the case analysis was 5 years, consisting of two time periods: one year, followed by four years. A length of one year for the first period was assumed appropriate in the context of implementing a five-year plan. The profit values were discounted by 5% in the first period to adjust for the time preference of money. 3  3  Company  *  o  £.  O  Period  Treatment  Intensity  1 2 1 2 1 2 1 2 1 2 1 2  Clearcut Clearcut Partial Cut Partial Cut Clearcut Clearcut Partial Cut Partial Cut Clearcut Clearcut Partial Cut Partial Cut  100% 100% 40% 40% 100% 100% 47% 47% 100% 100% 37% 37%  Table 3.5 - The maximum treatment intensities for the three companies in the Base Case.  Treatment intensities presented in Table 3.5 were used to calculate the maximum profit and volume values for each SU, company, and treatment that could be generated in each period. For simplicity, harvesting intensities were considered constant in both periods, for all the stewardship units. However, the companies were assumed to prefer different partial-cutting techniques and, therefore, the intensities varied between the companies. 35  3.4.2. The Multi-Criteria Timber Allocation In contrast with the Base Case, the Multi-criteria Timber Allocation accounted for all the allocation criteria and allowed companies to access timber located outside their own charts. A l l of the parameter values used in the Base Case (i.e. profit values, maximum volume capacities, treatment volume intensities, period lengths, and discounts) were used in this case. Objectives Profit (Million $) Employment (Person-years) Wildlife Visual Recreation  Targets 266 6,573 140 145 133  Table 3.6 - The target values for the profit, employment, wildlife, visual and recreation goals. Note: The values for the wildlife, visual, and recreation targets are incommensurable.  Unlike the Base Case, which dealt with just one allocation criteria (i.e. profit); goal targets for each of the allocation criteria were calculated. The model automatically calculated goal targets for the five allocation criteria (Table 3.6) before performing the multi-criteria allocation. Note that the wildlife, visual, and recreation goal targets do not have units of measurement, because their values are incommensurable (i.e. scores). With harvesting intensities presented in Table 3.5, the model calculated the employment, visual, recreation, and wildlife indicator values for each SU, company, treatment, and period. The Base Case generated a unique allocation solution that maximized the profit of each company. B y contrast, the Multi-criteria Timber Allocation generated a series of nondominated solutions depending on weights entered for each goal. Using the graphical form and assigning extreme weights to each of the allocation criteria, the user is able to construct the non-dominated solution set. This procedure is usually performed with pairs of criteria. In this case, the profit was chosen as the criterion against which all the other criteria values were plotted. Profit was chosen because it is well understood by analysts and supports most meaningful trade-off analyses. To construct the non-dominated solution set, the results of 29 scenarios presented in Table 3.7 were generated with the Multi-criteria Timber Allocation model.  36  1  • y  1 1  Profit (Million $)  Employment (Pers-years)  145.00 145.00 118.07 117.05 144.30 111.03 118.51 95.80 138.78 101.38 96.82 102.96 134.21 107.93 100.09 105.99 103.24 126.14 104.31 106.20 118.55 105.37 107.80 105.54 106.12 104.61 104 49 104.61 106.45  Recreation  100 1 100 1 1 1 . 1 1 1 100 1 50 1 1 1 20 1 1 1 10 1 1 1 1  Wildlife  Visual  100 100 1 100 1 1 100 1 1 500 1 1 1' '1 •>.-. ."1: 100 1 1 100 1 1 50 1 1 1 1 50 1 1 20 1 1 1 1 1 1 20 10 1 1 1 1 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1  ACHIEVEMENT VALUES Wildlife  1 1 1 1 1 1 1 1 100 1 1 100 .1 • .,'-.1 100 1 100 1 100 1 100 1 100 1 100 1 100 50 100 1 100 1 100 100 100 1 100 1 100 1 100 1 100 50 100 1 100 1 100 1 100 20 100 ' 1 100 10 100 2  Visual  Profit  1 2 3 4 5 6 , 7 8 g 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  Recreation  Scenario  Employment  WEIGHTS  140.00 133.00 2,126 $73.97 112.60 104.52 5,231 $171.46 140.00 120.29 5,901 $201.94 121.72 133.00 6,144 $213.34 76.90 62.98 6,045 $226.48 117.61 108.71 6,566 $226.54 • 125.59 ^-123104 84.81 132.26 6,255 $245.58 85.90 72.53 6,214 $249.91 137.86 72.45 6,244 $252.48 87.97 126.75 6,267 $254.76 134.29 74.52 6,282 $255.73 92.40 76.15 6,234 $257.37 104.36 87.32 6,484 $258.16 88.56 118.13 6,272 $260.49 126.92 78.61 6,266 $261.62 93.43 82.54 6,438 $261.69 93.92 79.32 6,276 $261.84 93.38 108.86 6,265 $263.39 120.05 80.17 6,260 $263.75 96.30 81.41 6,247 $264.17 95.53 86.26 6,347 $264.95 95.71 83.41 6,237 $265.70 93.58 88.07 6,244 $265.79 99.39 82.08 6,243 $265.88 94.44 85.05 6,294 $265.91 94.50 83.57 J S I S 2 4 3 4 i $ 2 6 5 ^ 4 94.97 84.08 6,269 $265.95 96.50 85.52 6,241 $266.00  Table 3.7 - Scenarios used in the estimation of the non-dominated solution set. Shaded areas indicate the values generated by the Equal Weights and the Profit M A X scenarios (7 and 27 respectively).  Each goal was first allowed to reach its target (maximum achievement). A weight of 100 was then applied to one goal at a time, while the rest of the weights were assigned values of 1. The weight of the profit goal was kept at 100, while each of the other goals was given an incrementally higher value, in order to plot the variation of different indicators against the profit goal. Note that there are no null or negative values in Table 3.7 because all of the goal weights must be greater than zero, therefore generating non-zero solutions. In addition, all of the indicator values (including the profits) were positive, resulting in positive results. After the non-dominated set was constructed, two allocation scenarios were chosen and compared with the Base Case allocation. Shaded areas in Table 3.7 indicate the weights and the results of these two scenarios. The first scenario, called Profit M A X (Scenario # 27), emphasized the profit goal, which supported the comparison with the Base Case, also profit based. Table 3.7 indicates that the profit goal was assigned a weight of 100 in this 37  scenario, while the weights for the other goals were 1. The second scenario, called Equal Weights (Scenario # 7), was generated by setting all the goal weights to 1. In contrast to the Profit M A X scenario, this scenario presented an alternative closer in scope to the principles of sustainable forest management. Note that in this study the main role of these two scenarios was to demonstrate the Multi-criteria Timber Allocation model. For practical implementation, a larger number of scenarios would normally be required. However, where necessary, the possible implementation of these two scenarios was addressed.  3.5.  Results  3.5.1. Estimating the Non-dominated Solution Set  o o d  o o  o o  d  d LO  — .m  o o  o o  o o  O O  O o  d  d CO  d  d  CM  CM  d LO CM  — .  T — — . Profit (Million $) •Si  T —  m  o O d  r-  CM  <J=>  Figure 3.2 - The area of non-dominated solutions and the trade-off area for the visual criterion. The large dots indicate the Profit Max and Equal Weights scenarios. The numbers indicate scenarios that delimit the area of non-dominated solutions (Table 3.7).  Figure 3.2 presents the values of the visual criterion achieved by the Timber Allocation Model when the weights in Table 3.7 were applied. The shaded area in the graph represents the estimated set of non-dominated solutions. This is the area in which all the solutions generated by the Multi-criteria Timber Allocation model are expected to lie. The dotted area is the trade-off area, in which the visual criterion decreases with every increase in profit value. The results of the scenarios plotted in the trade-off area indicated that the visual indicator achieved maximum values and remained constant when low profit values were achieved and decreased slowly between a profit value of $171 million and $226 million and more abruptly after that. 38  Profit (Million $)  Figure 3.3 - The area o f non-dominated solutions and the trade-off area for the wildlife criterion. The large dots indicate the Profit M a x and E q u a l Weights scenarios. The numbers indicate scenarios that delimit the area o f non-dominated solutions (Table 3.7).  Figure 3.3 presents the area of non-dominated solutions and the trade-off area for the wildlife criterion. For this criterion, the results generated a narrower trade-off area than that of the visual criterion. This implied that a larger emphasis on profit could have a stronger influence on the wildlife than on the visual criterion. The graph shows that the wildlife criterion values achieved the maximum wildlife goal of 140.00 until the profit equaled $202 million, after which they started decreasing slowly between a profit value of $202 million and $262 million and more abruptly thereafter.  39  160.00 150.00  Profit (Million $)  Figure 3.4 - The area o f non-dominated solutions and the trade-off area for the recreation criterion. The large dots indicate the Profit M a x and Equal Weights scenarios. The numbers indicate scenarios that delimit the area o f non-dominated solutions (Table 3.7).  Figure 3.4 presents the estimated set of non-dominated solutions and the trade-off area for the recreation criterion. Note that the trade-off area for this criterion is narrower than those of visual and wildlife criteria are which suggests that an increasing emphasis on profit triggers a stronger effect on this criterion than the other two. However, the recreation criterion values did not drop as steeply as those of the previous two criteria did. A very slow decrease in the recreation criterion values was registered between a profit of $213 million and $246 million and the decline became steeper after that (as opposed to $262 million in the wildlife criterion case).  40  _  7.00 -•  Profit (Million $)  Figure 3.5 - The area of non-dominated solutions and the trade-off area for the employment criterion. The large dots indicate the Profit Max and Equal Weights scenarios. The numbers indicate scenarios that delimit the area of non-dominated solutions (Table 3.7).  Figure 3.5 represents the non-dominated set and the trade-off area for the employment criterion. The shape of this set was different than those of wildlife, recreation and visual criteria, which suggests a different type of relationship between the employment and profit criteria. The employment criterion values presented a steady increase with every increase in profit and a very slow decrease after profit reached $227 million. The employment criterion values tended to decrease much faster when the profit reached its maximum, at approximately $266 million. The trade-off area was the narrowest of all the criteria, suggesting that employment criterion was most affected when the profit criterion was emphasized. However, the overall decrease in the employment criterion value was small, registering only a 5% decrease relative to its maximum value.  3.5.2. Results Generated in the Equal Weights and Profit MAX Scenarios The two scenarios analyzed with the Multi-criteria Timber Allocation model, one with emphasis on profit (the Profit M A X scenario) and the other with equal weights (the Equal Weights scenario) , are represented in Table 3.7 by shaded areas and in Figures 3.2 to 3.5 by larger dots. Note that the points for the Profit M A X scenario were extreme points, since 9  9  The allocation results for the two scenarios are presented in Table 6.7 and 6.8 in Appendix 2.  41  the profit weight was set to an extreme value, while the points for the Equal Weights scenario were located in the trade-off area. • Company 1 • Company 2  $254  $266  • Company 3  $235 $104  o  $97 $91  $52  Profit Max Base Case  Equal Weights  Multi-criteria Timber Allocation  Figure 3.6 - The comparison between the profit values generated i n the Base Case, the Profit M A X scenario, and the Equal Weights scenario for each company and i n total.  In Figure 3.6, a comparison is presented between the profit values obtained in the two Multi-criteria Timber Allocation scenarios and in the Base Case. The profit values are presented for both the total and for each of the three companies. The graph indicates that the total profit value in the Base Case was $254 million, or 4% smaller than that obtained in the Profit M A X scenario and 7% higher than that of the Equal Weights scenario ($235 million). In the Base Case, Company 1 contributed the most toward the total profit value (41%), followed by Company 3 (39%) and Company 2 (20%). In both Multi-criteria Timber Allocation scenarios, however, Company 3 generated the most profit (45% of the total profit in the Profit M A X scenario and 42% in the Equal Weights scenario), followed by Company 1 (36% in the Profit M A X scenario and 39% in the Equal Weights scenario) and Company 2 (19% in both the Profit M A X and the Equal Weights scenarios).  42  • Company 1 • Company 2 • Company 3  6,221  6,243  6,409  2,903  2,896  2,954  704  2,620  Base Case  2,643  2,768  Profit Max  Equal Weights  Multi-criteria Timber Allocation  Figure 37 - The comparison between the employment values generated in the Base Case, the Profit M A X scenario, and the Equal Weights scenario for each company and in total.  Figure 3.7 presents the results for the employment goal. The results show that, in the Profit M A X scenario, the allocation generated a total employment of 6,243 person-years, or 0.4% larger than that of the Base Case (6,221 person-years). In the Equal Weights scenario, the total employment reached 6,409 person-years, 3% larger than the values obtained in the Base Case and 2.6 % larger than in the Profit M A X Scenario. The contribution of each company to the total was similar in both cases: Company 1 produced the most employment (47% of the total employment in the Base Case, 46% in the Profit M A X scenario, and 46% in the Equal Weights scenario), followed by Company 3 (42% in the Base Case, 43% in the Profit M A X scenario and 43% in the Equal Weights scenario) and Company 2 (11% in the Base Case and the Profit M A X and Equal Weights scenarios).  43  • Recreation • Visual • Wildlife  *~ CO  1  Profit Max Base Case  in m  Equal Weights  Multi-criteria Timber Allocation  Figure 3.8 - The comparison between the recreation, visual, and wildlife criteria values generated i n the Base Case, the Profit M A X scenario, and the Equal Weights scenario.  Figure 3.8 presents the values for the recreation, wildlife, and visual criteria. These results emphasize that the majority of the values achieved by these goals were larger in the Multicriteria Timber Allocation scenarios than in the Base Case. This was true even in the Profit M A X Scenario where the visual goal value was 104 points and the wildlife value was 84 points, as opposed to the Base Case values: 101 points, and 78 points, respectively. However, these increases were achieved at the expense of the recreation goal value, which was smaller (84 points) in this scenario than in the Base Case (85 points). In the Equal Weights Scenario, a considerable increase in the values of all indicators took place: the recreation goal value increased to 123 points, while the visual value increased to 119 points and the wildlife value to 126 points.  44  • Recreation • Visual  14.3  • Wildlife  11.5  10.6  8.5  Profit Max Base C a s e  Equal Weights  Multi-criteria T i m b e r Allocation  Figure 3.9 - The comparison between the recreation, visual, and wildlife criteria values generated i n the Base Case, the Profit M A X scenario, and the Equal Weights scenario by stewardship units allocated to partial-cutting techniques.  Figure 3.9 presents the results of the visual, recreation and wildlife goal values achieved by the allocation of stewardship units to partial-cutting techniques. These values were included in the total indicator values presented in Figure 3.8 and did not have a large impact on the totals. However, it was interesting to study them separately because they were generated by harvesting activities and not by allocation to reserve. In the Profit M A X scenario, the allocation produced the largest values for all three goals (10.6 points for the recreation, 14.3 points for the visual, and 11.5 points for the wildlife criteria). In the Equal Weights scenario, however, the allocation generated a value for the wildlife goal that was 2 points higher than the Base Case, while the visual and recreation criteria generated smaller values (8.7 and 8 points) than those of the Base Case (9.2 and 9.6 points).  3.6.  Discussion  The Multi-criteria Timber Allocation model generated two categories of results. The first category was the set of non-dominated solutions, which contained important information regarding the relationships between each criterion and the profit criterion. Especially important was the delimitation of the trade-off area within each set of non-dominated solutions. The trade-off area indicated how fast each criterion values varied with increases  45  in profit. Moreover, the graphical representations of trade-off areas indicated that in order to have substantial increases in criteria values, losses in profit ranging between $40 million ($8 million/year) in the case of the employment criterion and $95 million ($19 million/year) in the case of the visual criterion were required. These values constitute estimates of the trade-offs between different criteria that the analysts could immediately gather. In turn, these values could guide the analysts toward adjusting the weights of different criteria so practical solutions are achieved faster. 10  Figure 3.5 presented an interesting case, in which the area of non-dominated solutions and the trade-off area for the employment criterion had different shapes and characteristics than those of other criteria. The difference consisted of a steady increase in employment value as profit increased, while the wildlife, visual and recreation criteria achieved maximum or close to maximum values. This increase was the result of the model transferring many stewardship units from sawmilling to reserve in order to achieve the wildlife, visual, and recreation targets. As a result, profit and employment values were considerably lower. The employment value reached its maximum when the weight of the employment goal was highest and declined slowly with every increase in profit values. The decrease in employment was not as steep as that of the other criteria for the same increases in profit values. This indicated that employment and profit did not have the same level of competition with each other as the other allocation criteria did. Consequently, allocating more volume to sawmilling increased both profit and employment values. The trade-off areas constructed by the Multi-criteria Timber Allocation model could also help analysts to identify those scenarios with most practical value (e.g. any loss in profit produces important increases in one or more of the other criteria). For example, the tradeoff area for the employment criterion in the Equal Weights scenario indicated that the employment goal achieved a value closest to the upper bound of the non-dominated set (i.e. the maximum achievement value) than any other criteria. This suggested that assigning equal priorities to all criteria did not have a large effect on the employment criterion. In contrast, the visual criterion in the same scenario achieved a value that was situated the farthest from the upper boundary of the non-dominated set. This suggested that the visual criterion would suffer the most under the Equal Weights scenario. This illustrates that analysts can use the graphical feature to analyze the trade-offs between the allocation criteria and to identify those scenarios that produce practical compromises. The second category of results generated by the Multi-criteria Timber Allocation model was that of the two allocation scenarios. In Figures 3.6,3.7, and 3.8, the results of three cases were compared: the Base Case, the Profit M A X Scenario, and the Equal Weights scenario. The results suggest that for the current allocation problem, the Profit M A X Scenario provided a more desirable allocation than that of the Base Case. This conclusion is validated by the fact that, in this scenario, the Multi-criteria Timber Allocation model generated larger values for most allocation criteria (except recreation) than those of the The graphical interface presented in Figure 6.2 in Appendix 2 contains the four sets of non-dominated solutions shown in Figures 3.2 to 3.5. After each run, the goal achievement values are plotted automatically so that the user can immediately visualize the solution and the trade-offs associated with it.  0  46  Base Case, yet incurred the smallest profit loss ($0.06 million). These results were justified by the fact that in the Profit M A X scenario weight values of 1 were assigned to all of the goals, except profit. These weights influenced the solution so that not only the profit, but also all the other criteria achieved better values than the Base Case. In addition, if the allocation is not constrained by chart areas, this resulted in larger criteria values in the Profit M A X scenario than in the Base Case. As a result, the Multi-criteria Timber Allocation model was able to match better the timber composition with the production requirements of each company. The map in Figure 3.10 shows how the stewardship units were allocated to companies from their own chart areas in the Base Case. In contrast to the Base Case, the map in Figure 3.11 indicates that the model in the Profit M A X scenario was unconstrained by these chart areas. Consequently, the model took advantage of the timber composition of all stewardship units. The map shows that many stewardship units were allocated from areas located outside of each company's chart.  47  Base Case Legend  Chart boundary Stewardship units allocated to Company 1 Stewardship units allocated to Company 2 Stewardship units allocated to Company 3 Stewardship units allocated to Reserve Stewardship units Inoperable  Figure 3.10 - The map o f the allocated stewardship units i n the Base Case.  Profit MAX Scenario Legend  Chart boundary I Stewardship units allocated to Company 1 J Stewardship units allocated to Company 2 Stewardship units allocated to Company 3 I Stewardship units allocated to Reserve J Stewardship units inoperable  Figure 3.11 - The map o f the allocated stewardship units i n the Profit M A X scenario.  Regardless of the increases in criteria values, the model used in the Profit M A X scenario generated similar results with those of the Base Case, as shown by the recreation, wildlife, and visual criteria (Figure 3.8). In addition, the results obtained in the Base Case, although smaller in value, mirror those of the Profit M A X scenario. The maps in Figures 3.10 and 3.11 indicate that the stewardship units allocated to harvesting and to reserve were almost identical in these two cases. However, the allocation of stewardship units to each company was different. This is because the Multi-criteria Timber Allocation model reacted similarly to an LP model when the profit goal was given a high preference (weight). In other words, it reacted similarly with the model used in the Base Case, which maximized the profit goal. The Equal Weights scenario modeled a balanced allocation between the sustainability criteria. As seen previously, its results fell within the trade-off areas of all the criteria. Therefore, important increases in criteria values were expected. Accordingly, the results presented in Figures 3.7 and 3.8 do show that the employment, visual, wildlife, and recreation criteria attained important increases. However, in order to achieve these increases, profit losses of $19 million ($3.8 million/year) and $31 million ($6.2 million/year) were incurred when compared with the Base Case and the Profit M A X scenario, respectively. By further analyzing the results against those of the Base Case, it is possible to assess which of the three companies was more affected by the conditions of sustainable forest management modeled in the Equal Weights scenario. The results suggest that, in order to achieve these conditions, Companies 1 and 2 would have to sacrifice 12% and 8% of their profits. In contrast with these two companies, Company 3 would actually benefit from the implementation of the Equal Weights scenario, increasing its profit by 2% or $2 million. While Company 1 could justify its profit loss by a 2% gain in employment, Company 2 would have to experience a loss in employment of 1.5% in addition to the profit loss. In contrast with the other two companies, Company 3 would increase its employment by 6% in addition to its profit gain in this scenario. The results clearly show that from the three companies considered in this exercise, the sustainable forest management conditions modeled in the Equal Weights scenario would affect Company 2 the most. This is because Company 2 was unable to compete against the other two companies in both profit and employment values. Competing against Company 3 was especially difficult because this company had a more diversified list of products (See Appendix 1), a larger market base, and employed more people than any other company. Therefore, based on the result of this scenario one could conclude that Companies 1 and 3 were able to adapt more flexibly to the requirements of sustainable forest management than Company 2. The allocation solution presented by the Equal Weights scenario may concern some decision makers, mainly because of the considerable profit losses. As seen, other scenarios should be generated by incrementally increasing the weights on profit until a more desirable solution was found, in which the losses in profits and employment were smaller and shared more equitably among the sawmills. The results presented in the Equal Weights scenario also suggest that the efforts toward more sustainable forest management practices should also include the processing operations. For example, Company 2 could consider  49  diversifying its product mix, which, in turn, could make the company more competitive in the region. In the Equal Weights scenario, increases in the values of wildlife, recreation, and visual criteria were so large, that the expected profit losses could be acceptable. For example, the wildlife and recreation criteria respectively achieved 38% and 31% higher values than in the Base Case. Although smaller than these two criteria, the increase of 15% in the visual criterion value was also notable. The large increases in wildlife and recreation achievement levels indicated that, when criteria other then profit were equally important, the Multicriteria Timber Allocation model preferred to allocate valuable timber to reserve rather than to harvesting, in order to meet the targets for these two criteria. Conversely, it could also be concluded that stewardship units containing wildlife and recreation features were more likely to contain valuable timber than any other stewardship units in the area were. It follows that those stewardship units with conflicting features (e.g. wildlife habitat and valuable timber for processing) could be better utilized when allocated to harvesting with partial-cutting techniques than to reserve or clear-cutting. This was especially true in the Equal Weights scenario, where 81 out of 154 stewardship units (53%) with conflicting features were allocated to partial-cutting techniques. Figure 3.9 presented the achievement levels of the wildlife, recreation, and visual criteria for the stewardship units allocated to partial-cutting techniques. By including partial-cutting in the model and allowing the harvested stewardship units to retain parts of indicator values proved to be of analytical and practical value. Based on this feature, different scenarios could be analyzed to understand the influence of different partial-cutting intensities and/or techniques on the allocations. For example, in the case of the Profit M A X scenario, the partial-cutting techniques included in the model generated values for the three indicators larger than in the Equal Weights scenario. This is because, when profit was emphasized, more stewardship units containing both valuable timber and wildlife, visual, and recreation features needed to be allocated to companies rather than to reserve. Still, in order to attain the wildlife, visual, and recreation goals, these stewardship units were allocated to partial-cutting, where portions of these indicator values were preserved.  3.7.  Summary  A Multi-criteria Timber Allocation model was developed on an integer goal programming framework to allocate forest management units to different forest products companies in order to meet the requirements of the sustainable forest management. The goal programming method proved to be beneficial to the development of the allocation model, especially due to its flexibility in handling any type and number of allocation criteria. In addition, it was able to model the multi-criteria timber allocation problem, while retaining the simplicity of a linear programming formulation. Consequently, the procedure of finding the desired multi-criteria timber allocation solution from the vast number of non-dominated solutions was greatly simplified. The difficulty of 50  specifying the weights that could yield the most acceptable solution was alleviated in the Multi-criteria Timber Allocation model by the graphical interface, which mapped each allocation solution within the non-dominated solution set of different allocation criteria. The graphical interface can help the analysts to understand better the trade-offs between allocation criteria and to generate more easily practical multi-criteria allocation solutions. The allocation procedure was demonstrated in a case analysis in which the results of two multi-criteria timber allocation scenarios were compared against the current method of allocation (i.e. the Base Case). In the Base Case, companies selected from their own chart areas those stewardship units that maximized profit at their sawmilling facilities. In contrast with the Base Case, the Multi-criteria Timber Allocation model allocated timber to companies based on a set of social, economic, and ecological criteria. These criteria were assumed to represent the sustainability concerns of the community affected by the allocation. In addition, the proposed method of allocation allowed companies to harvest stewardship units located outside their own chart areas. After generating a number of Multi-criteria Timber Allocation scenarios in order to construct the non-dominated solution set, two were selected for demonstrating the model. The first scenario, Profit M A X , modeled an allocation focused mostly on the profit criterion and was chosen to serve the comparison with the Base Case. The second scenario, Equal Weights, modeled an allocation in which all of the criteria were equally weighted. This scenario was chosen to present a more balanced alternative than the Profit M A X scenario, closer in scope to that of sustainable forest management. The two scenarios generated by the Multi-criteria Timber Allocation model provided allocation results, which, in contrast with the current allocation policy, were beneficial to both the sawmilling operations and the sustainability of the regional forest ecosystem. In addition, through the trade-off analyses performed for each of the scenarios, a better understanding of the multi-criteria decision problem was achieved. Besides their validation role, the two scenarios were examples of how the model was able to deal with the preferences set by the user on different allocation criteria. In addition, the capability of the Multi-criteria Timber Allocation model to represent the results graphically, improved the activity of prioritizing the allocation criteria and finding meaningful scenarios. Future research is needed to address the limitations of the model. First, the inclusion of spatial constraints (e.g. adjacency, green-up) could dramatically increase the number of integer variables and the computational time. Further validation of the model is required to analyze the number of integer variables that the model is able to sustain without dramatically increasing the computational time. Second, the separation of forest management and wood processing decisions within a hierarchical planning framework would benefit the implementation of this model in practice. Last, a dynamic allocation procedure could generate more accurate profit values, which reflect the timber composition of the allocated timber and the operational constraints of the sawmilling operations. Despite these limitations, the Multi-criteria Timber Allocation model demonstrated flexibility and practicality. The model could be tailored easily to assist with many 51  allocation policies and to accommodate social, economic, and ecological constraints. For each policy, a number of scenarios could be generated to reflect the priorities of different stakeholders in the areas under study. Therefore, these scenarios could become valuable foundations for public consultation or land use negotiations. In addition, by considering operational indicators, such as profits, the model could integrate forest to product decisions, which, in turn, could dramatically enhance the sustainability analyses.  52  CHAPTER 4. T H E DEVELOPMENT OF A TIMBER ALLOCATION MODEL USING DATA ENVELOPMENT ANALYSIS  4.1.  Introduction  The dramatic changes in forest management that took place in British Columbia, Canada, have led to a reduction in timber supplies. At the regional level, social, ecological, and cultural concerns have rapidly become equally important or, in some cases, even more important than wood availability. In their efforts to maintain a competitive position in global markets, forest product companies have given increased attention to forest certification and sustainable forest management. As a result, even the most efficient companies are rethinking their strategic and operational plans, consolidating their existing operations. The research presented in this chapter takes place in the Kootenay-Columbia Region, located in the southeastern part of British Columbia, Canada. The area under investigation is a landscape unit that supplies timber to a number of large and small forest products companies. It is an environmentally sensitive area, characterized by complex terrain, important ecosystems and wildlife habitat, and unique social conditions. Consequently, the area requires sensitive planning. In this region, the Crown (the public) owns most of the forests and forest products companies rely on forest areas licensed by the provincial government for their wood supplies. Often, companies have to present the government with a detailed forest management plan for each of these areas. Government agencies allocate timber cutting rights based on how well the companies, in their management plan, deal with a series of sustainability criteria, such as regional employment, wildlife conservation, social and cultural values, and profits. After provincial cutting permits have been issued, companies, depending on their size, will allocate the timber among their own operations (sawmills) usually based on economic criteria. Whether the allocation of timber is done at the government or at the company level, it is an important and complex planning decision, with great impacts on downstream economic and social activities. In the context of sustainable forest management, the problem of optimally allocating public timber to companies has to consider many allocation criteria, some of which are conflicting (e.g. profit and employment). Goal programming has been an accepted approach for these types of allocation problems (Field 1973; Arp and Lavigne 1982; Van Kooten 1995), but assigning priority weights to allocation criteria has proven a difficult process. Data envelopment analysis (DEA) is a method of calculating technical efficiencies (efficiency scores) of different decision-making units (e.g. organizations, companies, manufacturing facilities, etc.) based on a set of inputs and outputs (criteria). Among other strengths, the method does not require a predetermined weighting or prioritizing of these criteria in order to calculate the efficiency scores. The application of D E A in forestry and 53  forest products has identified new directions in assessing technical efficiencies of different operations. The works of LeBel (1996), Shiba (1997), Fotiou (2000), and Nyrud and Baardsen (2002) provide important technical and practical information about the use of D E A in forestry and wood processing. In these studies, various criteria were used to calculate the efficiency scores, such as volume of timber, budgets, and land area for the inputs, and total profit, total employment, and volume of lumber products for the outputs. In addition to being driving factors for efficiency improvement, these scores could be further utilized in making better allocation decisions. This chapter presents a novel application of D E A in a timber allocation model dealing with two allocation criteria: profit and employment. These criteria were selected due to their complex tradeoffs. On one hand, profit and employment are complementary criteria: by increasing employment, one expects more profit. On the other hand, they are competing: by maximizing profit, one implies minimizing employment. The timber allocation model proposed in this chapter took advantage of the capability of D E A method to deal with opposing criteria and exploited this capability in order to generate balanced timber allocations that maximized both the profit and the employment criteria. First, this chapter will present the theory of DEA, followed by the description of the D E A Timber Allocation model. Next, a case study and subsequent results will be analyzed. Some remarks and comments regarding the use of the D E A Timber Allocation model will conclude the chapter.  4.2.  Data Envelopment Analysis  Mathematically, the D E A methodology defines technical efficiency as the ratio of the weighted sum of outputs to the weighted sum of inputs of processes and organizations, called Decision Making Units (DMUs): Efficiency =  Weighted Sum of OUTPUTS Weighted Sum of INPUTS  (1)  For example, in cases where the DMUs are sawmills, the inputs could be volumes of logs, or operational costs and the outputs could be profits, volumes of different lumber products, share values, or employment rates. Data envelopment analysis (DEA) is a method of measuring the relative efficiency of DMUs introduced by Chames, Cooper, and Rhodes (Chames et al. 1978) based on Farrell's work (Farrell 1957). The authors determined that the weights, called multipliers, that are used in the efficiency ratio (1) could be calculated for each D M U using the following formulation:  54  T ry*j u  Max + H i ij i v  ( ) 2  r  x  Subject to:  < 1, for each D M U j  () 3  i u ,v >£ r  (4)  t  y •: Amount of output r from D M U j. Xy : Amount of input i to D M U j. u : Weight (multiplier) given to output r. T  v  : Weight (multiplier) given to input /.  s  : Small number.  t  * indicates that this model is applied to each of the j DMUs. In other words, by maximizing the efficiency ratio for each of the DMUs and constraining the ratios to be smaller or equal to one for all the DMUs (because efficiency is usually constrained by the interval [0,1]), one can find an efficiency score for each of the DMUs. The efficient units will have scores with values of one, meaning that these decision-making units best use their inputs in order to obtain their outputs. According to constraint (3), the inefficient units will have scores less than one. The actual score characterizes the level of inefficiency in relationship to those DMUs with similar input/output structures. In practice, the non-linear (fractional) program described in Equations (1) to (4) is converted into the following linear program, by constraining the denominator to have a constant value and maximizing the numerator: Max  u y*j r  () 5  r  Subject to:  YsiAj =  c  (6)  55  Z ry j u  r  r  -  Z iy v  x  ^  °>  f o r e a c h  (7)  DMuy  i  u ,v >£ r  (8)  t  Where c is a constant (usually 1) The above formulation is that of a C C R (Charnes-Cooper-Rhodes) model, which is a constant returns to scale model. Another D E A model is the B C C (Banker-Charnes-Cooper) model (Banker et al. 1984), which is a variable return to scale model. Returns to scale are changes in outputs (production) that occur when all inputs (resources) are proportionately changed in the long run. A l l D E A models build an envelopment surface around the DMUs (i.e. around the production possibility set), called the efficient frontier. The difference between the constant returns to scale and the variable returns to scale models originates in how each constructs the envelopment surface and subsequently calculates the efficiency scores.  Input  Figure 4.1 - The efficient frontier generated by the CCR model.  The efficient frontier illustrated in Figure 4.1 was built by a C C R model. The example consists of seven DMUs and a single input and output. In this case, one efficient decision making unit ( D M U 2) defines the efficient frontier and the other DMUs are deemed inefficient. Their level of inefficiency and, consequently, their efficiency scores are calculated based on the distance to the efficient frontier. The figure also shows that there are two types of orientations when calculating these distances (for D M U 5, in this example): output orientation (vertical line to the frontier) and input orientation (horizontal line to the frontier). Although the projection points are different in these two orientations, the fact that the C C R model constructs a linear frontier (or a conical hull in case of multiple 56  inputs/outputs) results in identical scores for all DMUs in both output and input orientations. Usually, analysts use output-oriented models (notation: "CCR-O") when the outputs are maximized, or input-oriented models (notation: "CCR-I") when the inputs are minimized.  •Inefficient D M U .  Input  Figure 4.2 - The efficient frontier generated by the BCC model.  The efficient frontier presented in Figure 4.2 was constructed by a B C C model. The graph indicates that, in contrast with the C C R models, the B C C models construct a different efficient frontier, comprised of a convex linear function (or a convex hull in case of multiple inputs/outputs). This frontier allows the efficiency scores to be calculated depending on the scale of each D M U . In other words, for each inefficient D M U , the score will now be calculated by projections on the frontier facet constructed by the convex combination of the relevant efficient DMUs, most similar in scale with the one analyzed. In this example, the projection points for D M U 5 (inefficient) will be on the facets built by D M U 2 and D M U 3 (efficient) for the output oriented model (notation: "BCC-O") and by D M U 1 and D M U 2 for the input oriented model (notation: "BCC-I"). Note that, unlike the C C R models, the B C C models could have different scores for the inefficient units in the output oriented than in the input oriented models. However, since both orientations build the same efficient frontier, the efficient DMUs are the same in the two orientations; only the inefficient ones could have different scores depending on the orientation used. Some D E A applications (see Chapter 2) use efficiency scores to re-allocate resources (inputs) in order to increase the efficiency of the inefficient decision-making units. In contrast with these models, the timber allocation model devised in this chapter uses the scores from a D E A sub-model to allocate resources (i.e. timber) to those units that will most efficiently use them. The development of the D E A Timber Allocation model required 57  the inclusion of allocation criteria as inputs and outputs in the D E A sub-model. In addition, a special type of decision-making unit (DMU), comprised of combinations of sawmills and stewardship units, was required.  4.3.  The D E A Timber Allocation Model  The D E A Timber Allocation model presented in this chapter consists of a series of interconnected sub-models. The model is tactical in nature (spanning over 5-10 years) and allocates forested areas, called Stewardship Units (SU), to different companies in order to maximize both the profit and the employment values generated by processing the timber into lumber products. These values were calculated for each stewardship unit and company with the FTP Analyzer®, the sawmilling model presented in Chapter 3. Only sawmilling activities (i.e. lumber production) were considered in this study. However, upon the availability of models for other uses (e.g. pulp mills, plywood mills, etc.), it would be straightforward to include them in the structure of the allocation model. Figure 4.3 shows the structure of the D E A Timber Allocation model. CRUISE DATA  1  FTP Analyzer Company 1  1  FTP Arlalyzer Comp any 2  FTP Analyzer Company 3  •  OPERATIONAL PARAMETERS (profits, hours of operation)  DEA SUB-MODEL  /  OTHER \ PARAMETERS (employment \ rates) /  MIP ALLOCATION SUB-MODEL  Stewardship units allocated to Company 1  Stewardship units allocated to Company 2  Stewardship units allocated to Company 3  Figure 4.3 - The structure of the DEA Timber Allocation Model.  58  The model starts with a list of available stewardship units and their specific cruise data files. These files are usually available before an area becomes available for harvesting and are produced by surveying teams that perform measurements on sampled trees located in each stewardship unit (SU). SU No. Height(m) Species DBH(cm) 1 49.2 Spruce 77.4 83.3 1 43.8 Spruce 73.4 1 50.7 Spruce 28.9 Balsam 32.6 1 1 54.3 33.0 Spruce 42.2 Spruce 71.3 1 1 77.0 53.5 Spruce 1 38.6 Spruce 87.0 1 46.7 Spruce 68.4 1 27.2 14.3 Balsam 24.4 Spruce 34.7 1 41.8 32.0 Balsam 1 1 25.0 Balsam 30.1 32.1 Balsam 48.1 1 34.7 24.1 Spruce 1 1 51.9 23.6 Pine 40.8 29.3 Spruce 1 1 27.9 Spruce 37.9 34.7 48.9 Spruce 1  Table 4.1 - An example of cruise data (simplified).  Figure 4.1 shows an example of the data contained in the cruise data file for SU 1. Each line of data in the table indicates the species code, the height, and the diameter at breast height (DBH) of each tree sampled in SU 1. This cruise data is fed into the FTP Analyzer which first compiles the data and then converts it into stem distributions for each stewardship unit. 4.3.1. The FTP Analyzer The FTP Analyzer® was described in Chapter 3. This sub-model maximizes the profit generated from lumber sales for each company considered in the study, subject to a series of market and production constraints that model the conversion of timber in each stewardship unit into lumber products. In the D E A Timber Allocation model, the FTP Analyzer® sub-model generates values of profit and hours of operation for each stewardship unit and company. The cruise data for each stewardship unit is entered into the FTP Analyzer® and the model is run separately for each company. The profit and hours of operation values for each stewardship unit and company are passed to the D E A sub-model.  59  4.3.2. The DEA Sub-model The Data Envelopment Analysis (DEA) sub-model calculates an efficiency score for each of the Decision Making Units (DMUs) defined by a Company-Stewardship Unit combination. For example, " 5 / 5 / ' means that this D M U refers to Company (Sawmill) 1 to which wood from Stewardship Unit 1 might be allocated. After running the D E A model, the highest scores will indicate which stewardship units will be allocated most efficiently to each sawmill. OUTPUTS:  INPUTS: VOLUME_Small DBH (1000 m ) 3  PROFIT (1000 $)  DEA Sub-model  VOLUME_Medium DBH (1000 m ) 3  EMPLOYMENT (1000 person hours)  VOLUME_Large DBH (1000 m ) 3  Figure 4.4 - The input and the output parameters into the DEA sub-model.  Figure 4.4 shows the composition of the inputs and the outputs into the D E A sub-model. The figure indicates that, for each D M U SjBi, there are three inputs and two outputs, as follows: The Inputs: volumes (1000 m ) of timber in each D B H (diameter at breast height) class: Small (< 30 cm), Medium (30 - 80 cm), and Large (> 80 cm) available in S U i. These values are retrieved from the FTP Analyzer® after the cruise data files are compiled for each stewardship unit. The breakdown of timber volume into D B H classes was necessary in order to capture the size structure of timber located within each stewardship unit. Because different sawmills utilize different log sizes, this input structure supports the allocation of the appropriate logs to each sawmill. 3  The Outputs: employment (1000 person hours) and profit (1000 $) generated by company j if it is allocated SU /. The employment values are calculated by multiplying the average annual employment of company j by the number of hours of production (broken down per machine centers) needed to process the timber in SU i. The FTP Analyzer® generates the profit values and the hours of operation.  60  OUTPUTS  INPUTS Volume DMU  Small DBH  Volume Medium DBH  Volume Large DBH  1000 m3  1000 m3  1000 m3  Profit  Employment  1000  1000 person hours  $  S1_B1 S1_B2  0.198 9.532  0.705 0.371  214.49 274.37  1.502 6.650  4.289 6.743 4.339 11.302  0.949 0.715  255.08 522.42  783 6186 1320 5273  S2_B1 S2_B2  0.198 9.532  4.289 6.743  0.705 0.371  179.81 354.94  149 1219  S2_B3 S2_B4  6.650  S3_B55  1.270  S1_B3 S1_B4  S3_B56 S3_B57 S3 B58  1.502  1.662 0.245 1.485  4.339 11.302  0.949  218.44  0.715  567.79  6.527  2.070  659.71  12.098 0.615 2.704  0.690 0.000 0.049  739.12 28.00 122.54  306 1024  747  1852 177 806  Table 4.2 - An example of the data input into the DEA sub-model.  Table 4.2 presents an example of the inputs and the outputs of the D E A sub-model. The D E A sub-model used in this application was the B C C - 0 model with super-efficiency (Cooper et al. 2000). The choice of variable returns to scale model originated from the assumption that the DMUs comprising the model were heterogeneous, due to the differences in timber composition of each SU and the different production parameters of each company. The output orientation was selected in order to maximize the profit and employment criteria. The super-efficiency allows the efficient DMUs, which normally would attain values of 1, to reach values greater than 1. This feature differentiates the scores for the efficient DMUs and consists of a simple set up procedure in the D E A solver. The software chosen to perform the calculation of efficiency scores was " D E A Solver Pro 2.1", developed by "SAITECH".  61  su  Company 1 Company 2 Company 3 86.4% 52.1% 99.3% 147.4% 77.8% 104.9% 84.4% 55.2% 103.4% 101.1% 70.0% 97.0% 92.7% 67.6% 92.0% 128.7% 96.5% 106.3% 125.9% 117.8% 107.7% 92.7% 75.5% 94.2% 101.0% 88.6% 92.1% 96.8% 95.9% 99.0%  1 2 3 4 5 6 7 8 9 10  50 51 52 53 54 55 56 57 58  99.5% 100.0% 87.3% 86.7% 157.7% 80.8% 97.4% 143.7% 93.4%  84.7% 77.4% 81.0% 41.9% 25.4% 46.5% 61.1% 97.8% 70.3%  93.6% 99.2% 97.8% 87.7% 175.2% 101.2% 93.0% 118.3% 80.7%  Table 4.3 - A n example o f efficiency scores.  Table 4.3 presents an example of efficiency scores generated by the D E A sub-model. These scores will support the allocation of each stewardship unit to the company that most efficiently uses its timber. 4.3.3. The Mixed Integer Programming Sub-model The scores generated by the D E A sub-model are used in the objective function of the Mixed Integer Programming sub-model, and become the basis for the allocation of stewardship units to companies. The reason for using an integer (binary) component is the straightforward condition that a stewardship unit has to be allocated to only one company. In addition, other constraints set the maximum and minimum production capacities for each sawmill in each period. Due to the binary nature of the timber allocation problem, a mixedinteger linear programming allocation (MILP) model was developed. The MILP model has the following mathematical formulation (Williams 1991): n k  Maximize £ Z ( -  ij  Bin  i  j  —  f/  B  x  j i)  S  B  (  9  )  Subject to: VB: x Bin I  = B--,i = l...n, j = \...k f/  (10) 62  k Y - ij Bin  B  ^ 1, J =  01)  l-.-n  j n  (12)  \...k A l l variables > 0, Bin B, = 0 or 1 Where:  VB  : Volume of timber in SU / (m ). 3  t  : Volume of timber in SU / allocated to company j. : Efficiency score for D M U "SjB" (combination of company j and SU /). Bin B;; '• Binary variable equal to 1 when SU i is allocated to company j and 0 otherwise. : Optimal time to process timber in SU / by company j (hours/m ). 3  : Maximum operational capacity of company j (hours). The objective function (9) maximizes the sum of efficiency scores by allocating the most efficient combination of stewardship units to each company in each period. Constraint (10) sets the volume of wood in SU / allocated to company j to be equal to the volume of timber available in S U i. Constraint (11) guarantees that the volume of wood in SU / is allocated to only one company. Constraint (12) sets an upper bound on the maximum production capacity (production hours) of company j. In order to precisely reach this upper bound, the model allows that a part of the volume in a SU be allocated to a company. However, constraint (11) does not allow the rest of the volume to be allocated to a different company. This sub-model produces a list of allocated stewardship units and their corresponding parameters (volume, generated profit and employment, optimum hours of operation) for each company. Based on these results, each sawmill is able to evaluate different production schedules. In addition, profit and employment gain/loss analyses can be performed. Decision-makers are able to analyze different allocation scenarios and their impact on regional socio-economic parameters.  63  4.3.4. Model Assumptions and Limitations Due to the use of linear programming in the FTP Analyzer®, D E A , and Mixed Integer Programming sub-models, the relationships among variables were assumed linear. Because of differences in timber composition in each stewardship unit and in the technological/marketing settings of the sawmilling operations, the B C C (variable returns to scale) model was assumed to better represent these conditions than the C C R (constant returns to scale) model. The composition of stewardship units taken from cruise files was assumed to reflect the real forest characteristics. When parts of the SUs were allocated, the volume was divided among all log classes (no selective cutting was considered). In this model, for simplicity, only spruce, pine, and fir species (SPF) were considered. The D E A Timber Allocation model also has some limitations. First, due to time horizon (medium-term planning), scope (timber allocation to different companies), and size (medium size) of the model, the spatial layout of different treatment activities was not considered. Second, the model implemented a static allocation procedure; under the assumption that the production possibility set that generated the efficiency scores would remain unchanged after the mix of stewardship units was allocated td companies. Last, the use of D E A method limited the number and type of input-output data into the D E A Timber Allocation model.  4.4.  Case Study  The case analysis concerns three large companies located in the Kootenay-Columbia Region of British Columbia, Canada. The current timber allocation method utilized in the district assures that certain timber supply areas (charts) are leased to each of the competing forest companies. Each year, the companies request permission to harvest timber from stewardship units in their own charts. These charts are diverse in timber types, sizes, and log qualities. The value of each cutting permit to a given company depends on their processing technologies, their markets for lumber and other products, and their current customer orders, factors that are constantly changing (Maness 1994). Three hypothetical companies, Company 1,2, and 3 were considered in this exercise. Each company manages one sawmill in the area. They were chosen based on the major differences in production parameters, markets, and size of their operations. Situated in the same geographical area, they all share the same timber supply; therefore, logistic differences between the three companies were assumed negligible.  64  Company 1  Company 2  Company 3  Products  SPF-Boards& Dimension  SPF-Studs  SPF-Dimension & Japanese Grades  Markets  Domestic&US  Domestic&US  Domestic.US&Japan  Employment (av. people/yr.)  70  23  46  Capacity (hrs.)  600  600  600  Table 4.4 - The technical parameters of the three companies.  Table 4.4 shows their main production/market characteristics Since stud mills are usually automated and cost efficient, Company 2 is assumed to manage the fastest, lowest cost sawmill. In terms of employment, however, it employs the least number of people/year. The other two companies (Companies 1 and 3), both manage sawmills with similar production parameters, although there are some major differences in their machine centers, product structures, and ages. Company 1 has an older, less diverse, and less automated operation than the Company 3. By contrast, Company 3 produces larger numbers and types of products destined for a variety of markets (domestic, US, Japanese). In terms of timber availability, the landscape unit consists of 58 stewardship units, with a total volume of 426,000 m of spruce-pine-fir (SPF) timber. 1  3  In order to demonstrate the D E A timber allocation model, four cases were analyzed: Base Case, Profit-based allocation, Employment-based allocation, and DEA-allocation. The Base Case allocation simulated the current allocation policy in the region. The Profit-based and Employment-based allocations addressed the optimal allocation of timber based on a single criterion (profit and employment, respectively). The DEA allocation generated a timber allocation solution that balanced both profit and employment criteria. 4.4.1. The Base Case Allocation In the Base Case allocation, the stewardship units were assigned to companies without regard to allocation criteria. To simulate this case, stewardship units were randomly allocated until the maximum capacity of each sawmill was reached (able to sustain 600 hours of operations in each sawmill). 4.4.2. The Profit Based Allocation In the Profit-based allocation, the stewardship units were allocated to maximize profit. To simulate this type of allocation, the Mixed Integer Linear sub-model (standalone) was run 11  For sawmilling parameters please refer to Tables 6.1 to 6.6 in Appendix 1. Note: Lumber prices were taken from Random Lengths (May 2001).  65  and profit values generated by each sawmill from timber in each stewardship unit were entered in this model. Similar to the Base Case, 600 hours of operation for each sawmill were considered in this case. 4.4.3. The Employment Based Allocation The Employment-based allocation was similar to the Profit-based allocation, with the only difference being that the stewardship units were allocated to maximize employment. Instead of profit, employment values were entered into the Mixed Integer Programming sub-model (standalone). 4.4.4. The DEA Allocation The D E A allocation presented the allocation of stewardship units when both profit and employment were maximized. The D E A Timber Allocation model was used under the same operational condition: a maximum operational capacity of 600 hours for each sawmill .  4.5.  Results  Allocation results from the four cases presented above are compared based on three performance measures: profit ($/1000 m ), employment (person hours/1000 m ), and total volume (1000 m ) of wood allocated to the three companies . Relative values (per thousand cubic meters) instead of absolute values were used for the performance measures because, in each allocation procedure, different total timber volumes were allocated in order to meet the maximum operational capacities of sawmills (i.e. 600 hours of operation). 3  3  3  13  Data input into the DEA model is presented in Table 6.9 in Appendix 3. The efficiency scores on which the allocations were based are presented in Table 6.10 in Appendix 3. The resulting allocation of stewardship units to companies is presented in Table 6.11 in Appendix 3.  3  66  80000  • Base C a s e Allocation 70000  • Profit Allocation 0 D E A Allocation  if)  60000 -  • Employment Allocation  me  & o 50000  -Q 3  O •o  c 40000  f-  CO CO  hous  CO UD  CM" CO  CO  co co" CO  CM  iq  CM" CO  OD OD  cn co" CO  30000  2  20000  0. 10000  Sawmill 1  Sawmill 2  TOTAL  Sawmill 3  Figure 4.5 - Profit (per thousand cubic meters) comparison between the Base Case, Profit-based, Employment-based, and the DEA allocations in each company and in total.  Figure 4.5 presents the comparison between the profit values per thousand cubic meters attained by each of the three companies in the four cases. The values indicate that Company 3 was the most profitable one, in all cases, followed by Company 2 and Company 1. As anticipated, the total profit per thousand cubic meters achieved was highest in the Profit-based allocation (42,471 S/1000 m ) and smallest in the Employment-based allocation (33,964 $/1000 m ). The D E A allocation achieved 41,488 S/1000 m , situated between the results of the Profit-based and Employment-based allocations, but closer to the one generated in the Profit-based allocation. 3  3  3  The total profit value in the Base Case (36,398 $/1000 m ) was lower than in the Profitbased and D E A allocations, but larger than that of the Employment-based allocation. As far as each company was concerned, Companies 1 and 2 reached higher values in the Employment-based allocation (33,210 $/1000m and 33,988 $/1000 m , respectively) than those of the Profit-based and D E A allocations. To make up for the overall difference in the total profit values, Company 3 attained a large value (64,394 $/1000 m ) in the Profit-based allocation, as opposed to that of the Employment-based allocation (35,036 $/1000 m ). For all three companies, the total profit values generated by the D E A allocation were smaller than those of the Profit-based allocation were, but followed them closely. 3  3  3  3  3  67  300  Sawmill 1  Sawmill 2  Sawmill 3  TOTAL  Figure 4.6 - Employment (per thousand cubic meters) comparison between the Base Case, Profit-based, Employment-based, and the DEA allocations in each company and in total.  Figure 4.6 shows that Company 1 was generating the largest employment per thousand cubic meters in all cases. This was not surprising since Company 1 was the largest employer of the three (see employment figures in Table 4.4). In addition, the lowest total employment value was generated in the Profit-based allocation (125 person hours/1000 m ) and the largest in the Employment-based allocation (136 person hours/1000 m ). The D E A allocation attained a value between the two (128 person hours/1000 m ), closer to that of the Profit-based allocation. In the Base case, the total employment value (131 person hours/1000 m ) was very close to that of the Employment-based allocation and larger than those of Profit-based and D E A allocations were. The distribution of employment values by each company suggested lower employment values in the Employment-based allocation for Company 1 (224 person hours/1000 m ) and Company 2 (49 person hours/1000m ) than for the Profit-based and D E A allocations. Company 3, however, showed a larger increase in employment value (182 person hours/1000 m ) in the Employment-based allocation than those of the D E A (93 person hours/1000 m ) and Profit-based (90 person hours/1000 m ) allocations. 3  3  3  3  3  3  3  3  3  68  450  Sawmill 1  Sawmill 2  Sawmill 3  TOTAL  Figure 4.7 - Volume comparison between the Base Case, Profit-based, Employment-based, and the DEA (One Input and Three Inputs) allocations in each company and in total.  Figure 4.7 presents the distributions of timber volume allocated to each company. The largest total volume was attained in the Profit-based allocation (394,000 m ) and the lowest in the Employment-based allocation (382,000 m ). The D E A allocation reached a value of 389,000 m , situated between the two and again closer to that of the Profit-based allocation. The volume allocated in the Base Case (391,000 m ) was second largest after that of the Profit-based allocation. The largest volume was allocated to Company 2 in all four cases. However, in the Employment-based allocation, the total volume allocated to Company 2 (172,000 m ) greatly exceeded those of the Profit-based (151,000 m ) and D E A (149,000 m ) allocations. The source of this difference was Company 3, where the timber volume allocated in the Employment-based allocation (84,000 m ) was dramatically smaller than those of the Profit-based (127,000 m ) and D E A (125,000 m ) allocations were. 3  3  3  3  3  3  3  3  3  4.6.  3  Discussion  The Employment-based allocation presented in Figure 4.6 attained increases in total employment values of 11 person hours/1000 m against the Profit-based allocation and of 6 person hours/1000 m against the Base Case allocation. According to the results presented in Figure 4.5, these increases could cost the region 8,507 $/1000 m in total profit (the Employment-based allocation) and 6,073 S/1000 m (the Base Case allocation). By contrast, the D E A allocation achieved a compromising solution, increasing the employment by 3 person hours/1000 m while decreasing the profit by only 983 S/1000 m . 3  3  3  3  3  3  69  A drop in profit was expected when introducing additional criteria. When using the D E A allocation model at the regional level, the above loss in profit might not be considered very large. However, some profit losses might not be acceptable for decision makers, especially when one or more companies experience a large decrease in profit with no sensible increase in employment. In an initial case analysis, the D E A allocation model was run with just one input (the total volume of timber in each SU) instead of three inputs (the volumes in each D B H class). The results portrayed in Figures 4.8, 4.9, and 4.10 for the D E A Allocation (One-Input) were similar in total values to those of the D E A Allocation (Three-Inputs). However, they posed some equity questions about how the D E A model allocated resources to each individual company. For example, Figure 4.8 indicates that, in order to boost the total employment value, Company 1 experienced a drop of 7,236 S/1000 m . Figure 4.9 shows that this loss in profit increased the employment value by 70 person hours/1000 m . Given the large decrease in profit of this company, this allocation solution could certainly disconcert some analysts and sawmill owners. 3  3  Figure 4.8 - Profit (per thousand cubic meters) comparison between the Base Case, Profit-based, Employment-based, and the DEA (One Input and Three Inputs) allocations in each company and in total.  70  350  • Base Case Allocation • Profit Allocation Q DEA Allocation (One Input) H DEA Allocation (Three Inputs) • Employment Allocation  Saw mill 1  Saw rrill 2  SawrriH 3  TOTAL  Figure 4.9 - Employment (per thousand cubic meters) comparison between the Base Case, Profit-based, Employment-based, and the DEA (One Input and Three Inputs) allocations in each company and in total.  450  • Base Case Allocation  400  • Profit Allocation 0 DEA Allocation (One Input)  350  H DEA Allocation (Three Inputs)  £ 300  • Employment Allocation  250 200 150  Sawmill 1  Sawmill 2  Sawmill 3  TOTAL  Figure 4.10 - Volume comparison between the Base Case, Profit-based, Employment-based, and the DEA (One Input and Three Inputs) allocations in each company and in total.  71  The D E A Allocation (Three-Inputs), however, did not create the above inequity problem. Figure 4.8 shows how the D E A allocation (Three-Inputs) was able to spread the profit loss among all companies. In addition, Figure 4.9 indicates how each company benefited from the D E A allocation (Three-Inputs) in terms of employment increases. Consequently, by using three volume inputs, the D E A allocation model was able to fit better the volume distributions in each stewardship unit with the production capability of each company, generating a more equitable allocation. Therefore, in order to generate a desirable allocation solution, one needs to be careful how the inputs and the outputs of the D E A submodel are set up. Figure 4.10 reiterates the compromising nature of the D E A allocation model by situating the total allocated volume between those of the Profit-based and Employment-based allocations. Timber volumes show that the D E A allocation method used 5000 m less than Profit-based allocation while keeping the three sawmills working at full capacity (600 hours). Again, using the D E A allocation, each of the three companies experienced a decrease in volume, unlike the Employment-based allocation, which increased the volumes allocated to Company 1 and 2 and decreased those of Company 3. 3  Note that the results generated by the D E A allocation followed closely those of the Profitbased allocation. Usually, this indicates that profit and employment criteria are not independent. The cause of this might be that the employment values were calculated based on the hours of operation generated by the same model that generated the profit values. In order to avoid these situations, the values for the two criteria should be produced by two independent models or calculated from field-collected data. In contrast with the current allocation policy (the Base Case), all the other cases presented better control over the allocation process. However, the D E A allocation model proved to generate more equitable and balanced allocations than those generated by the Profit-based and Employment-based allocations.  4.7.  Using Weights in the DEA Timber Allocation Model  One of the most important benefits of using D E A in the development of the timber allocation model is that the decision maker does not need to prioritize or weigh the allocation criteria. However, cases may arise (e.g. Company 1 experiencing a large profit loss) in which the decision maker would like to weight the allocation criteria (inputs or outputs) on which the allocation decisions were made. This is a straightforward activity when using D E A software and involves entering an algebraic relationship between the different input and output criteria. Many scenarios could be generated and analyzed and form the basis of informed and equitable allocation decisions.  72  Figure 4.11 - The convergence of the profit and the employment criteria toward the one criterion allocation when different weights were used in the DEA Timber Allocation model.  Figure 4.11 shows the variation of employment and profit values when weights are used to set preferences between them. The weighting starts from the left of the graph with a preference toward the employment criterion (i.e. the weights on the employment outputs are 25 times bigger than those of profit) and varies toward the right side of the graph, where increasing preferences are given to the profit criterion (i.e. the weights on profit outputs are 50 times bigger than those on employment). Figure 4.11 also contains the results for the Profit-based allocation on the far right side and the Employment-based allocation on the far left side. The figure shows a steady convergence of the total values for the employment and revenue criteria toward the one criteria allocation. This convergence indicates that the D E A allocation model is able to generate reliable scenarios with different preferences set on the allocation criteria.  4.8.  Summary  Timber allocation problems for sustainable forest management involve the inclusion of numerous and complex allocation criteria. To solve these problems, analysts need easy to use and flexible multi-criteria allocation models. In this chapter, a new timber allocation model was developed using data envelopment analysis (DEA). This method proved to be beneficial to the development of the allocation model, especially because it did not require the prioritization of the allocation criteria. To demonstrate the concept of using D E A in the development of the multi-criteria timber allocation model, the model was employed with two allocation criteria: profit and employment. The D E A Timber Allocation model was demonstrated against three cases: a random allocation (the Base Case), a Profit-based allocation, and an Employment-based allocation. The results have shown how the D E A Timber Allocation model was able to allocate optimally timber to the three companies, while generating a compromising solution 73  between the Profit-based and the Employment-based allocations. This ability of the D E A Timber allocation model to deal with the two allocation criteria in a harmonizing, flexible, and reliable way makes this model a good candidate for applications dealing with more complex sets of allocation criteria than those presented here. However, the expansion of the D E A Timber Allocation model has to be approached carefully, due to its limitations. Although many types of D E A models exist, their practical application has to account for a range of procedural conditions sUch as the homogeneity of the DMUs and the input/output selection (Dyson, R.G. et al. 2001). Consequently, the inclusion of criteria and indicators for sustainable forest management is not straightforward and more research is needed to find a D E A procedure capable of allowing their inclusion in the model. In addition, future research should also include the development of a dynamic allocation procedure that will ensure the reliability of the final production possibility set. The D E A Timber Allocation model and the results presented in this chapter are just a first step in solving forest management problems dealing with a wide array of allocation criteria. The major benefit of using this model is the integration of the overall forest to product decision system. In addition, the model could provide better forest valuation, accompanied by valuable trade-off analyses between different allocation criteria.  74  C H A P T E R 5. L I N K I N G T H E F O R E S T T O T H E P R O D U C T : T H E D E V E L O P M E N T OF A H I E R A R C H I C A L T I M B E R ALLOCATION MODEL  5.1.  Introduction  This chapter addresses two issues in sustainable forest management planning: the integration of different planning levels (operational and long-term), and the multi-criteria nature of the forest planning. The first issue arises from the concept that organizations must secure their long-term success and survival by improving their effectiveness, rather than their efficiency (Hofer and Schendel 1978). Most forest products companies are examining methods and subsequent benefits of adding value to their current products (Cohen 1992) in order to become more efficient. They should also integrate the operational measures into the broader context of their strategic and tactical goals in order to increase their effectiveness. Therefore, forest products companies need new and improved methods of addressing current operational problems, while concurrently meeting their medium and long-term commitments, such as: maximizing net social benefits and minimizing forest ecosystem disturbance. Sustainable forest management planning has relied on timber allocation models to connect decisions at different planning levels (strategic, tactical, and operational). According to Colberg (1996), analysts have formulated large mathematical models with structural variables representing every conceivable resource allocation in order to serve the forest to product planning range. The works of Westerkamp (1978), Barros and Weintraub (1982), Hay and Dahl (1984) are just a few examples of forest to product timber allocation models. These models integrated various activities, such as managing timberlands, buying/selling logs, and supplying timber to processing plants. Although they were valuable planning tools, they tried to deal with everything at once and made no distinction between the relevance of variables in addressing different levels of decision-making. In order to alleviate these situations, decision-makers usually had to either discard or aggregate variables of interest. Valuable information was therefore lost or disregarded. For example, by integrating lumber processing decisions into timber allocation models, the resulting models become so large and complex that details such as lumber and intermediary log products need to be either aggregated into classes of products, or discarded altogether. Consequently, valuable relationships between the timber allocation and the manufacturing decisions (e.g. what product should be made from what log) are ignored, resulting in inaccurate allocation decisions. The second issue in sustainable forest management planning is dealing with the multiple objectives of many stakeholders. The challenge occurs when, at the regional level, social, ecological, and cultural issues rapidly become of equal or, in some cases, even more importance than wood availability. Timber allocation models used in forest to product 75  integration and optimization are shifting their focus toward a multi-criteria approach. Goal programming (GP) has been the method mostly used in multi-criteria allocation models in forestry. The works of Arp and Lavigne (1982), Ludwin and Chamberlain (1989), Van Kooten (1995), Bertomeu and Romero (2001) are just a few examples of how GP was applied to sustainable forest management problems. They dealt mostly with multiple-use planning of forestlands, such as recreation, timber harvesting, and wildlife. Other studies focused on wildlife habitat selection and on managing the biodiversity of forestlands. In Chapter 3, a Multi-criteria Timber Allocation model was developed based on the goal programming framework to assist with the analysis of sustainable forest management decisions. The purpose of the model was to allocate forest stewardship units (SUs) to different forest products companies, considering economic, social, and ecological allocation criteria. By including the profit among the allocation criteria, the model attempted to integrate medium-term forest management with operational decisions. Profit values were generated for each company and each stewardship unit with the FTP Analyzer®, a sawmilling optimization model. Although essential to the integration of medium-term and operational decisions, the inclusion of these profit values in the Multicriteria Timber Allocation model raised some theoretical and practical questions. First, the implementation of the Multi-criteria Timber Allocation model at different levels of management could be difficult and its results inaccurate, because it deals simultaneously with allocation decisions spreading over different time horizons (medium and short term). For example, woodland managers interested in timber allocation decisions spanning over larger time horizons (e.g. 5-10 years) might find it difficult to understand and accurately input all the sawmilling parameters and variables included in the model. Conversely, sawmilling managers could have problems using those parts of the model dealing with forest management issues. Second, the Multi-criteria Timber Allocation model was developed under the assumption that profit values calculated for each stewardship unit and company would remain constant after the mix of stewardship units was allocated to the companies. In fact, these profit values could change depending on the timber composition of the stewardship units comprising the mix; therefore, the resulting allocations could be inaccurate. For example, the allocation of stewardship units containing large diameter stems, although valuable when the stewardship units are allocated individually, could create bottlenecks at the sawing lines, decreasing the profit. In other words, the total profit generated from a mix of stewardship units could be smaller than the sum of the profits generated from each of the stewardship unit in the mix. In order to alleviate these two problems, the Multi-criteria Timber Allocation model would need to separate medium-term and operational decisions, while maximizing the achievement levels for all of the allocation criteria, including profit. Based on organizational theory and multilevel systems, the hierarchical planning (HP) method fits well with the goals and characteristics of the forest to product decision problems, such as timber allocation. HP is a method in which large and complex problems are disaggregated according to the management levels, the time horizons, and sometimes the geographical 76  ranges that they address. The connectivity between the levels is essential to the functioning of the hierarchical decision process. The links between the levels need to insure consistency of data aggregation and disaggregation, so that the decision goals at each level are met. The resulting hierarchical allocation model is easier to implement because the sub-models at each level deal with decisions and goals that are specific to a certain time horizon and management problem. Consequently, the accuracy and the practicality of the allocation results improve dramatically. Many applications of HP in forestry have opened the door to current research. The studies of Hof et al. (1992), Colberg (1996), Ogweno (1994), Dewhurst et al. (1997), Feunekes and Cogswell (1997), Cea and Jofre (2000) applied the HP method to assist with forestry planning decisions at the strategic, tactical and operational levels, such as the allocation of timber to processing activities, the allocation of output target values to district forests, the production of logs, and the selection of silvicultural treatments to address forest sustainability issues. These applications reinforced the potential of HP in developing timber allocation models able to retain an increasing level of detail, while accounting for the integration of forest to product decisions. This chapter presents the development of a two-level Hierarchical Timber Allocation model designed to deal with both the multiple horizon and the multi-criteria requirements of sustainable forest management decisions. The two planning levels are a medium-term level, in which the Multi-criteria Timber Allocation model developed in Chapter 3 was implemented, and an operational planning level consisting of sawmilling optimization models (FTP Analyzer®). The goal of the medium-term level is to allocate timber to different forest products companies so that the achievement levels of the sustainability criteria (profit, employment, visual, recreation, and wildlife) are maximized. The goal of the operational level is to maximize the profit generated by processing into lumber products the timber allocated by the medium-term level to each company. A third, long-term level was not included in the model because of theoretical and practical limitations. However, the list of stewardship units available for allocation by the medium-term level model was assumed to be generated by such model. The connectivity between the two levels is based on an algorithm inspired by Heal (1969) and Hof et al. (1992). In this algorithm, the medium-term level model generates optimal timber allocations that are negotiated iteratively with the operational level models. In turn, these models communicate back to the medium-term model the marginal values (i.e. shadow prices) of the allocated resources. Then, the medium-term level model generates a new allocation and the iterative procedure continues until the operational level reaches optimality (i.e. maximization of total profit). At that point, both the medium-term and the operational levels reach their goals and the optimal allocation is achieved. This chapter will first present a background on the theory of HP, followed by the description of the Hierarchical Timber Allocation model, developed for this research. Then, the model and the iterative negotiation algorithm will be tested in a case consisting of two scenarios. The chapter will conclude with a series of policy analyses performed using the Hierarchical Timber Allocation model and with a summary of the findings. 77  5.2.  Theoretical Background  5.2.1. Hierarchical Planning According to the theory of hierarchical systems, a hierarchy is a vertical arrangement of subsystems, with priority of action or right of intervention of the higher-level subsystems on the lower level ones and a dependence of the higher-level subsystems on the performance of the lower level ones. Figure 5.1 illustrates a hierarchical system with n levels and the data flow within and between the levels. Hierarchical System — INPUT  Level n subsystem  I intervention  -INPUT-  -INPUT  Performance feedback  Level n-1 subsystem  Intervention  OUTPUT-  OUTPUT-  Performance feedback  Level 1 subsystem  OUTPUT-  Figure 5.1 - The structure of a multi-level hierarchical system and the data used at each level (Mesarovic et al., 1970).  A hierarchical system deals with two classes of data: the input-output and the inter-level connectivity data. The input-output data consists of the parameters and the variables pertaining to the part of the system described at each level. The inter-level data is comprised of the intervention data communicated from the higher levels to the lower ones, usually comprised of aggregated parameters, describing the decisions imposed by the upper levels on the lower ones. The feedback data is usually disaggregated, detailed data (e.g. marginal productivities, utilization rates for each resource variable) describing the response of the lower levels to the decisions imposed by the upper-levels. Anthony (1965) classified decisions into three categories: strategic or long-term planning, tactical or medium-term planning, and operations control. The strategic and tactical levels keep the organization in the right direction: they guarantee its effectiveness. The operational level is concerned with the organization's increase in efficiency. Consequently, the variables, parameters and constraints involved in the models at different levels need to 78  reflect the characteristics of the decisions involved at each particular level. According to Hax and Meal (1975), tactical decisions are associated with aggregate production planning (e.g. material requirements planning), while operational decisions are an outcome of the disaggregation process (e.g. daily/weekly production scheduling). However, the differentiation of different levels in a hierarchical system could be based on principles other than temporal and managerial. In forestry, for example, the levels of a hierarchical system could be based also on the spatial or geographical composition of the planning problem (e.g. provincial, regional, landscape-unit, forest levels). According to Gunn (1996), the most important aspects of hierarchical planning are: 1. HP uses separate models at each level of the hierarchy. This provides flexibility and practicality to the decision making process. Smaller models are easier to use and maintain, while addressing a larger level of detail. 2. HP implements a rolling planning horizon methodology. Only the first period decisions at each level are implemented immediately. Before implementing the decisions of later periods, decision makers need to develop an updated plan for that level. Consequently, the length of the first period in each level should be equal with the length of the whole time horizon of the subsequent level. Jun  02  Medium-Term Level Update  Medium-Term Time Horizon ( 5 Years I Jan 03  Jan 02  Jan 04  Jan 05  Jan 06  Operational Time Horizon (1 Year)  Jan 07  Jan 03  Jan 02  Updated/Reset Time Horizons Medium-Term Time Horizon (5 Years Jurt 02  Jun 02  Jan 03  Jan 04  Operational Time Horizon (1 Year) Jan 03  Jan 05  Jan 06  Jan 07  Jun 07  Jun 03  Figure 5.2 - Example of the rolling horizon principle applied to a five year medium-term and a one year operational plans.  Figure 5.2 shows a five-year medium-term plan horizon (January '02 - January '07) and a one-year operational plan horizon (January '02 - January '03). Notice that the first period of the medium-term plan is equal to the time horizon of the operational plan. At a 79  certain point in time (in this example, June '02), if new information becomes available, the time horizons are reset, or "rolled". Consequently, the updated medium-term planning horizon will begin in June '02 and end in June '07, while the operational planning horizon will begin in June '02 and end in June '03. As a result, the hierarchical planning system will always function with the newest and most accurate information possible. 3. HP deals well with uncertainty. Detailed decisions are made at lower levels, where information that is more accurate is available, while the upper levels deal with more aggregated information. Consequently, the risk of taking the enterprise in the wrong direction is reduced drastically in the event of erroneous decisions being made at lower levels. 4. HP follows the organizational structure. Each level of the hierarchical planning model is aimed at each level of management in an organization. Although this helps the implementation of HP models, it might be required that managers have restricted access to the models at different levels of the planning hierarchy. The hierarchical approach decomposes decisions into sub-problems, which, in the context of the organizational hierarchy, link the higher-level decisions with those of the lower level in an effective manner. Decisions at the higher level impose constraints on lower level decisions. In turn, they provide the necessary feedback to evaluate the quality of the upperlevel decisions. Depending on the problem, some upper level decisions could have a strong influence on lower level decisions by imposing strict constraints (e.g. resource availability, ownership, proprietary and regulatory restrictions). Others could have a coordinating influence, achieved by upper levels containing some decision parameters or simplified submodels of the lower levels (e.g. allocation of resources based on production/operational parameters). Conversely, lower level decisions could, respectively, update the upper level models after each run, or influence their decisions.  5.2.2. Dynamic Inter-Level Connectivity In some cases, the connection between levels is dynamic and requires iterations until a mutually beneficial solution is achieved. For example, an upper level could allocate resources to a lower level, where operational models optimally convert them into products. The feedback data from the lower level (e.g. shadow prices, productivity rates) could trigger a new resource allocation at the upper level. The most relevant study regarding the inter-level dynamic connectivity (Heal 1969) proposed a quantity-guided routine, in which the upper level planned the allocation of resources to the production facilities modeled at the operational level, in order to maximize the sum of outputs produced by these facilities.  80  The routine started with the upper level suggesting an initial feasible allocation of resources to the production facilities in the lower level. In response to the initial proposal (allocation), the facilities reported the marginal productivity (shadow price) of each resource to the upper level. The upper level then calculated an average shadow price for each resource and adjusted the allocation of resources to each facility proportional to the distance of the shadow prices from their respective averages (See Appendix 4). The procedure stopped when no increase of output was generated by the production facilities at the lower level. Heal's procedure had the following characteristics: Re-allocations caused the objective function (i.e. maximization of outputs) to increase monotonically. Every reallocation satisfied the necessary conditions of optimality. For a feasible initial allocation, all the subsequent allocations were also feasible. Based on Heal's procedure, Hof et al. (1992) developed an allocation model in which a regional control model (upper level) iteratively adjusted the output targets of forest level models (lower level) in order to minimize the cost of meeting those targets (see Appendix 4). In each iteration, the regional control model increased or decreased the output targets of each forest according to the departure of their reduced costs from the average. The procedure proved to generate proposals that monotonically decreased the total cost of forest level activities. The adjustment procedure designed in this chapter between the mediumterm and the operational level of the Hierarchical Timber Allocation model was derived from the studies presented here. 5.2.3. Marginal Productivities (Shadow Prices) In order to understand how the shadow prices are generated, a brief introduction to linear programming methodology is necessary. A typical formulation of a linear programming model is (Williams 1991): Maximize cx Subject to: Ax<b x>0  (1)  Where c is the row vector of prices, x is the column vector of decision variables (products), b is a column vector of scarce (limited) resources, and A is the matrix of conversion parameters. The optimization problem is to find the optimum level of converting scarce resources b into products x so that the profit cx is maximized. Problem (1), called the primal formulation, can be expressed also in the following form, called the dual formulation: 81  Minimize yb Subject to: yA > c y>0  ( 2 )  At optimum, the duality theory (Gale et al. 1951) states that the primal (1) and the dual (2) problems must meet the following condition: cx* = y*b  (3)  where x* andy* are the optimal solutions of problems (1) and (2). From the optimality condition (3) results that, at optimum, an additional unit of resource b could increase the profit by y*. The.y* values are called shadow prices, because they reflect the maximum price that a producer of products x would pay for a unit of resource b in order to break even. Shadow prices are valuable post optimality indicators because they show which resources are more desirable than others are. They can be utilized further in multi-level allocation procedures, such as those of Heal (1969) and Hof et al. (1992), to identify what resources should be allocated to what uses.  5.3.  Methods  The model developed in this chapter is the Hierarchical Timber Allocation model. The model is comprised of two levels: a medium-term level and an operational level.  Medium-term Data Sustainability Indicators Employment Data Treatment Intensities  Operational Data Stand and stock data Harvesting Costs Production Parameters Log Selling/Purchasing Lumber Prices Fiber Prices/Forecasts  Multi-Criteria Timber Allocation Model  FTP Analyzer® Sawmill 1  FTP Analyzer® Sawmill 2  FTP Analyzer® Sawmill n  Medium-term Level 5-10 Years Outlook  Operational Level 1 Year Outlook  Figure 5.3 - The structure of the Hierarchical Timber Allocation model.  Figure 5.3 shows the sub-models assigned to each level and the data flow between these sub-models. At the medium-term level, the Multi-criteria Timber Allocation model 82  presented in Chapter 3 was implemented to allocate stewardship units to a number of forest products companies. The operational level sub-models consist of sawmilling optimization models (FTP Analyzer®), one for each of the facilities considered in the allocation. Connectivity through the flow of data between models at each level is essential. There are two classes of data in this model. The first class is comprised of the input-output data that guarantees the functioning of the sub-models and presents the intermediary and final results at each level. For example, the input data is comprised of product prices, production parameters (for the operational models) and sustainability indicator values, treatment intensities, and employment values (for the medium-term model). The output data contains the results generated by each sub-model, such as achievement levels for sustainability criteria, stewardship units (SU) and volumes allocated to each company (for the medium-term model), and lumber product volumes and profits (for the operational level models). The second class of data is the decision data (i.e. intervention and feedback data). The intervention data consists of allocations of stewardship units made at the medium-term level, which are sent to the operational level models. The operational level models run the allocations and send the medium-term level feedback data consisting of marginal values for each of the stem classes and the profit values attained by each company. The medium-term level has the right of intervention over the operational level by stopping the iteration process when all the allocation criteria are maximized. 5.3.1. The Medium-term Level The goal of the medium-term level is to maximize the profit, employment, visual, recreation, and wildlife criteria values, by optimally allocating stewardship units to different forest products companies. The time horizon for this level is 5-10 years. The model used at this level is the Multi-criteria Timber Allocation model presented in Chapter 3. In order to accommodate a dynamic relationship with the operational level models, profit values were substituted with stewardship unit composite values for each sawmill and stewardship unit. After each iteration, the medium-term model calculates these composite values based on the marginal stem values reported by the operational level models and generates a new timber allocation. According to the rolling horizon principle, only the first period allocation (i.e. one year) is sent to the operational level where it is disaggregated by the operational models into optimal processing schedules. Feedback data from the operational level models is then entered into the medium-term model and a new allocation is generated. The medium-term level model stops the iteration process when an optimal allocation is achieved. For more information about the medium-term level model, please refer to Chapter 3.  83  5.3.2. The Operational Level The goal of the operational level is to maximize the total profit generated by processing the timber allocated by the medium-term level to each company. The FTP Analyzer® (described in Chapter 3) models the sawmilling processes for each facility considered at this level. The time horizon for this level is one year. In each iteration, the model performs the optimal conversion of the allocated timber into lumber products for each company. The operational level then sends the marginal stem values and profit values back to the medium-term level for a possible timber reallocation. 5.3.3. Inter-level Connectivity There are two types of interaction between the operational and medium-term levels: a negotiating and an updating interaction. In the negotiating interaction, data exchanged between the operational level and medium-term level is used to evaluate how close the allocations are to achieving the operational and medium-term goals. The updating interaction occurs after the allocations are implemented, when new data becomes available or parameter changes take place. For example, when new stewardship units are available for harvest, or some parameters have changed, the medium-term level asks the operational level for an updated list of data (e.g. unused stewardship units). According to the rolling horizon principle, the time horizons and their respective periods in each level reset (roll) to start at the current time. The model is run again and new timber allocations are generated with up to date information. In the Hierarchical Timber Allocation model, the negotiating interaction between the two hierarchical planning levels was developed in an iterative fashion, according to the procedures developed by Heal (1969) and Hof et al. (1992). Because the sawmilling models (FTP Analyzer®) at the operational level are based on linear programming methodology, they are able to generate shadow prices for each stem class S (length and small end diameter) . To illustrate how the shadow prices are derived from these models, a simplified version of their mathematical formulation is provided below. The full model can be found in Maness and Adams (1991). The objective of the sawmilling model is: 14  Maximize  Z, wm _ Sales^ •Lum_ Pr^ - Y Stem • Stem _ Pr - £ Tot _ Op _ Costs (4) S s  a  s  Subject to:  Y X Stm_ BuckSB =H S  tem  SB  S  () 5  S  In this formulation, stems are obtainedfromthe trunks of the felled trees, cut to length and ready for transportation to sawmills.  14  84  Z X  - BuckSB ' Log _ Recov  LSB  S B  = ^ Log _ Sawn , for each L LC  (6)  C  X XLog _ Sawn  LC  • hum _ Recov  ilLC  = ^ ^ w m _ Sales^  (7)  Where:  Stem  s  The volume of stem class 5 that was used in lumber processing.  Stm Buck„  n  SB  The volume of the stem class S bucked with the bucking pattern B.  Log_Recov  The recovery factor for the stem class S when bucked with the pattern B and converted to log class L.  Log_ Sawn^  The volume of the logs class L sawn with the sawing policy C.  LsB  hum Recov, „ The recovery factor for the lumber with dimensions / and /, sawn from ULC  The sale price of a unit volume of lumber with dimensions i and /.  Lum_Pr  il  hum Sales, ~  a log of class L, using sawing policy C.  il  Stem_ Pr^  The volume of lumber of dimensions i and / sawn. The stem price (e.g. stumpage, purchasing price) of a unit volume of stem class S.  Tot_Op_Costs The aggregate operating cost for activities such as: bucking, sawing, finishing, packaging, etc.  The objective (4) of the sawmilling model is to maximize the revenue generated by the sales of lumber products, minus the costs of raw materials and operations. Constraints (5) to (7) deal with the conversion of stems of different classes S into lumber products of dimensions i and /. If the dual formulation of the model presented in equations (4)-(7) was constructed according to the dual formulation presented in expression (2), at optimum, shadow values would be available for each stem of class S, each log of class L, and each lumber product of dimensions i and /. In practice, these shadow values are generated by the LP solver used by the FTP Analyzer®. The shadow values for constraint (5) indicate the relative value of stem classes to each sawmill. Since each stewardship unit (SU) contains a unique stem class distribution, its value to each sawmill (company) depends on how much volume of each desirable stem 85  class exists in the stewardship unit. In order to assess how valuable each SU is to each company, the medium-term level model calculates a composite value for each SU and company:  CV_Bt.Sk  Y Vol _ Stem • y S Si  for each SU i and company k  Sl(  (8)  where: CV B  Vol  : The composite value for SU i when calculated with the shadow values from the FTP Analyzer® model for company k. There are k x i such composite values.  S,  Stem„ —  : The volume of stem class S in SU i.  Si : The marginal value (shadow price) for stem class S generated by the FTP Analyzer for company k.  The search for an optimal timber allocation can be achieved through an iterative process, in which the medium-term level model finds an allocation of stewardship units that maximizes the sum of profits achieved at the operational level. According to the duality condition (3), at the optimum, each of the sawmilling models achieves a profit equal to: Pj =Yli intern Sk'ySk)^ S  or  e a c  (  h  c o m  P  a n  y  ()  k  9  where Stem^ is the volume of stem class S allocated to company k. By substituting the expression (8) with (9), the optimal timber allocation is achieved when the medium-term model maximizes the sum of the SU composite values, as follows:  maximizoYYjYjiVol_Stem k i S  Si  • y ) <^> maximize^ ] T C y _ i ? Sk Sk  () 10  ;  k i  Concomitantly, according to the procedure devised by Heal (1969), the medium-term model proportionally increases the allocation of those stem classes with shadow prices above the average and decreases the allocation of those with values below the average. To achieve this increase, the shadow prices of each stem class are adjusted proportionally to their departure from the average before the medium-term model is run in each iteration. The adjustment is achieved using an expression derived from Hof et al. (1992). The SU composite values are then calculated and included in the objective function (10). Consequently, by running the medium-term model with these adjusted SU composite values, the allocation of those stewardship units that contain the most valuable stem classes guarantees monotonically increasing profit values in each iteration. 86  Iniatialization S U allocated to Sawmill 1  Iniatialization S U allocated to Sawmill 2  Iniatialization S U allocated to Sawmill 3  in  s«.CM  t3 c 3  *-  LL  =  11  NO  Stem class shadow prices Sawmill 1  Stem class shadow prices Sawmill 2  Stem class shadow prices Sawmill 3  Calculation of composite S U values Sawmill 1  Calculation of composite S U values Sawmill 2  Calculation of composite S U values Sawmill 3  0) co 15" CO O  MULTI-CRITERIA TIMBER A L L O C A T I O N M O D E L Minimizes the deviation from the targets: visual, wildlife, recreational, employment, profit  Figure 5.4 - The inter-level negotiating algorithm between the medium-term and operational level submodels in the Hierarchical Timber Allocation model. NOTE: The initialization SU allocated to each of the three sawmills is fictional. It contains all the stem classes present in the area and ensures that all sawmilling models generate an initial feasible solution.  87  Figure 5.4 presents the algorithm of the iterative negotiating process between the mediumterm and the operational level models according to the procedure described in Heal (1969). The iteration process starts with an initialization stewardship unit allocated to each company. This initialization SU is fictional and is comprised of all the stem classes present in the available stewardship units. The volume of the initialization SU is equal to the maximum volume capacity of each company. Consequently, the initialization SU meets the initial allocation constraints presented in Heal (1969) and guarantees that, if the initial allocation is feasible, all the subsequent allocation solutions are also feasible. After running the operational level models with the initial allocation, the shadow values are generated for all stem classes, in each company. Figure 5.4 also shows that the profit values attained at each company are stored and that the initialization SU is dropped after the first iteration. The shadow values are then sent to the medium-term level model where they are adjusted proportionally with the distance from their averages according to the following expression:  (y  S k  -ys"  )^y  s )  for each stem class S and company h s k  where: y Sk y ^ y( s) • K  y s k  : The new, adjusted shadow price for the stem class S allocated to company k. : The shadow price for stem class 5" allocated to company k in the previous iteration. : The average of the shadow prices for stem class S calculated based on the set (K ^  K  s  = {k : Stem  Sk  > 0, or Stem  sk  = 0 b\ity  Sk  >y  s k  }  With these adjusted shadow prices, the composite stewardship unit values are calculated for each SU and each company. Consequently, stewardship units containing desirable stem classes (with shadow prices above the average) will increase their composite values, whereas the others will decrease them. The Multi-criteria Timber Allocation model then generates a new allocation of stewardship units, which are sent to the operational level models. The medium-term model stops the iterative negotiating process when the total profit value achieved at the operational level is equal to that of the previous iteration. According to the procedure devised by Heal (1969), this indicates that an optimum allocation was found and that the goals of both medium-term level (i.e. maximizing sustainability criteria) and operational level (i.e. maximizing total profit) are attained.  88  5.3.4. Data and Data Handling The same study area and GIS database used by the Multi-criteria Timber Allocation model presented in Chapter 3 were used for the Hierarchical Timber Allocation model. However, increased database and code development was required to accommodate the interactions between the medium-term and the operational level models. New tables were designed to store the marginal stem values and the profit values generated by the sawmilling models. Also, new queries were developed in order to create a seamless data flow for each iteration. The Hierarchical Timber Allocation model required the development of an interactive interface, which presented intermediary results of each iteration. A graphical form plotted the increase and the convergence toward the maximum of the profit values . A connection with the GIS database provided the automation of data input and the visualization of different allocation scenarios on the map. 15  The automation and coordination of the models at each hierarchical level was performed with routines developed in Visual Basic for Applications and C++. For each of the sawmilling models, a console was designed to monitor the activity of each sawmilling model . The results generated by these models (i.e. the shadow prices and profit values) were automatically loaded into the main database where they were processed, a new allocation was generated and a new iteration was triggered. The model was run on an Intel Pentium 2.2 GHz, 1.99 GB R A M , dual processor PC. 16  5.3.5. Model Assumptions A l l of the assumptions presented in Section 3.3.4, for the Multi-criteria Timber Allocation model also apply to the Hierarchical Timber Allocation model.  5.3.6. Model Testing The allocation procedure used in the Hierarchical Timber Allocation model was demonstrated using the same case presented in Chapter 3. The study area is located in the Kootenay-Columbia Region of British Columbia, and consists of two landscape units. In this area, the Multi-criteria Timber Allocation model allocated a set of 463 stewardship units (SUs) either to three hypothetical forest products companies or to reserve. The allocation criteria were profit, employment, visual, recreation, and wildlife. The profit values entered in the Multi-criteria Timber Allocation model were generated by the FTP 15  The form is presented in Figure 6.3 in Appendix 4.  16  The FTP Analyzer® consoles are presented in Figure 6.4 in Appendix 4.  89  Analyzer for each SU and company. The allocation parameters entered in the Hierarchical Timber Allocation model remained unchanged, except the profit values, which were substituted with SU composite values, according to the iterative procedure presented previously. Similar to the case analyzed in Chapter 3, two scenarios were analyzed with the Hierarchical Timber Allocation model: the Equal Weights and the Profit M A X scenarios . The Equal Weights scenario consisted of an allocation that balanced the allocation goals (i.e. all goal weights were set to 1); whereas the Profit M A X scenario presented an allocation that emphasized the profit goal (i.e. profit weight was set to 100 and all the others to 1). 17  Before demonstrating the allocation procedure devised in the Hierarchical Timber Allocation model, the lists of stewardship units allocated to each of the three companies by the Multi-criteria Timber Allocation model were fed into the FTP Analyzer®. This operation was performed in order to examine if the resulting profit values were consistent with those guaranteed by the Multi-criteria Timber Allocation model. Any differences would indicate the magnitude of profit losses that could occur if the allocation generated by the Multi-criteria Timber Allocation model was implemented in practice and demonstrate the dynamic nature of the allocation decision. These differences would also confirm the need for the iterative negotiating process devised in the Hierarchical Timber Allocation model. A n analysis of the iterative negotiating process was also performed in order to showcase the capability of the Hierarchical Timber Allocation model to find those timber allocations that matched the production requirements of the three companies, consequently increasing total profit. In this analysis, only the results of the Profit M A X scenario were analyzed because they required more iterations than those of the Equal Weights scenario. Consequently, the convergence toward the optimal solution provided a better understanding of the allocation process. After each iteration, the intermediary allocation results were stored and then used to analyze how the model converged toward the optimal allocation decision. 5.3.6.1.  Multi-criteria vs. Hierarchical Timber Allocation  In this section, a comparison was performed between the allocation results generated by the Multi-criteria Timber Allocation model and those of the Hierarchical Timber Allocation model. Figure 5.5 shows the total profit values generated in the two scenarios by the Multicriteria Timber Allocation model and the Hierarchical Timber Allocation model.  17  For the allocation results, please refer to Tables 6.12 and 6.13 in Appendix 4.  90  • Profit Max • Equal Weights C  o  $60.44 $57.16  $54.89  E o  $49.84  0_  o  Multi-criteria Timber Allocation Model  Multi-criteria Timber Allocation Model (after FTP Analyzer run)  Hierarchical Timber Allocation Model  Figure 5.5 - The comparison between the profit results (one year) generated by the Multi-criteria Timber Allocation and the Hierarchical Timber Allocation models (Profit MAX and Equal Weights scenarios).  In Figure 5.5, two sets of profit values are presented for the Multi-criteria Timber Allocation model. The bars on the left show the total profit values (first one-year period) generated by the model in Chapter 3. The bars in the center indicate actual total profit values calculated by the FTP Analyzer® with the timber in the mix of stewardship units allocated to the three sawmills. The results show that the actual total profit values were considerably smaller than those forecasted by the Multi-criteria Timber Allocation model ($1.7 million smaller in the Profit M A X Scenario and $1.8 million smaller in the Equal Weights Scenario). These differences indicate that the assumption in the Multi-criteria Timber Allocation model that the allocation of stewardship units would maintain their total profit value regardless of what mix of stewardship units was allocated to the companies is unsupported. Furthermore, this confirms the need for the Hierarchical Timber Allocation model, which is capable of separating the medium-term and operational planning horizons and generating more accurate profit values. Figure 5.5 also suggests that, when the Hierarchical Timber Allocation model was run, the total profit values (the bars on the right) were noticeably higher than those of the Multicriteria Timber Allocation model were. Profit gains were even more important when compared with the actual profit values (the bars in the center of the graph): in the Profit M A X Scenario, a profit increase of $7.2 million was registered, whereas a profit gain of $7.3 million occurred in the Equal Weights Scenario. These large differences reiterate the importance of developing the Hierarchical Timber Allocation model.  91  Profit MAX Scenario Multi-criteria Hierarchical Profit Employment Wildlife Visual Recreation  100% 95% 67% 72% 63%  100% 96% 70% 74% 64%  Equal Weights Scenario Multi-criteria Hierarchical  93% 97% 95% 83% 72%  94% 98% 91% 82% 92%  Table 5.1 - Comparison between the criteria achievement values for the Profit MAX and Equal Weights Scenarios - The Multi-criteria Timber Allocation model vs. The Hierarchical Timber Allocation model.  Table 5.1 indicates that, in contrast with the above differences in profit, the values of the other criteria generated by the two models were, for most criteria, similar. Differences could be attributed to the substitution of profit values in the Multi-criteria Timber Allocation model with the composite values in the Hierarchical Timber Allocation model. Because both models use relative weights (i.e. relative to the goal target value), the differences in profit target values were reflected in the differences in weight values. This difference, although small, influenced the achievement levels of the goals. For example, in the Equal Weights scenario, the recreation achievement increased from 72% to 92% and the wildlife achievement decreased from 95% to 91%. 5.3.6.2. The Iterative Negotiation Procedure The iterative procedure designed in the Hierarchical Timber Allocation model to negotiate the timber allocations between the medium-term and the operational level models produced a series of intermediary results. These were analyzed in order to understand the convergence toward the optimal solution and further demonstrate the model.  92  $70  —•—Company 1 —•—Company 2  $60  —A—Company 3 —®—TOTAL  $57.16  $57.16  $10.25  $10.25  $50 $42.70 o  *  w  I o  $30  CL  $20  $10  $16.99 $16.44 $9.26  Iteration  Figure 5.6 - The convergence of the profit values of each company and in total toward the optimal solution in the Equal Weights scenario.  In the Equal Weights scenario, the optimal solution was achieved in one iteration. Figure 5.6 shows the profit values obtained at the operational level by each of the operational models and in total. The graph suggests that, in Iteration 0 (i.e. the model initialization), the allocation of the initialization stewardship units produced different profit values for each company. The reasons for this are: a) the differences in product structures and prices between companies, b) the incompatibility between the timber composition of the initialization SUs and the production parameters of each company, and c) the maximum volume capacity of each company. In Iteration 1, the profit values of all three companies increased considerably due to the shadow price adjustments that were applied after Iteration 0. A n interesting case occurred with Company 3, which did not respond well to the initial allocation. In iteration 1, however, this company achieved a profit value higher than those of both Companies 1 and 2 did. In Iteration 2, the total profit value was identical with that of Iteration 1; therefore, the medium-term level model stopped the procedure.  93  $70  -Company 1 -Company 2  $60  -Company 3  $59.94  $60.44  $60.44  $11.33  $11.33  —•  -TOTAL  $50 $42.70  1 o  $30  $20  $10  $16.99 $16.44  $11.31  $9.26  $Iteration  Figure 5.7 - The convergence of the profit values of each company and in total toward the optimal solution in the Profit M A X scenario.  In contrast to the Equal Weights scenario, the Profit M A X scenario achieved optimality in two iterations. Figure 5.7 indicates that, because the initial iteration was identical in both allocation scenarios, the same profit values were achieved as in the Equal Weights scenario. In Iteration 1, however, all profit values were higher than those in the Equal Weights scenario were which was expected given that the Profit M A X scenario emphasized the profit goal. Unlike the Equal Weights scenario, Iteration 2 did not produce the same allocation as in the Iteration 1. In this iteration, Companies 1 and 2 increased their profit values, which indicated that they were allocated a different mix of stewardship units than in the previous iteration. Company 3, however, did not change its profit value, which suggested that it received the same mix of stewardship units as in previous iteration. In Iteration 3 no change occurred in the total profit values, therefore the procedure was stopped. The above results indicate that the iterative procedure produced increasing profit values, converging toward the maxima. Unlike the Equal Weights scenario, the Profit M A X scenario reached the optimum in two iterations. Therefore, its results were considered more relevant to the analysis of the iterative procedure. In this analysis, the stewardship units allocated to each company were converted into stem class distributions. They were generated for all the iterations of the Profit M A X scenario. By plotting these distributions, one is able to visualize how, after each iteration, the Hierarchical Timber Allocation model  94  was able to fit the raw material requirements of each company with the timber composition of the allocated stewardship units.  0.00%  3  3  i 10-15  16-21  22-27  Length class (ft) and SED class (in)  Figure 5.8 - The stem class distributions of timber allocated to Company 1 in Iteration 0 to 3 in the Profit M A X scenario.  Figure 5.8 presents the stem class distributions of stewardship units allocated to Company 1 in Iteration 0 (the hatched bars) to Iteration 3 (the white bars). These distributions are presented as percentages of the total volume of allocated timber. The stem classes are combinations of small end diameter (SED) (4-9 in., 10-15 in., 16-21in., and 22-27 in.) and length (8-20 ft., 21-33 ft., 34-46 ft., and 47-60 ft.) classes. Since the initialization SU was allocated to each of the three companies in Iteration 0, the stem distribution in this iteration was identical for all the companies. Figure 5.8 suggests that the initialization SU contained a large volume (80%) of the small SED (4-9 in.), large length (34-60 ft.) stem classes. The most dramatic changes in volumes occurred in Iteration 1, where the product structure of Company 1 (i.e. most lumber products had widths between 4 and 12 in.) required the model to increase the volumes of 10-15 in. SED / 34-46 ft. length class, while drastically decreasing the volume of stem in 4-9 in. SED / 47-60 ft. length class. These adjustments were the result of the allocation model shifting the allocation of stewardship units toward the ones that could produce the most valuable lumber products (2x10 and 2x12). The distributions presented in Iterations 2 and 3 confirm this presumption by further adjusting the volumes of the two stem classes. Note that in Iteration 2, the model needed to adjust the volumes of the stem classes allocated in the previous iteration, which indicates that Company 1 contributed considerably to the need for additional iterations. 95  45.00%  Figure 5.9 presents the volume distributions of stem classes allocated to Company 2, in Iterations 0 to 3. The graph suggests that, in Iteration 1, the allocation model increased the volumes of stems in the 4-9 in. SED / 34-46 ft. length class and 10-15 in. SED / 34-46 ft. length class. However, the model decreased the volumes of 10-15 in. SED / 47-60 ft. length class. This action was justified by the need of Company 2 to produce studs with widths of 4 and 6 inches and lengths of 8 and 9 feet. The next two iterations did not produce considerably large adjustments in the allocated stem class distributions, an indication that the model reached the desired timber distribution for Company 2 faster than for Company 1.  96  45.00%  40.00%  o 35.00% 5 fj 30.00% -i  (Q cu  e  * 25.00% re  |  "(3 » 20.00%  S 15.00%  o  5.00%  0.00%  i _ 3  & 10-15  22-27  Length class (ft) and SED class (in)  Figure 5.10 - The stem class distributions of timber allocated to Company 3 in Iteration 0 to 3 in the Profit M A X scenario.  Figure 5.10 presents the distribution of stem classes allocated to Company 3 in Iterations 0 to 3. At first glance, the graph indicates that Iterations 1, 2 and 3 produced the same allocations, which was expected because the profit values generated by Company 3 in these iterations were identical. The fact that the allocation model found an optimal solution quickly could be partially explained by the distinct set of products that Company 3 produced (e.g. vertical grain Japanese grades - Hirakaku), for which there were no other similar competitors. In turn, the sawmilling parameters (sawing and bucking patterns) required that the timber allocated to Company 3 contain larger SED classes than those required by Companies 1 and 2. The distribution of stem classes presented in Figure 5.10 supports this supposition: in Iterations 1, 2, and 3, the model drastically reduced the volumes of stems in the 4-9 in. SED classes and substantially increased the volumes of stems in 10-15 in. and 16-21 in. SED classes. The above analyses demonstrate how the Hierarchical Timber Allocation model was able to achieve increasing profit values at the operational level by allocating the right raw materials to the right sawmill. The results indicate how the iterative procedure shifted the composition of raw materials from an inappropriate distribution of stem classes (initialization SU) to those distributions required by each company. These outcomes demonstrated the iterative negotiating procedure and showed how the Hierarchical Timber Allocation model could produce optimal multi-criteria timber allocations that satisfy the conditions of sustainable forest management.  97  5.4.  Policy Analyses  In the previous section, the Hierarchical Timber Allocation model was used in the Equal Weights and the Profit M A X optimization scenarios. In the model, timber located in two landscape units, containing 463 stewardship units, was allocated to three forest products companies in order to satisfy their operational capacities and to maximize the achievement levels of the sustainability criteria (profit, employment, visual, recreation, and wildlife). Other than the usual constraints regarding timber volumes, technological and marketing characteristics, no other constraints were included in the model. In this section, the Hierarchical Timber Allocation model was demonstrated by analyzing various sustainable forest management policy questions. In order to reflect accurately each policy question, constraints were added to the model. To study the impact of each policy on the two optimization scenarios, the differences in results were analyzed between the constrained arid the unconstrained scenarios. Each policy analysis concluded with a comparison between the results of the Equal Weights and the Profit M A X optimization scenarios. Suggestions were made also regarding the appropriateness of implementing the scenarios in practice. 5.4.1. The Wildlife Corridor Policy Wildlife conservation plays an important role in increasing the biodiversity of forest ecosystems. According to the Forest Practices Code of British Columbia Act (2002), special programs are required to monitor, manage, and conserve different species of wildlife. The basic goal of these programs is to conserve core habitat areas in which a large number of wildlife species cohabitate. Connectors between core habitat areas, called wildlife corridors, allow these animals to migrate, interbreed, and feed. Wildlife corridors must be large enough to allow for easy movement of the largest species and must be managed carefully. This is especially important for migratory animals, large predators, and those with large home ranges (such as ungulates). Some of the most important concerns that are addressed usually in the areas affected by the wildlife corridors involve new road construction, harvesting intensities and techniques, and human interaction. Generally, in order to limit human access to these areas, no new roads are opened, consequently decreasing the volume of recreation activities involving hunting and fishing. In addition, in order to preserve the forest ecosystems (e.g. maintain the crown cover), timber harvesting in wildlife corridors is usually avoided or harvesting takes place in the form of low intensity partial-cuts. The GIS data file used for the area under investigation indicated that a wildlife corridor comprised of 34 stewardship units existed on the Eastern border . In order to analyze the 18  The GIS database indicates the presence of different features, such as wildlife corridor, with a series of 0 and 1 values for each of the polygons comprising the area under investigation.  98  allocation of timber under the Wildlife Corridor policy, some conditions needed to be implemented in the model. The first condition addressed the harvesting intensities that were allowed in the corridor. Consequently, clear-cuts were banned in the stewardship units comprising the corridor. However, partial-cuts were allowed, because of their lower intensity (see Table 3.5). In general, this condition alone would satisfy the practice of protecting the wildlife corridors against high intensity harvesting activities. However, if in addition to this condition a way of controlling the timber allocation from the wildlife corridor was devised, this could greatly benefit the multi-criteria timber allocation and the subsequent trade-off analyses. Consequently, a second condition dealing with the continuity of the corridor was added to the model. The continuity condition implied that the stewardship units located in the corridor must be given an increased chance of being allocated to reserve than those located outside the corridor. To achieve this condition, all stewardship units in the corridor were assigned wildlife indicator values greater than 1. The values reflect the increased importance of the stewardship units located in the corridor to achieve the wildlife goal as opposed to those located outside the corridor. Generally, higher values would be assigned in order to restrict increasingly the harvesting activities in the corridor and to improve further the free movement of the wildlife thorough it. In other words, the users of the model were provided with a procedure of setting higher allocation standards for those stewardship units located in the corridor than for the others. Therefore, unless timber harvesting in these stewardship units was considerably more important than achieving the wildlife goal, the continuity condition would not be compromised. Since changes in any one of the allocation criteria influenced the results of the other criteria in the model, a series of trials were needed in order to find a wildlife indicator value that would generate a suitable allocation for the analyzed problem. The effects of the Wildlife Corridor policy on the allocations generated by the Hierarchical Planning Allocation model were analyzed in the Equal Weights and the Profit M A X scenarios . Three trials were performed with wildlife indicator values for the SUs located in the corridor of 1.1,1.3, and 1.5, respectively. In the Equal Weights scenario, every trial changed the results of the goal values, but consistently allocated all the SUs in the corridor to reserve (i.e. the allocations fully met the continuity condition). In the Profit M A X scenario, however, stewardship units located in the corridor were still allocated to harvesting, in all trials. In this scenario, the volume of timber harvested in the corridor first decreased when wildlife indicator values of 1.5 were assigned. 19  The different outcomes in the two scenarios could be justified by the fact that, in the Profit M A X scenario, the profit goal and therefore the timber value were highly emphasized, whereas, in the Equal Weights scenario, the other goals became equally important as the profit goal. As a result, in the Profit Max scenario, some of the stewardship units located in the corridor and containing valuable timber were targeted for harvesting rather than for reserve. Therefore, the increasingly higher wildlife indicator values during the trials 19  For a complete set of results, please refer to Table 6.14 in Appendix 5.  99  established increasing levels of competition in the corridor between the profit and wildlife goals. The trial in which the wildlife indicator values of 1.5 were assigned to the SUs located in the corridor was selected for the analysis of the Wildlife Corridor policy. This trial was assumed to reflect a more practical compromising solution than the other trials. As expected, the change in the wildlife indicator values triggered a change in the target value for the wildlife goal, from 140 points in the unconstrained model to 160 points when the constraints of the Wildlife Corridor policy were added. 5.4.1.1.  The Equal Weights Scenario  Figure 5.11 presents the spatial allocation of the stewardship units generated by the unconstrained model in the Equal Weights scenario (all goal weights were 1). In contrast, Figure 5.12 shows the results of this scenario under the Wildlife Corridor policy. The stewardship units located within the corridor are identified by the red contour line. The maps show that the Wildlife Corridor policy caused one stewardship unit located in the wildlife corridor to be reallocated from Company 2 to reserve. The maps also show that the reallocation of this stewardship unit from harvesting to reserve triggered only few stewardship units to be allocated differently. Consequently, the Wildlife Corridor policy is not expected to generate large changes in the results of the Equal Weights Scenario.  100  Equal Weights Scenario  Figure 5.11 - The map of the allocated stewardship units in the Equal Weights scenario (unconstrained). Wildlife Corridor Policy - Equal Weights Scenario  Legend  Figure 5.12 - The map of the allocated stewardship units in the Equal Weights scenario, under the Wildlife Corridor policy.  25%  20%  o. o  15%  1  -5%J Profit  1  1 Employment  Recreation  ! Visual  Wildlife  Figure 5.13 - The impact of the Wildlife Corridor policy on the Equal Weights scenario - criteria.  Figure 5.13 shows the changes incurred in the criteria results because of the Wildlife Corridor policy in the Equal Weights scenario. As expected, the increase in the wildlife goal value was triggered by the increase in wildlife indicator values of the stewardship units located in the corridor. A loss in profit of $232,564 and a loss in employment of 3 person-years were the only losses registered as a result of this policy. These values were small, under 2%, which indicated that, in the Equal Weights scenario, the model did not have to make radical changes in the allocation criteria in order to accommodate for the Wildlife Corridor policy. Other changes in the results were registered also for the visual and recreation criteria, which increased by 1 % and 3%, respectively. This increase occurred because the model, in order to attain a higher wildlife target, increased the volume of partial-cuts from 1,471 m to 7,526 m . Because of this increase, more stewardship units with recreation and visual quality features, usually associated with wildlife features, were allocated to partial-cutting. 3  3  102  4,000  34^6  47-60 10-15  34-46  47-60  16-21  SED (in) and Length (ft) Classes  Figure 5.14 - The impact o f the W i l d l i f e Corridor p o l i c y on the E q u a l Weights scenario - volume differences o f small end diameter - S E D (bottom scale) and length classes (top scale). Note: there were no changes i n the timber composition allocated to Company 3.  As a result of the Wildlife Corridor policy, a change in the stem class distribution of timber allocated to the companies also occurred. Figure 5.14 indicates that these changes in raw material composition affected Companies 1 and 2, but not Company 3. This outcome was the result of the model allocating a similar list of stewardship units to Company 3. The only difference consisted in the substitution of stewardship units SU 214 and SU 487 with stewardship units having similar timber compositions: SU 27 and SU 370. In contrast to Company 3, the Wildlife Corridor policy affected the volumes of stem classes allocated to Companies 1 and 2. For Company 1, the most notable differences occurred in the small end diameter (SED) class 10-15 in., where the volume of longer stems (47-60 ft.) decreased by 2,500 m , while the volume of medium length stems (34-46 ft.) increased by 2,000 m . For Company 2, the differences spread over more stem classes than for Company 1. For example, an increase of 3,500 m in the volume of 4-9 in. SED / 47-60 ft. length stem class occurred under this policy. In addition, the volumes of timber allocated to Company 2, in all SED classes, decreased by approximately 1,000 m . Since the largest volume losses occurred in those stem classes that were vital to the production of the most valuable lumber products of Companies 1 and 2 (i.e. SED 4-15 in.), it was expected that the production parameters of these two companies would be most affected by these changes in raw material. 3  3  103  10%  8%  J  6%-^  fo  4%  J.  -2%  J  .4%  J  10 01  I  Area Harvested Companyl  I  Area Harvested Company2  I  I  Area Harvested Company 3  Profit Company 1  1  Profit Company 2  Profit Company 3  Figure 5.15 - The impact of the Wildlife Corridor policy on the Equal Weights scenario - differences in the harvested areas and the profits of the three companies.  Figure 5.15 confirms that the raw material changes caused by the Wildlife Corridor policy mostly affected Companies 1 and 2. Since Company 3 produced a more complex and flexible product mix than the other two companies did, the model was able to better match its production characteristics with the raw material composition and, therefore, this company did not lose any profit under this policy. Companies 1 and 2 however, because of their less flexible product mix, were the only ones that contributed to the total profit loss in the Equal Weights scenario. The graph also shows changes in the areas harvested by the three companies, which suggest that the ban on clear-cut harvesting in the wildlife corridor resulted in increases of harvesting areas for Companies 1 and 3. The increases were due mostly to more volumes of timber being harvested with partial-cuts (5,138 m for Company 1 and 2,233 m for Company 3), which resulted in larger harvesting areas. In contrast, Company 2 relied mostly on clear-cutting techniques (just 155 m in partial-cuts) and its harvesting area decreased. 3  3  3  5.4.1.2. The Profit MAX Scenario Figures 5.16 and 5.17 present the maps of the Profit M A X scenario allocations for the unconstrained model and under the conditions of Wildlife Corridor policy, respectively. Seven out of the eight stewardship units located in the corridor that were originally allocated to clear-cut harvesting, were allocated to partial-cut harvesting under the Wildlife Corridor policy. The change from clear-cuts to partial-cuts could be attributed to the 104  condition that only partial-cuts were allowed in the wildlife corridor. The fact that one of the eight stewardship units originally allocated to harvesting was allocated to reserve under this policy could be attributed to increases in the values of the wildlife indicators for the stewardship units located in the corridor. By allocating this SU to reserve, the model was able to increase the wildlife achievement level (due to a large indicator value), while contributing to the continuity of the wildlife corridor (due to less SUs being harvested in the corridor). The fact that the other seven stewardship units were still allocated to harvesting despite their increased wildlife indicator suggests that they contained valuable timber and could not be substituted with other stewardship units located outside the corridor. In addition, the model allocated the seven stewardship units to harvesting because the Profit M A X scenario emphasized the profit criterion and took advantage of the valuable timber in order to achieve this goal. In addition, the maps show a visible impact of this policy on the spatial allocation of the stewardship units. A large number of stewardship units were exchanged between companies, while others were transferred from reserve to harvesting. Therefore, it was expected that the Wildlife Corridor policy would affect the total harvesting area and would have a great impact on the allocation criteria.  105  Profit MAX Scenario Legend Stewardship units allocated to Company 1  B  Stewardship units allocated to Company 2  ~J  Stewardship units allocated to Company 3 •  Stewardship units allocated to Reserve Stewardship units inoperable  Figure 5.16 - The map of the allocated stewardship units in the Profit M A X scenario (unconstrained). Wildlife Corridor Policy - Profit MAX Scenario  Legend •  Stewardship units in wildlife corridor  •J  Stewardship units allocated to Company 1  J  Stewardship units allocated to Company 2  J  Stewardship units allocated to Company 3  jj  Stewardship units allocated to Reserve  ~~]  Stewardship units Inoperable  Figure 5.17 - The map of the allocated stewardship units in the Profit M A X scenario under the Wildlife Corridor policy.  106  25%  20%  - : .-I-  °- 15%  0%  I". • ••>»«'i«Bi!ri|  Profit  Employment  Recreation  Visual  Wildlife  Figure 5.18 - The impact of the Wildlife Corridor policy on the Profit M A X scenario - criteria.  Figure 5.18 shows the impact that the Wildlife Corridor policy had on the criteria results of the Profit M A X scenario. As expected, a large increase in the value of the wildlife criterion occurred because of increasing the wildlife indicator values for the stewardship units located in the corridor. Under this policy, the volume of timber allocated to partial-cut harvesting increased from 22,608 m to 102,621 m . This large increase suggested that the model, in order to achieve the increased wildlife goal target, needed to allocate more stewardship units to partial-cut harvesting in order to take advantage of the fractions of wildlife indicator values that could be achieved with this technique. The large increases in the volumes allocated to partial-cuts, also increased the visual goal value by 3%. This indicated that the majority of stewardship units allocated to partial-cuts contained wildlife and visual features. 3  3  However, some criteria registered losses. First, a profit loss of $483,557 occurred under this policy, mostly a consequence of the ban on clear-cutting techniques in the corridor, resulting in loss of valuable timber. Second, the value of the recreation criterion dropped by 3%, as a result of the Profit M A X scenario focusing on profit rather than other criteria. In addition, the loss in recreation indicated that, under the Wildlife Corridor policy, those stewardship units with valuable timber allocated to partial-cuts lacked the recreation indicator.  107  25,000 • Sawmill 1 20,000  • Sawmill 2 • Sawmill 3  «  15,000  >. = o  10,000  Q.  °  5,000  3 </>  V)  0  re V)  o  O)  c re  -5,000  JZ  u 4)  -10,000  E  -15,000  -20,000  8-20  21-33  34-46 4-9  47-60  34-46  47-60  34-46  34-46  47-60  16-21  10-15  22-27  S E D (in) a n d L e n g t h (ft) C l a s s e s  Figure 5.19 - The impact of the Wildlife Corridor policy on the Profit MAX scenario - volume differences of small end diameter - SED (bottom scale) and length classes (top scale). Note: there were no changes in the timber composition allocated to Company 2.  Figure 5.19 shows the changes in the volumes of stem classes allocated in the Profit M A X scenario under the Wildlife Corridor policy. Companies 1 and 3 were the only ones that had changes in raw material compositions because of this policy. Company 1 experienced the largest changes in the timber composition, mostly in the small SED class (4-9 in.), where 15,000 m of stems of length class 34-46 ft. were substituted by 20,000 m of longer stems (47-60ft.).This substitution was caused by the strong demand that Company 2 had on stewardship units containing medium-length/small-diameter stems for the production of studs. This substitution is likely to happen every time Company 2 is restricted access to stewardship units containing these stem classes. Because stewardship units with such characteristics are rare in the area, Company 1 was allocated SUs containing longer stems. In turn, long stems caused increases in the production costs at the bucking lines and Company 1 was expected to incur profit losses because of this policy. 3  3  Company 3 experienced changes of raw materials in almost all stem classes. In contrast to Company 1, these changes were considerably smaller (under 4,000 m ) and consisted of many stem classes increasing their volume. The largest loss in volume (4,000 m ) occurred in the SED class 10-15 in. and the largest increases occurred in the large SED class (16-27 in). Because of this change in timber composition, Company 3 substituted the production of dimension lumber with Japanese products and, therefore, large profit losses were not expected for this company. 3  3  108  10%  8% ]  o. 0% L_  -2% -  1  •4% -I Area Harvested Company 1  Area Harvested Company 2  1  I  1 Area Harvested Company 3  Profit Company 1 Profit Company 2  1 Profit Company 3  Figure 5.20 - The impact of the Wildlife Corridor policy on the Profit M A X scenario - differences in the harvested areas and the profits of the three companies.  Figure 5.20 suggests that, because of the change in the raw material distribution, Company 1 absorbed most of the total profit loss incurred under this policy. The cause was the policy restricting Company 1fromharvesting in the wildlife corridor. As a result, the volume of valuable timber allocated to this company was reduced drastically. This also resulted in a large increase in the harvesting area for this company. Company 3, although subject to changes in raw material composition, was able to adapt its production parameters and product mix. It experienced a drop of only $16,000 in profit.  109  5.4.1.3. Equal Weights vs. Profit MAX  $59,955,461  6,199 people years  $56,927,167  6,375 people years  • Equal Weights Scenario • Profit MAX Scenario  Profit  Employment  CM  oo  o  m CM  o  CM  Recreation  Visual  m ,—  Wildlife  Figure 5.21 - The comparison between the results of the Equal Weights and the Profit M A X scenarios under the Wildlife Corridor policy.  Figure 5.21 shows that the Equal Weights scenario reduced profits by $3 million compared to the Profit M A X scenario, in order to increase the values of all the other criteria and implement a more balanced allocation between all sustainability criteria. The largest increases were achieved in the recreation and the wildlife criteria, by 43 points and by 28 points, respectively. Given the 5% loss in profit and the important increases in the other criteria, the Equal Weights scenario could be considered a good candidate for implementation under the Wildlife Corridor policy. The analyses of the two scenarios demonstrated the capability of the Hierarchical Timber Allocation model to model realistically the Wildlife Corridor policy. When all allocation criteria were equally important in the Equal Weights scenario, the model allocated all the stewardship units to reserve in order to meet the continuity condition of the corridor. When the profit criterion was emphasized in the Profit M A X scenario, the valuable timber located in the corridor was allocated to harvesting, despite the increased wildlife indicator values assigned to the stewardship units located in the corridor. The results analyzed in the two scenarios indicated that the model reacted as expected to the conditions imposed by the Wildlife Corridor policy: a balanced, controlled allocation of stewardship units to reserve and harvesting in the corridor. In addition, the analysis showed the ability of the model to produce valuable outputs, such as the graphical representations of the allocations, the values for all of the allocation criteria, the opportunity costs of different scenarios, the stem  110  distributions for the allocated timber, and the reactions of each company to the conditions imposed by the Wildlife Corridor policy. 5.4.2.  The A ccessibility Policy  Accessibility conditions have always had a severe impact on timber availability and, therefore, have constituted an essential constraint in timber allocation activities. Generally, due to scarce networks of forest roads, large forested areas are deemed inoperable. Roads are usually costly to build and maintain, and therefore many forest products companies prefer to harvest in the stewardship units that contain valuable timber and are located close to existing roads. As a result, the distance to roads and the subsequent costs of building and maintaining them are deciding factors in timber allocation decisions. The Accessibility policy would require that the stewardship units allocated to companies (i.e. harvesting) are located as close as possible to existing roads. This policy may be beneficial to forest ecosystems, because it creates large, continuous reserve areas located further from human activities. In the two landscape units under investigation, the GIS data indicated those stewardship units containing roads (Figure 5.22). Two forest roads are located in the area: one on the Southern part (positioned east - west) and the other on the Eastern part (positioned north south). From the 463 stewardship units, 164 have access to these roads (i.e. at least one road traverses the SU). In order to model the Accessibility policy, the Hierarchical Timber Allocation model minimized the sum of distances between those stewardship units allocated to harvesting and the closest roads. Instead of distances, the costs of building and maintaining roads to access each stewardship unit could be used, upon availability. In this study, the distances between each stewardship unit and the closest road were measured on the map. These were included in the model as objective coefficients for the binary sawmilling variables. The resulting timber allocations minimized the distance of the allocated stewardship units to the closest road in addition to minimizing the deviations from the goal targets. In order to study the Hierarchical Timber Allocation model and analyze the effects of the Accessibility policy on the timber allocations, the model was 20  employed using the Equal Weights and Profit M A X scenarios . 5.4.2.1.  The Equal Weights Scenario  Figure 5.22 shows a map of the timber allocation in the Equal Weights scenario in which the stewardship units with full timber accessibility (i.e. containing roads) were identified by a red contour line.  For a complete set of results, please refer to Table 6.15 in Appendix 5.  Ill  Accessibility Policy - Equal Weights Scenario Legend  Figure 5.22 - The map o f the allocated stewardship units i n the Equal Weights scenario under the Accessibility policy.  The map indicates that in the Equal Weights scenario the model harvested many stewardship units that were located on or adjacent to roads. This implied that the model responded as expected to the conditions imposed by the Accessibility policy. However, not all of the stewardship units containing roads were allocated to harvesting. This suggested that the model harvested farther from the road in order to make better use of the valuable timber, while conserving the ecological features.  112  5%  -20%  J  1 Profit  1  1 Employment  1  Recreation  Visual  Wildlife  Figure 5.23 - The impact of the Accessibility policy on the Equal Weights scenario - criteria.  Figure 5.23 presents the impact of the Accessibility Policy on the criteria in the Equal Weights scenario. The results indicate large losses in the profit and the employment criteria. These are caused mainly by the decrease of 65,000 m in the allocated timber volume that occurred because of this policy. The loss in employment of 751 person-years (12%) was caused directly by this loss in timber volume. The graph also shows that the profit and the employment criteria suffered different losses, mainly because the employment was not sensitive to the timber composition, while the profit was. This further clarifies why the employment goal achieved high values in policies in which the total timber volumes did not suffer decreases (e.g. the Wildlife Corridor policy), while the profit goal did. In this scenario, because the loss in timber volume was so large, the profit loss of $9.5 million could be attributed partially to the volume loss. In addition, this loss indicates that, under the Accessibility policy, the stewardship units allocated to harvesting did not contain much valuable timber. 3  Besides the losses in profit and employment, the Accessibility policy also caused losses in the recreation and wildlife criteria by 3% and 1%, respectively. The only increase occurred in the visual criterion, by 3%. These results suggest that constraining the harvesting to take place closer to roads shifted the allocation of a large number of stewardship units containing wildlife and recreation features from reserve to harvesting. In addition, these outcomes indicate that wildlife and recreation activities coexisted in areas located closer to the roads. Because the assessment of visual quality objectives was not performed from these roads, the stewardship units located in their vicinity did not contain large visual  113  indicator values. Consequently, the Accessibility policy caused the visual criterion to increase. 30,000  SED (in) and Length (ft) Classes  Figure 5.24 - The impact of the Accessibility policy on the Equal Weights scenario - volume differences of small end diameter - SED (bottom scale) and length classes (top scale). Note: Company 2 experienced large decreases in the volume of raw materials.  Figure 5.24 presents the impact of the Accessibility policy on the raw materials allocated to sawmills in the Equal Weights scenario. The graph indicates a large decrease in the timber volume allocated to Company 2, occurring especially in those classes essential to the production of studs (i.e. small diameters). The changes in the raw material composition allocated to Company 1 consisted of the substitution of longer lengths (47-60 ft.) with shorter stems (34-46 ft.), in both the 4-9 in. and the 10-15 in. SED classes. This substitution was favorable to Company 1 because it competed with Company 2 for these stem classes, which were now available to it. This explanation is supported by the exchange of stewardship units between Company 2 and Company 1 (e.g. SU 70) in this scenario. Therefore, Company 1 was expected to experience a considerably smaller profit loss than Company 2. Company 3 did not experience large differences in the raw material composition and was not expected to incur large profit losses.  114  40%  20%  -100%  -120%  J  1  !  !  1  Area Harvested Area Harvested Area Harvested Profit Company Profit Company Profit Company Company 1 Company 2 Company 3 1 2 3  Figure 5.25 - The impact of the Accessibility policy on the Equal Weights scenario - differences in the harvested areas and the profits of the three companies.  Figure 5.25 confirms the large profit loss of Company 2 under the Accessibility policy. The graph shows that this company was allocated just a small amount of timber and consequently was on the brink of closing its operations. Companies 1 and 3, however, were not affected considerably by this policy, although their raw material composition suffered changes and the companies had to increase their harvest area by 5% and 15%, respectively. The results presented in the Equal Weights scenario demonstrated that the Accessibility policy changed the composition of the available timber considerably, to the point where profitability and flexibility of production facilities became a determining factor in the timber allocation. Because, in this scenario, the model needed to balance all the other allocation criteria besides profit, companies that proved to have a higher value and more flexible product mixes (i.e. Companies 1 and 3) withstood the changes brought on by this policy. In contrast, Company 2, which was the least flexible and produced the least profitable products, was allocated very small amounts of timber. Company 1 capitalized on this situation and was allocated valuable timber that would have otherwise been allocated to Company 2. 5.4.2.2. The Profit MAX Scenario Figure 5.26 presents the map of the allocated stewardship units in the Profit M A X scenario under the Accessibility policy. The map indicates that many of the stewardship units 115  allocated to harvesting were situated further from the roads than in the Equal Weights scenario and, in some cases, not even adjacent to them. This spatial arrangement suggests that, in the Profit M A X scenario, the model selected SUs located farther from the roads in order to access the most valuable timber. Accessibility Policy - Profit MAX Scenario  Legend  Figure 5.26 - The map of the allocated stewardship units in the Accessibility policy - The Profit M A X scenario.  116  14%  -2%  •4%  -6%  -I Profit  1  1 Employment  Recreation  '  Visual  1  Wildlife  Figure 5.27 - The impact of the Accessibility policy on the Profit M A X scenario - criteria.  Figure 5.27 indicates that the Accessibility policy caused only the profit criterion to decrease. However, the profit loss of $2.1 million was considerably smaller than in the Equal Weights scenario. This shows that the model could easily find valuable timber situated closer to the roads when just the profit criterion was emphasized. However, the Accessibility policy created a situation in which stewardship units with wildlife, visual, and recreational features were re-allocated from harvesting to reserve. Consequently, the wildlife, recreation, and visual criteria increased by 13%, 12%, and 6%, respectively.  117  30,000 • Company 1  25,000  E  • Company 2 • Company 3  20,000  ><  _o Q. Q O  CO  15,000 10,000 5,000  in  ra in CD ra ra J=  0  o  -5,000  E _2  -10,000  cu  >o  -15,000  8-20  21-33  34-46 4-9  47-60  34-46  47-60  34-46  10-15  47-60  16-21  34-46 22-27  S E D (in) a n d L e n g t h (ft) C l a s s e s  Figure 5.28 - The impact of the Accessibility policy on the Profit M A X scenario - volume differences of small end diameter - SED (bottom scale) and length classes (top scale). Note: there were no changes in the timber composition allocated to Company 3.  Figure 5.28 shows how the composition of the timber allocated to companies was changed by the Accessibility policy. The graph indicates that this policy dramatically changed the timber composition allocated to Company 1. By contrast, the timber composition allocated to Company 3 was not affected. A n increase in volume of 25,000 m occurred in Company 1, in the 4-9 in. SED class, in which stems in the 34-46 ft. length class were substituted with stems in the 47-60 ft. length class. Losses in timber volume allocated to this company of approximately 7,000 m occurred in 10-15 in. and 16-21 in. SED classes. This substitution was caused by the strong competition of Company 2 for the same stem classes required by Company 1. The competition was even stronger because of Company 2 being allocated more volume of small-diameter/long-length stem classes. The impact of the policy on the raw material composition allocated to Company 1 and the loss in timber volume of 12,000 m in the 10-15 in SED class experienced by Company 2 implies that these two companies are expected to suffer important profit losses. 3  3  3  118  10%  5%  o a °  at c ra  0%  -5%  0. -10%  -15%  Area Harvested Area Harvested Area Harvested Profit Company Profit Company Profit Company Company 1 Company 2 Company 3 1 2 3  Figure 5.29 - The impact of the Accessibility policy on the Profit M A X scenario - differences in the harvested areas and the profits of the three companies.  Figure 5.29 confirms the expected profit losses incurred by Companies 1 and 2. Company 2 was the most affected by the Accessibility policy, losing more than 10 % of its profit, while Company 1 experienced a 4% profit loss. The results show that the least profitable companies (i.e. Companies 1 and 2) were the most affected by the Accessibility policy in the Profit M A X scenario. This negative impact on profit contributed to the increases in the visual, wildlife and recreation criteria presented in Figure 5.27 because the concentration of harvesting within the road areas resulted in large areas of forest available for conservation. Figure 5.29 also shows how the Accessibility policy affected the harvesting areas of the three companies. The graph shows that Company 3 reduced its harvesting area by 10%. The fact that the distributions of stems allocated to this company remained identical and that the harvesting area decreased suggest that Company 3 was allocated stewardship units with large stem density (i.e. stems/ha). Similarly, Company 2 reduced its harvesting area by 13 %, while receiving smaller diameter stems. Company 1, however, increased its harvesting area by 6% despite decreases in volumes of stems in larger SED classes. This suggests that the model allocated many stewardship units with low density and small diameter stems to Company 1.  119  5.4.2.3. Equal Weights vs. Profit MAX  I Equal Weights Scenario • Profit MAX Scenario  Profit  Employment  Recreation  Visual  Wildlife  Figure 5.30 - The comparison between the results of the Equal Weights and the Profit M A X scenarios under the Accessibility policy.  Figure 5.30 presents the goal values achieved under the Accessibility policy in the Equal Weights and Profit M A X scenarios. The results indicate that the visual, wildlife, and recreation criteria had larger values in the Equal Weights scenario than in the Profit M A X scenario. However, a profit loss of $10.7 million and a reduction in employment by 614 people years would be necessary to sustain these increases. In addition, Company 2 received a much lower amount of timber than its maximum capacity in the Equal Weights scenario and was on the brink of closing down its sawmilling operation. As such, other scenarios should be generated to reach a more equitable allocation. However, if the Equal Weights scenario were implemented, it would increase noticeably the ecological and social wellbeing of the forest ecosystem through increased wildlife, visual, and recreation criteria. Nonetheless, actions could and should be taken by Company 2 to improve its profitability and become more competitive against the other two companies. In this endeavour, the model could provide valuable information to Company 2. Especially important are the post optimality values (reduced costs, shadow values) that are generated at the operational level model. These values indicate what changes in profit are expected if new products are introduced and what their effect on the raw material composition is. By improving its product diversity, Company 2 would be able to compete better for the same raw materials (especially with Company 1). 120  The results presented in this section demonstrate the capability of the Hierarchical Timber Allocation model to generate multi-criteria allocations that reflected the conditions of the Accessibility policy. In both scenarios, the model was able to allocate to harvesting those stewardship units located closer to the roads, therefore increasing their accessibility. However, this policy proved to be very restrictive to the less profitable companies. In the Equal Weights scenario, this policy dramatically reduced the volume of timber allocated to Company 2 and greatly increased the wildlife, visual, and recreation criteria. In the Profit M A X scenario, despite the allocation of timber volumes to all the companies, this policy caused a large decrease in profits for Companies 1 and 2. Moreover, the other sustainability criteria suffered losses. The implementation of these optimization scenarios in practice would be difficult and could result in unpopular decisions. However, similar analyses could facilitate the generation of solutions to increase the profitability of sawmills and to develop a network of roads capable of increasing the accessibility to valuable timber, while maintaining the ecological and social objectives of the area. 5.4.3. The US / Canada Softwood Lumber Trade Policy According to the Softwood Lumber Updates (BC Ministry of Forests 2003), on April 2, 2001 the U.S. Coalition for Fair Lumber Imports filed an anti-dumping duty petition with the U.S. government. Under U.S. trade law, an anti-dumping case is an investigation of whether an importer is selling goods in the U.S. at prices lower than in the home market or is selling goods at prices below cost. On October 31, 2001, the U.S. Department of Commerce announced its decision to impose both countervailing and anti-dumping duties to the softwood lumber exported to the U.S. from Canada (herein called the U.S./Canada Trade Policy). The combined countervailing /anti-dumping duty rate of nearly 32% (19.31% plus 12.58%) was in effect until mid-December 2001, since the World Trade Organization did not allow provisional countervailing duties to extend beyond four months. Only the anti-dumping duty of 12.58% was applied from mid-December 2001 to early May 2002. On May 22, 2002, the U.S. Department of Commerce published the final orders in the countervailing and anti-dumping cases. Since then, the Canadian and the U.S. government have tried to find a solution to end this situation. The latest U.S. proposal (December 2003) wanted to restore a quota system in which Canadian forest product companies were allowed to export lumber to the U.S., up to a certain amount, without paying duties. Until recently, this proposal was under study by the two parties involved in the dispute and Canadian forest products companies were suffering large profit losses; some were considering permanently closing down their operations. In order to analyze the effects of the duties on the multi-criteria timber allocation and sawmilling operations, the conditions imposed by the U.SVCanada Trade policy were applied to the Hierarchical Timber Allocation model, by reducing the prices of the lumber exported to U.S. by: 25.9% for Company 1 and 26.9% for Company 2 and 3. Tables 6.4, 6.5, and 6.6 in Appendix 1 indicate these changes. The tables also show the volume 121  percentage targeted for each grade and market. These values indicate that 80% of the lumber volume produced by Company 2 is destined for the U.S. Therefore, this company is expected to suffer the most under the U.S./Canada Trade policy. Despite its increased product diversity, Company 1 exports a large volume of dimension products (i.e. 2x6 to 2x12) to the U.S. markets. This company produces all of its board products (i.e. 1x4 and 1x6) and most of the 2x4 products for domestic markets. As a result of the changes in prices imposed by the U.S./Canada Trade policy (Table 6.4, Appendix 1), the volumes of products exported to U.S. by this company were expected to decrease and of domestic products to increase. Company 3 is the only company that is somewhat protected from the effects of this policy because some of its products are destined for the Japanese market. Although large volumes of dimension lumber products are exported to the U.S., the products exported to Japan are considerably more valuable. It is expected that these products will prevent this company from experiencing a large profit loss because of the U.S./Canada Trade policy. The above changes in product prices are expected to increase the production of domestic and/or Japanese lumber products. It is therefore essential to assume that the domestic markets will be able to absorb the additional lumber volumes that are available. Unlike the previously examined policies in which the data input changes took place at the mediumterm level, the U.S./Canada Trade policy changed the input data (lumber prices) at the operational level. After these changes were made, the Hierarchical Timber Allocation model was run in the Equal Weights and the Profit M A X scenarios . Because the settings of the operational models were identical in both scenarios, the lumber mixes produced by each company were similar in the two scenarios. However, because the lumber mixes changed because of this policy, the model matched the timber with the new raw material requirements and changes occurred in the timber allocated to the three sawmills.  21  For a complete set of results, please refer to Table 6.16 in Appendix 5.  122  5.4.3.1.  The Equal Weights Scenario  5%  -20%  J  1  Profit  1  Employment  1  Recreation  Visual  •  Wildlife  Figure 5.31 - The impact of the U.S./Canada Trade policy on the Equal Weights scenario - criteria.  Figure 5.31 presents the impact of the U.S./Canada Trade policy on the criteria results in the Equal Weights scenario. The graph indicates a profit loss of 17% (or $9.6 million) in this scenario. Since the restrictions (prices) imposed by the U.S./Canada Trade policy were applied to the operational level and not to the medium-term level, the large change in the profit goal value was the most important. However, a small increase of 1% in the recreation goal and a decrease of 1% in the wildlife goal were also notable changes. The fact that these changes were small was expected in this scenario, because equal weights were assigned to the goals and, therefore, the model was able to find a balanced allocation. However, these outcomes indicate that the policy changed the product structure, by penalizing the products destined to U.S. markets, which consequently affected the stem class composition of the timber allocated to each company.  123  25000  20000  -20000  1  -25000 J  1 1x4  ' 1x6  1 2x4  1 2x6  1 2x8  2x10  2x12  Figure 5.32 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 1 in the Equal Weights scenario.  Figure 5.32 shows how the U.S./Canada Trade policy changed the list of lumber products manufactured by Company 1. First, the policy caused the volumes of the most valuable products (i.e. 2x6 to 2x12) to drop by more than 50% (28,000 MBF). Although a large decrease in lumber volume, this outcome was expected considering that 80% of the volume of these products is affected by the duties. In addition, the model increased the production of 1x4 and 1x6 boards by more than 50% (7,500 MBF). This increase was an expected reaction of the model to the U.S./Canada Trade policy, because boards were sold exclusively to Canadian markets. In addition, under this policy, the volumes of 2x4 lumber products increased by 70% (18,000 MBF) due to their large domestic component. No changes occurred with the 2x10 lumber products. Their uncompetitive prices precluded their production both during and before this policy was enacted.  124  1200  > -400  J  1  2x4 Studs  2x6 Studs  Figure 5.33 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 2 in the Equal Weights scenario.  Figure 5.33 presents the impact of this policy on the volumes of products manufactured by Company 2. Since this company produced products (i.e. studs) that were all destined to the U.S. market, it was not able to readjust its product mix under the U.S./Canada Trade policy. The graph shows that an increase of just 4.5% (1,100 MBF) in the volume of 2x6 studs occurred, while the production of 2x4 studs was reduced by less than 1% (175 MBF). This reaction of the model occurred because Company 2 had to increase the production of the more profitable products (i.e. 2x6 studs) for the domestic market. However, the company still exported most of its products to the U.S. at lower prices and was expected to experience a large profit loss.  125  6000  -6000  J  1  2x4  1  2x6  1  2x8  1  2x10 '  1  Baby  1  Hirakaku 1  Hirakaku 2  Squares  Figure 5.34 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 3 in the Equal Weights scenario. Note: The production of 2x6 products was discontinued under this policy.  Figure 5.34 presents the effect of the US/Canada policy on the volumes of products produced by Company 3. The entire range of dimension lumber products (i.e. 2x4 to 2x12) was affected directly by this policy because most of their volume was exported to the US. The least valuable of them was the 2x6 and the model decided to discontinue its production. Because 90% of the volume of 2x4 products was destined to domestic markets, the model increased their production by 4,200 M B F . In addition, to make up for the loss in profit from dimension lumber, the model increased the production of Hirakaku 1 by 7% (200 MBF). Because Company 3 is the most diverse company and its products were not entirely destined for the U.S. market, it is expected that this policy will have less of an impact on this company than on the others.  126  15,000 • Company 1 • Company 2  10,000  E  w a in a  • Company 3  5,000  -5,000  f to  -10,000  E = o  -15,000  x: o ai  > -20,000  8-20  21-33  34-16 4-9  47-60  34-46  47-60  |  10-15  34-16  47-60  16-21  34-16 22-27  SED (in) and Length (ft) Classes  Figure 5.35 - The impact o f the U.S./Canada Trade policy on the E q u a l Weights scenario - volume differences o f small end diameter - S E D (bottom scale) and length classes (top scale). Note: there were no changes i n the timber composition allocated to Company 3.  Figure 5.35 presents the effects of the U.S./Canada Trade policy on the structure of raw materials allocated to the sawmills in the Equal Weights scenario. The graph shows that this policy had no effect on the raw material distribution allocated to Company 3. This was possible, in part, because it could afford to discontinue or reduce the production of less valuable products, being the most profitable of the three companies. In addition, Company 3 had the most flexible production and market parameters, which enabled it to change quickly in order to manufacture different products from the same or similar raw materials. However, Companies 1 and 2 were affected more by this policy than Company 3 was, incurring larger changes in the raw materials composition. Consequently, Company 1 increased the volumes of stems in the small SED classes, while drastically reducing (by 16,000 m ) the volumes of stems in the larger SED classes (i.e. 10-15 in. and 16-21 in.). In addition, Company 2 experienced a reduction of 11,000 m in the volume of large stems in the 4-9 in. SED class. This situation was exploited by Company 1, which outcompeted Company 2 for the stems in this class. 3  3  127  20%  10%  -40%  1  J  Area Harvested Company 1  1  Area Harvested Company 2  1  1  1  Area Harvested Profit Company 1 Profit Company 2 Profit Company 3 Company 3  Figure 5.36 - The impact of the U.S./Canada Trade policy on the Equal Weights scenario - differences in the harvested areas and the profits of the three companies.  Figure 5.36 shows that Company 3 was the only company that withstood the conditions imposed by the U.S./Canada Trade policy. This company increased its harvesting area by 6% and lost $0.8 million. These changes could, however, be considered insignificant in comparison with the losses in profit incurred by Company 1 and Company 2 (25% and 35%, respectively). Company 2, in particular, was the one that suffered the most under this policy because its limited product structure did not allow it to readjust the production to the conditions imposed by the U.SVCanada Trade policy.  128  5.4.3.2. The Profit MAX Scenario  5%  us 1  0%  o  -5%  Q.  0) Ul  -10%  c n  o  0.  -15%  -20%  J  1 Profit  1 Employment  1 Recreation  1  Visual  Wildlife  Figure 5.37 - The impact of the U.S./Canada Trade policy on the Profit MAX scenario - criteria.  Figure 5.37 presents the impact that the U.S./Canada Trade policy had on the criteria in the Profit M A X scenario. The results show that the profit loss was larger (i.e. 18%) in the Profit M A X scenario than in the Equal weights scenario. In addition, the values of all the other criteria registered a small increase. These results imply that, because the restrictions imposed by the U.S./Canada Trade policy reduced the production of the least profitable products, many stewardship units were re-allocated from harvesting to reserve. Consequently, the wildlife, visual, and recreation criteria increased their values. Figures 5.38, 5.39, and 5.40 present the impact of this policy on the volume of products manufactured in each company under the Profit M A X scenario.  129  25000 20000  CQ  15000  o  10000  o Q.  5000  in ra 0) O)  c ra  £ U  a> E 3  5  0  -5000 -10000 -15000 -20000 -25000  1x4  1x6  2x4  2x6  2x8  2x10  2x12  Figure 5.38 - The impact o f the U . S . / C a n a d a Trade p o l i c y on the lumber products produced by Company 1 in the Profit M A X scenario. 1200  u. m  1000 800 600  CD  400  CO M  n a oi c  10 JZ  o E O >  200 0 -200 -400  2x4 Studs  2x6 Studs  Figure 5.39 - The impact o f the U . S . / C a n a d a Trade p o l i c y on the lumber products produced by C o m p a n y 2 in the Profit M A X scenario.  130  e c  e  c  ^ o  o  o o  ro o  C C3 C3  C3  o  - 5  3 3 3  olume ch ange as a result of policy (MBF)  -  cnnn  2x4  2x6  2x8  2x10  Baby  Hirakaku 1  Hirakaku 2  Squares  Figure 5.40 - The impact of the U.S./Canada Trade policy on the lumber products produced by Company 3 in the Profit M A X scenario.  The results presented in these figures are similar to those obtained by the Equal Weights scenario. This suggests that, under this policy, the operational level of the model reacted similarly in the two scenarios. This was expected since the settings of the sawmilling models in both scenarios were identical. However, the medium-term level of the model reacted differently in the two scenarios, allocating stewardship units that best fit the goals of each scenario, while meeting the timber requirements of each company.  131  • Company 1 • Company 2 • Company 3  ro tn 0) O)  c ro o o E o >  21-33  3446 4-9  34-46  47-60 10-15  3446  47-60 16-21  34-46 22-27  S E D (in) a n d L e n g t h (ft) C l a s s e s  Figure 5.41 - The impact of the U.S./Canada Trade policy on the Profit M A X scenario - volume differences of small end diameter - SED (bottom scale) and length classes (top scale).  Figure 5.41 confirms that a different allocation took place in the Profit M A X scenario than in the Equal Weights scenario. The results show that, in the Profit M A X scenario, all three companies suffered changes in the stem class composition, whereas in the Equal Weights scenario only two companies were affected by the policy. Figure 5.41 suggests that Company 1 incurred the largest changes in raw materials, especially in the small SED class (4-9 in.), where 30,000 m of stems of 34-46 ft. length class were substituted by almost 50,000 m of stems of 47-60 ft. length class. As explained previously, this change occurred as a result of the competition between Company 2 and Company 1 over these stem classes. Company 2 and 3 however did not experience the same level of change as Company 1. For example, Company 2 experienced a small shift toward the larger SED classes (10-15 in. and 16-21 in.), whereas for Company 3, the model substituted the stems of47-60 ft. class with stems of lower lengths (34-46 ft.). Despite the small change in timber composition allocated to Company 2, this company was expected to incur a profit loss due to its incapability to adapt its product mix to the conditions imposed by the U.S./ Canada Trade policy. 3  3  132  20%  10%  >> u  0%  o a 3 lit O  -10%  in  ra o oi c -20% ra c  0>  e  -30%  0> 0. -40% Area Harvested Area Harvested Area Harvested Company 1 Company 2 Company 3  Profit Company 1  Profit Company 2  Profit Company 3  Figure 5.42 - The impact o f the U . S . / C a n a d a Trade p o l i c y on the Profit M A X scenario - differences i n the harvested areas and the profits o f the three companies.  Figure 5.42 further confirms the similarities between the results obtained in the Profit M A X and the Equal Weights scenarios. Like the Equal Weights scenario, Companies 1 and 2 experienced the largest profit losses, at 35% and 27%, respectively. However, in the Profit M A X scenario, Company 2 increased its harvesting area by 14%, while Companies 1 and 3 reduced theirs by 5%.  133  5.4.3.3.  Equal Weights vs. Profit MAX  $47,556,168 1  1  Profit  to  t  Recreation  r-  o>  •!  1  cn  o  CM  Employment  cn  CO  CO  6,367 people years  $49,673,302  6,210 people years  • E q u a l Weights S c e n a r i o • Profit M A X S c e n a r i o  CM  1  Visual  '  1  Wildlife  Figure 5.43 - The comparison between the results o f the E q u a l W e i g h t s and the Profit M A X scenarios under the U . S . / C a n a d a Trade p o l i c y .  Figure 5.43 indicates a $2 million difference in the profit values between the Equal weights and Profit M A X scenarios. The other criteria values were considerably larger in the Equal Weights scenario. The most notable increases were recorded in the recreation and the wildlife criteria, by 30% and 25%, respectively. These increases and the minimal profit loss suggest that the Equal Weights scenario could constitute a viable solution to the multicriteria timber allocation under the U.S./Canada Trade policy. In contrast to the previously examined policies that added constraints to the medium-term level model, the U.S./Canada Trade policy affected the settings of the operational models. The Hierarchical Timber Allocation model, although reacting similarly in the two scenarios at the operational level, produced different allocations at the medium-term level. The results were valuable at both the medium-term and operational level because they increased the knowledge with respect to the effect of the U.S./Canada Trade policy on decisions taking place at both levels. At the operational level, Company 3 demonstrated how product and market diversity might help forest product companies during similar economic difficulties. At the medium-term level, the model matched the timber compositions allocated to each company with the new product structures resulting from the U.S./Canada Trade policy. These outcomes further demonstrated the capability of the Hierarchical Timber Allocation model to deal with different sustainability policy questions, regardless of the planning level at which they occur. 134  5.4.4. The Cum ulative Effect of Policies So far, a series of forest management policies were analyzed using the Hierarchical Timber Allocation model. The Wildlife Corridor and the Accessibility policies affected the input data of the medium-term level, whereas the U.S./Canada Trade policy affected that of the operational level. In this section, the cumulative effect of all policies will be examined in order to study the effects of data changes at both planning levels. The model was run in the Equal Weights and the Profit MAX scenarios . 22  5.4.4.1.  The Equal Weights Scenario  j  60%  50%-  40%-  30%-  ^ a  20%  40%  J  Profit  !  1  Employment  1  1  Recreation  Visual  Wildlife  Figure 5.44 - The cumulative effect of all policies in the Equal Weights scenario - criteria.  Figure 5.44 shows the impact of all policies on the criteria in the Equal Weights scenario. The graph indicates that a profit loss of 30% and a decrease in employment of 12% could occur. These losses are attributed to the cumulative effect of the U.S./Canada Trade and the Accessibility policies, with the former dramatically decreasing the profit, and the latter allocating less volume to Company 2, consequently decreasing the employment value. The increase in the wildlife goal value is attributed mainly to the Wildlife Corridor policy, which increased the values of the wildlife indicators to those stewardship units located in For a complete set of results, please refer to Table 6.17 in Appendix 5.  135  the corridor. The 3% increase in the visual goal and the 2% decrease in the recreation goal is attributed mostly to the Accessibility policy. 20,000  -20,000  ^0,000  CO  CO  rji  -60,000  c ra  J:  o a E 3  • Company 1  -80,000  o >  • Company 2 • Company 3 -100,000  8-20  21-33  34-46 4-9  47-60  34-46  47-60 10-15  34-46  47-60 16-21  34-46 22-27  SED (in) and Length (ft) Cla  Figure 5.45 - The cumulative effect of all policies in the Equal Weights scenario - volume differences of small end diameter - SED (bottom scale) and length classes (top scale).Note: Company 2 was allocated no timber.  Figure 5.45 shows the effects of the policies on the composition of raw materials allocated to the sawmills in the Equal Weights scenario. The results show that Company 2 was not allocated no timber (was closed) when the three policies were applied in this scenario. Weakened already by the requirements imposed by the Accessibility policy, which caused this company to receive just a small fraction of its required timber volume, it was unable to survive the conditions imposed by the other two policies. The graph also shows that Company 1 suffered a decrease in the larger SED stem classes and an increase in the lower SED classes, mainly because of the U.S./Canada Trade policy. In addition, the results show that less volume was allocated to this company. This is a sign that its profitability and product structure makes this company vulnerable if other policies are imposed. Company 3, however, survived well the Cumulative policy. Figure 5.45 shows that this company suffered some reductions in the volumes of larger SED classes. This could contribute to a profit loss, because Company 3 manufactured the most profitable products from these classes. However, since this company had a flexible production structure, it was expected that this loss would be much smaller than those of the other two companies would.  136  Figure 5.46 - The cumulative effect of all policies in the Equal Weights scenario - differences in the harvested areas and the profits of the three companies.  Figure 5.46 confirms that Company 3 was the only one to tolerate the conditions imposed by the three policies. This company experienced just a small decline in profit (2%), mostly because of the U.S./Canada Trade policy. The figure also shows that Company 2, as reported previously, was not allocated any timber (i.e. 100% reduction in harvested area). The graph also supports the observation that Company 1 was affected increasingly by the three policies, experiencing a 30% decrease in profit. In addition to the profit values, the graph shows that both Companies 1 and 3 increased their harvesting areas by 5% and 35%, respectively. These increases could be explained by the large increases in the volumes of partial-cuts, from 1,471 m in to 155,159 m . 3  3  137  5.4.4.2.  The Profit MAX Scenario  40%  30%  20%  JT o  10%  Q. O  f  0%  8, " % 10  CD C  -20%  -30%  40% Profit  Employment  Recreation  Visual  Wildlife  Figure 5.47 - The cumulative effect of all policies in the Profit MAX scenario - criteria.  Figure 5.47 shows that the three policies caused the profit to drop by 20% in the Profit M A X scenario. This decrease is attributed mostly to the U.S./Canada Trade policy. The large increase in the wildlife goal value is the result of the Wildlife policy, which assigned larger values for the wildlife indicator of those stewardship units located in the corridor. The 12% increases in recreation and 5% in visual goal values are mainly the result of the Accessibility policy, which forced the model to harvest timber situated closer to the roads, causing the allocation to reserve of more stewardship units containing these indicators.  138  60,000 • Company 1  50,000  • Company 2 • Company 3  40,000 =  30,000  Z  20,000 10,000  10  ro to  <D  D) C  ro O a E  3 O >  -10,000 -20,000 -30,000 8-20  21-33  34-46  47-60  4-9  34-46  47-60  10-15  34-46  47-60  16-21  34-46 22-27  SED (in) and Length (ft) Classes Figure 5.48 - The cumulative effect o f all policies i n the Profit M A X scenario - volume differences o f small end diameter - S E D (bottom scale) and length classes (top scale).  Unlike the Equal Weights scenario, the companies received all of the timber volume that they required in order to sustain their operations. This was expected since this scenario emphasized the profit goal and therefore caused the model to allocate volumes to all companies regardless of losses in other criteria. Figure 5.48 shows that Company 1 experienced an increase of almost 50,000 m in small SED class (4-9 in.) and a large decrease in the volumes of larger SED classes. Therefore, it was expected that this company would contribute considerably to the total loss in profit. By contrast, Companies 2 and 3 suffered only small changes in the composition of timber allocated to them under the three policies. 3  139  20%  0%  -20%  -40%  -60%  £  -80%  -100%  -120% Area Harvested Company 1  Area Harvested Company 2  Area Harvested Company 3  Profit Company 1  Profit Company Profit Company 2 3  Figure 5.49 - The cumulative effect of all policies in the Profit M A X scenario - differences in the harvested areas and the profits of the three companies.  Figure 5.49 shows that Companies 1 and 2 were the most affected by the three policies. They experienced profit losses of 30% and 40%, respectively. These losses were mostly the result of the U.S./Canada Trade policy. Company 3, however, experienced a profit loss of just 5%, showing once again that its production and market characteristics protected it from the cumulative effects of policies.  140  5.4.4.3. Equal Weights vs. Profit MAX  I Equal Weights Scenario • Profit MAX Scenario  Profit  Employment  Recreation  Visual  Wildlife  Figure 5.50 - The comparison between the results of the Equal Weights and the Profit M A X scenarios under the cumulative effects of policies.  Figure 5.50 indicates that increases of 24 points in the recreation, of 21 points in the wildlife, and of 11 points in the visual criteria occurred in the Equal Weights scenario. However, in order to achieve these increases, losses of $9 million in profit and 176 personyears in employment occurred. In addition, if the Equal Weights scenario were considered for implementation in practice, Company 2 would close because no timber volume was allocated to it. If required, running the Hierarchical Timber Allocation model with other weights than those used in the Equal Weights scenario could generate a more equitable allocation. This would eventually increase the volume allocated to Companies 1 and 2, but would not address their efficiency problems. Managers could use the operational level models to find ways of increasing the product and market diversity of these two companies. The results generated by the model under the cumulative effects of the policies assisted the sustainability analysis of the area under study. They indicated the extent to which these policies could affect each of the allocation goals. In the Equal Weights scenario, although large increases in the wildlife, recreation, and visual goal values occurred, the cumulative effects required the closing of Company 2 and the reduction in capacity of Company 1. The Profit Max scenario generated an allocation that caused large reductions in profits and compromised the wildlife, recreation, and visual criteria results. 141  In addition to the impact that the policies had on the sustainability criteria and on the sawmilling activities, the source of each change could be traced back to the policy that caused it. In conclusion, the Hierarchical Timber Allocation model responded well to the cumulative conditions imposed by the three policies. This demonstrates that other policies could be analyzed either separately or cumulatively using this model. 5.4.5. Summary In order to provide a better understanding of the effects of each policy on different allocation criteria and parameters, a graphical summary of the results for all the analyzed policies was compiled. $62  n  ~ $54  o °-  $46  -  $38  -j  ,  Unconstrained Model  ,  Wildlife Corridor  ,  Accessibility  ,  US/Canada  Cumulative  Figure 5.51 - The effect o f the policies o n the profit criterion.  In Figure 5.51, profit values are plotted starting with the unconstrained model (the largest value) and ending with the cumulative effect of policies (the smallest values). The graph shows that the Equal Weights and the Profit M A X scenarios present a similar trend, with the exception of the Accessibility Policy, when the profit registered a larger drop in the Equal Weights Scenario. This large profit loss indicates how strict the Accessibility Policy was: in order to meet both the multi-criteria and the accessibility requirements, profitability became an increasingly important allocation factor. As a result, timber volume allocated to sawmilling decreased and less profitable companies (e.g. Company 2) registered large profit losses. In addition, the U.S./Canada Trade Policy also had a great impact on the profit criterion. Under this policy, the closeness of the two profit values indicates that the model reacted similarly to this policy at the operational level. The graph also shows that the 142  Accessibility and the U.S./Canada Trade policies were the most responsible for the large profit loss registered in the cumulative case.  • Equal Weights 6,600 _  • Profit Max  6,400  ro CD >-  a>  6,200  CL  O CU  6,000 ! c  CD  £ o  5,800  Q.  E  LU  5,600 5,400  Unconstrained Model  Wildlife Corridor  Accessibility  US/Canada  Cumulative  Figure 5.52 - The effect o f the policies on the employment criterion.  Figure 5.52 shows that the largest decrease in employment value occurred in the Equal Weights Scenario under the Accessibility policy. Consequently, the Accessibility policy was the only policy that contributed to the large drop in employment in the cumulative case. This decrease was a direct reaction of less volume being allocated to Company 2. In contrast with the Equal Weights scenario, the Profit M A X scenario did not produce large fluctuations in the employment levels, because the model insured that all three companies, regardless of their profitability, were allocated the necessary timber volume.  143  —•—Equal Weights  50%  ]  1  1  Unconstrained Model  Wildlife Corridor  1  1  Accessibility  US/Canada  Cumulative  Figure 5.53 - The effect of the policies on the recreation criterion.  Figure 5.53 shows the recreation achievement levels plotted for each policy. Overall, the graph suggests an important difference in the recreation achievement levels between the two scenarios. This difference indicates that, when the profit criterion had an increasing priority in the allocation, the recreation criterion suffered. This was especially true under the Wildlife Corridor policy, in which the reduced volume of timber available for harvest forced the model in the Profit M A X scenario to allocate more stewardship units with recreation features to harvesting. However, the Equal Weights scenario did not produce large differences in recreation achievement levels, even in the cumulative case, because of a balanced prioritization of the allocation criteria.  Achievement levels indicate the relative departure of criteria from their targets.  144  •  32  5  Equal Weights  60% -  50%  -I  —, Unconstrained Model  , Wildlife Corridor  , Accessibility  , US/Canada  Cumulative  Figure 5.54 - The effect of the policies on the wildlife criterion.  Figure 5.54 indicates that the largest impact on the wildlife criterion occurred under the U.S./Canada Trade policy, which decreased the achievement level to less than 70% in the Profit M A X scenario. The Equal Weights Scenario, however, presented a balanced distribution of the achievement levels under all policies. It is interesting to note that the wildlife achievement level in the Profit M A X Scenario, under the Accessibility policy, reached the largest value of all the policies modeled in that scenario. This indicates that more stewardship units containing the wildlife indicator were spared from harvesting under this policy, because they were located farther from the existing roads.  145  —•—Equal Weights  < rs  « >  60%  50% \  ——-  Unconstrained Model  —,  Wildlife Corridor  ——-  Accessibility  —,  US/Canada  Cumulative  Figure 5.55 - The effect o f the policies on the visual criterion.  In contrast with the recreation and wildlife goals, Figure 5.55 shows that the visual achievement levels did not vary considerably in the Profit M A X and the Equal Weights scenarios. This indicates that the visual criterion was not affected much by the emphasis on profit. In addition, the results show that the visual achievement levels for the analyzed policies did not vary greatly in the two scenarios. This suggests that not all of these policies, except the U.S./Canada Trade policy, were detrimental to this criterion. Interestingly, in the cumulative case, the visual goal achieved its largest values in both scenarios. This shows that the stricter the conditions of these policies, the more stewardship units containing the visual indicator were allocated to reserve rather than to harvesting.  146  —•—Equal Weights  80%  • - P r o f i t Max  50%  Unconstrained Model  Wildlife Corridor  Accessibility  US/Canada  Cumulative  Figure 5.56 - The effect of the policies on the reserve area.  Figure 5.56 plots the percentages of area allocated to reserve, under different policies. The graph indicates that, in the cumulative case, the reserve area decreased in size in the Profit M A X Scenario, whereas it increased in the Equal Weights Scenario. This outcome was expected because, under the requirements imposed cumulatively by the three policies, the emphasis on profit forced the model to allocate more stewardship units to harvesting, which otherwise would have been allocated to reserve. In contrast, when a more balanced set of weights was applied in the Equal Weights scenario, more emphasis was put on the visual, wildlife, and recreation criteria and therefore more areas containing these indicators were allocated to reserve. In addition, under the Accessibility Policy, the reserve areas increased considerably because the preference given to harvesting closer to the roads allowed many stewardship units to be allocated to reserve. Overall, the reserve areas exceeded 50% of the total area, which indicated that, even under the most restrictive policies (i.e. cumulative case), the constraints were not able to decrease the amount of timber available for harvesting to the point where increasingly more reserve area was sacrificed.  —•—Equal Weights  Unconstrained Model  Wildlife Corridor  Accessibility  US/Canada  Cumulative  Figure 5.57 - The effect of the policies on the volume harvested with partial-cutting techniques.  Partial-cutting techniques have been given increasing emphasis in sustainable forest management. It is, therefore, useful to analyze how different policies affected the volumes allocated to partial-cuts. Figure 5.57 suggests that the largest increase in volume generated by partial-cuts occurred in the Equal Weights scenario under the cumulative case. To find valuable timber, while still achieving the employment, wildlife, recreation, and visual goals, the model allocated a large number of stewardship units to partial-cuts. The figure also shows a large increase in the volume of partial-cuts in the Profit M A X scenario under the Wildlife Corridor policy, mainly because only partial-cuts were allowed in the wildlife corridor. The results of the scenarios analyzed in this chapter have demonstrated the capability of the Hierarchical Timber Allocation model to assist with the analyses of different policy questions. The most important impacts occurred, as expected, in the cumulative case and resulted in the reduction of timber allocated to harvesting, the closing of a processing operation, the reduction in timber allocated to another operation, and the increase of the reserve area. By studying the effects of each policy question individually, a better understanding of the causes of these impacts was achieved. Forest management policies presented in this chapter were chosen to represent some issues specific to the area under study. However, many other policies could be modeled and analyzed. The analysis of the Profit M A X and the Equal Weights scenarios for each policy provided a useful comparison between the case in which emphasis was put on profit and the case in which a more balanced approach was sought. Since the imposition of policies in these two scenarios created some extreme situations (closing of sawmills, loss of profits and employment, loss of ecological features), scenarios other than Profit M A X and Equal 148  Weights could be generated and analyzed. Such analyses could bring managers, analysts, and researchers closer to a better understanding of the complex decisions related to sustainable forest management.  5.5.  Conclusion  This chapter presented the development of a Hierarchical Timber Allocation model capable of iteratively finding the optimum timber allocation that meets the goals of both the medium-term (i.e. maximization of forest sustainability indicators) and the operational (i.e. maximization of profits in each company) plans. By incorporating the Multi-criteria Timber Allocation model at the medium-term level and connecting it with the sawmilling models at the operational level, the objectives of the multi-criteria allocation and the forest to product integration were met. Designing a dynamic connectivity between the medium-term and operational level was essential to the development of the Hierarchical Timber Allocation model. Based on the iterative procedure proposed by Heal (1969) and later used by Hof et al. (1992), the algorithm devised for the Hierarchical Timber Allocation model guaranteed that the timber allocation produced by the medium-term level generated monotonically increasing total profit values at the operational level. Consequently, when the optimum solution was reached, the goals of the two levels were met and the dynamic link between the forest and the product was achieved. In this chapter, the need for a dynamic connectivity was demonstrated in a case analysis where the profit results of the Multi-criteria Timber Allocation model were compared against those of the Hierarchical Timber allocation model. The latter model produced results that were more accurate because the operational level models iteratively guided the allocation taken place at the medium-term level. Therefore, the profit values obtained with this model were guaranteed to reflect the most current operational parameters. In addition, the intermediary allocation results generated after each iteration were presented. They not only demonstrated the convergence of the profit values toward the optimum solution, but also the capability of the model to match the lumber production requirements of each sawmill with the composition of the timber allocated to them. In order to further demonstrate the model and show its capabilities, a series of policy questions were analyzed. The Wildlife Corridor and the Accessibility policies affected the input data at the medium-term level, while the U.S./Canada Trade policy affected the input data at the operational level. The cumulative case included all three policies and affected both planning levels. The results of these policy questions, in both numerical and graphical format, and the trade-off analyses, illustrated possible implementation and opportunity costs and the complex relationships between sustainable forest management and wood processing activities.  149  CHAPTER 6. THESIS SUMMARY AND CONCLUSIONS  The need for multi-criteria, forest to product, timber allocation models is the result of the shift from sustained yield to sustainable forest ecosystem. Currently, increased social pressure is applied to manage and conserve forest ecosystems in a way that benefits all of the stakeholders and future generations. Criteria and indicators for sustainable forest management have been developed to represent the views of a multitude of stakeholders. Criteria such as employment, harvesting costs, biodiversity indicators, product diversity and many others will have to be included in timber allocation models and to influence how forest resources are allocated to different operations in a sustainable manner. In return, the tradeoffs between various criteria, usually difficult or impossible to assess, should be able to indicate the impact that multi-criteria allocations might have on the forest operations. This requires timber allocation models to cover the whole range of forest to product decisions, usually difficult to address in one large allocation model. A n impressive amount of research has taken place in the last few years in the area of multicriteria optimization and hierarchical planning. In Chapter 2, the most relevant applications of these methods were presented. They opened the door for new and improved methods of timber allocation that could benefit sustainable forest management decisions. In Chapter 3, a Multi-criteria Timber Allocation model was developed. It demonstrated how goal programming could be implemented into multi-criteria timber allocation models, despite the difficulties associated with assigning weights/priorities to different allocation criteria. The issue of weight setting was analyzed and a method was presented in which the set of non-dominated solutions could help users find solutions to the multi-criteria timber allocation problems. In addition, the case analysis in which the model was employed demonstrated that the two proposed optimization scenarios (the Profit M A X and the Equal Weights) accommodated the allocation criteria better than the current methods of timber allocation. The results showed the usefulness of the model in problems dealing with a larger number of allocation criteria aimed at sustainability, such as profit, employment, visual quality, recreation, and wildlife habitat. Chapter 4 presented data envelopment analysis (DEA), a method of assessing the efficiencies of different operations, companies, organizations based on different inputs and outputs (criteria). Unlike goal programming, the D E A method did not require the prioritization of criteria. D E A was used in an original manner to assess how appropriate timber resources were to maximize both the profit and employment criteria if allocated to sawmilling facilities. This method provided a flexible, reliable, and straightforward alternative to multi-criteria timber allocation activities. Therefore, it was used to develop a D E A Timber Allocation model able to find solutions for the allocation of timber to three hypothetical forest products companies. The allocation procedure was demonstrated in a case analysis. However, due to strict requirements regarding the types of input/output data that could be used in the D E A sub-model, caution must be applied if criteria other than profit and employment are entered.  150  In Chapter 5, a Hierarchical Timber Allocation model able to deal with the forest to product planning activities was developed. Through the inclusion of the Multi-criteria Timber Allocation model into the medium-term level and of the FTP Analyzer® into the operational level, multiple-criteria and multiple-time horizon decisions were made in an integrated manner. The iterative negotiating procedure designed between the medium-term level and the operational level ensured the achievement of an optimal allocation that satisfied the goals of both levels. The results of the policy analyses have shown that the Hierarchical Timber Allocation model was able to respond successfully when data changes were made at both the medium-term and the operational level. In addition, these analyses generated insights into the relationships between the sustainable forest management and the processing operations. A series of conclusions can be drawn about the methods/models presented and the results generated. In general, the three models addressed well the research objectives for which they were developed. Although they dealt with the same goal of allocating timber to sawmilling facilities based on multi-criteria procedures, they approached it differently. The differences originated in how each method addressed the multi-criteria allocation problem and alleviated the procedural difficulties. For example, the D E A method provided a smart alternative to the difficult task of criteria prioritization. In addition, the capability of the D E A method to combine the effects of all criteria into one score was practical. This resulted in a less complicated model and a shorter solution time than the other models. The only restriction concerned the numbers and types of criteria that could be entered in the D E A models. Usually, D E A models work well with few criteria (inputs/outputs) and those that have non-zero values (meaning that the inputs will always generate outputs). In contrast with the D E A method, which helped find a unique solution to the multi-criteria allocation problem, the goal programming (GP) method required the generation of many solutions (allocation scenarios). Despite an increase in computation time, these scenarios were essential in constructing the non-dominated solution set, which brought to light the trade-offs between different criteria. In addition, the search for the most appropriate multicriteria solution was dramatically simplified. Because GP can deal with any number and type of data (i.e. whether or not commensurable), the method is recommended in timber allocation models for sustainable forest management. In addition, the mathematical formulation of this method allowed the integration with other methods. The most valuable application was the use of a goal programming model at the medium-term level of the Hierarchical Timber Allocation model. Combining hierarchical planning (HP) with goal programming (GP) in the Hierarchical Timber Allocation model accomplished all the goals of this dissertation. The GP method provided the procedure for the multi-criteria timber allocation, while the HP method integrated the forest to product decisions. The resulting model matched well the timber characteristics with the sawmilling production requirements. Moreover, the HP method allowed the Multi-criteria Timber Allocation and the sawmilling models to work concomitantly, while representing the concerns of different levels of management. The features of the Hierarchical Timber Allocation model were helpful in the analysis of different policies and could be used in the future to equitably allocate timber to sawmilling 151  facilities so that they do not close down or receive inappropriate timber. Conversely, efficiency studies can be performed at the sawmill level to better use the allocated resources and to meet the sustainability criteria. The model can also reveal the impact that these efficiencies have on the sustainability of the area and on the profitability of different sawmilling operations. The models presented in this thesis could benefit from future research efforts. First, the application of D E A in the development of the D E A Timber Allocation model should be further researched in order to allow other allocation criteria to be included and, therefore, to enhance the flexibility of the model. In addition, more research is needed in order to make the model multi-period. Second, the Hierarchical Timber Allocation model could be expanded to include other sets of allocation criteria than those presented in this thesis (e.g. product diversity, biodiversity, watershed conservation, etc.). However, before implementing these criteria, more research studies need to analyze how representative the indicators are for the sustainability of forest management in the areas under study. In addition, other forest management policies than those analyzed here should also be considered. Different partial-cutting techniques could also be included in the model and their impact on allocations could be analyzed. 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Alternative measurement of productive efficiency in the global bleached softwood pulp sector. Forest Science 46: 558-569.  159  A p p e n d i x 1 - The  .  - •  Bucking Line 1 Sawing Line 1 Sawing Line 2 Trimmer Information  S a w Kerf Band Saws Edger/Gang Headriq Productivity Chain Speed Log Gap Downtime Mill Cost  S a w Kerf Band Saws Edger/Gang Headriq Productivity Chain Speed Log Gap Downtime Mill Cost  Sawmilling Data  - v S A W M I L L ' l f D A T A S U M M A R Y ^ ; * >•. : ;,f-. S m a l l E n d D i a m R a n g e (in) L e n g t h R a n g e (in) Min Max Incr Min Max Incr 96 720 24 3 31 1 3 10 1 96 240 24 8 37 1 96 240 24 Boards Down P e r H o u r T i m e (%) 4914 18 Sawing|Eih^||D>\fAjSUMMARY 0.121 0.121  in in  325 FPM 4 Feet 10% 1000$ /Hr  Board Lenaths Produced Minimum Length 96 in Maximum Length 240 in Length Increment 24 in 0 Max Side Brds  fgfllSawin^Lm#2r DATA*SUMMARYMtf#ij^^ 0.135 0.121  in in  235 FPM 6 Feet 10% 1350$ /Hr  Board Lenqths Produced Minimum Length Maximum Length Length Increment Max Side Brds  96 in 240 in 24 in 4  Table 6.1 - The operational parameters of Company 1.  160  SAWISi!l.l^>:.QAJA''SUMMi9RY Small End Diam Range (in) Min Max Incr 3 31 1 3 8 1 6 37 1  Bucking Line 1 Sawing Line 1 Sawing Line 2  Min 96 96 96  Trimmer Information Sawing L i h e ^ i R A T A SUMMARY  • Saw Kerf Band Saws Edger/Gang Headriq Productivity Chain Speed Log Gap Downtime Mill Cost • Saw Kerf Band Saws Edger/Gang Headriq Productivity Chain Speed Log Gap Downtime Mill Cost  Length Range (in) Max Incr 720 12 108 12 108 12 Down Boards Per Hour Time (%) 5000 5  0.1 in 0.1 in Board Lenqths Produced Minimum Length Maximum Length Length Increment Max Side Brds  400 F P M 2 Feet 5% 500$ /Hr -  96 in 108 in 12 in 0  SawirigTLinef 2- DATA SUMMARY'J*'* ;  0.1 in 0.1 in 350 F P M 3 Feet 5% 850$ /Hr  Board Lenqths Produced Minimum Length Maximum Length Length Increment Max Side Brds  96 in 108 in 12 in 4  Table 6.2 - The operational parameters of Company 2.  161  S A W M I L L S - B A T A SUMMARY Small End Diam Range (in) Length Range (in) Min Max Incr Min Max Incr 3 3 8  Bucking Line 1 Sawing Line 1 Sawing Line 2  31 10 37  1 1 1  96 96 96  720 240 240 Boards Per Hour 3500  Trimmer Information  24 24 24 Down Time (%) 10  I Sawing Line 1-DATA SUMMARY, Saw Kerf Band Saws Edger/Gang  0.121 in 0.121 in  Headriq Productivity Chain Speed Log Gap Downtime Mill Cost  300 F P M 8 Feet 7% 1100$ /Hr  > ^  Sawing<Line*2*'DATASUMMARY* -'' ~ ' f  j.< i 4/< v ^ * . ^ r  Saw Kerf Band Saws Edger/Gang Headriq Productivity Chain Speed Log Gap Downtime Mill Cost  Board Lenqths Produced Minimum Length Maximum Length Length Increment Max Side Brds r  96 in 240 in 24 in 0  <-*  s  0.121 in 0.121 in Board Lenqths Produced Minimum Length Maximum Length Length Increment Max Side Brds  250 F P M 10 Feet 10% 1400$ /Hr  96 in 240 in 24 in 4  Table 6.3 - The operational parameters of Company 3. COMPANY  Length (in)  1 Target  Product  Grade  Market  96  120  144  Percentage  Rough Rough Std.&Btr. Std.&Btr. #2&Btr. Framing Framing Framing Framing Framing Framing Framing Framing  Domestic Domestic Domestic US* Domestic Domestic US Domestic US Domestic US Domestic US  100% 100% 10% 30% 60% 20% 80% 20% 80% 20% 80% 20% 80%  192  216  240  400 400 408 302 416 416 308* 448 332* 400 296* 448 331*  376 278 424 421 311* 464 343* 400 296* 432 320*  376 278 424 416 308* 464 343* 400 296* 432 320*  Price ($/MBF)  Volume  1x4 1x6 2x4 2x4 2x4 2x6 2x6 2x8 2x8 2x10 2x10 2x12 2x12  168  400 400 368 272 392 371 275* 400 296* 328 243* 408 302*  400 400 352 261 392 358 265* 400 296* 320 237* 392 290*  400 400 363 269 376 333 246* 448 332* 344 255* 448 331*  400 400 368 272 376 285 211* 408 302* 357 264* 400 296*  Table 6.4 - The product mix and the market structure of Company 1. Note: Prices of products destined to US markets (*) were used only in the US/Canada Policy presented in Section 5.4.3. Otherwise, the products destined to US markets had the same prices as those destined to domestic markets.  162  COMPANY  Length (in)  2 Target  Product  Grade  Market  Percentage Volume  96  | 120  Price ($/MBF)  2x4  KD Studs Domestic  20%  376  400  2x4  KD Studs  80%  275*  292*  2x6 2x6  KD Studs Domestic KD Studs US  20% 80%  416 304*  432 315*  US  Table 6.5 - The product mix and the market structure of Company 2. Note: Prices of products destined to US markets (*) were used only in the US/Canada Policy presented in Section 5.4.3. Otherwise, the products destined to US markets had the same prices as those destined to domestic markets. COMPANY  3 Target  Product  Grade  Market  96  120  144  Percentage  2x6 2x6 2x8 2x8 2x10 2x10 2x10 4x4 4x6 5x6  Std.&Btr. Domestic Std.&Btr. US #2&Btr. Domestic J-Grade (#2&Btr.) Japan J-Grade (Studs) Japan Framing Domestic Framing US Framing Domestic Framing US Framing Domestic Framing US J-Grade Japan Hirakaku-1 Japan Hirakaku-2 Japan Baby Squares Japan  168  192  216  240  Price ($/MBF)  Volume  2x4 2x4 2x4 2x4 2x4  Length (in)  10% 10% 20% 30% 30%  368 268* 392  352 257* 392 576 584  363 265* 376 576 584  368 269* 376 576 584  408 298* 416 584 592  20% 80%  371 271*  358 261*  400 292*  400 292*  448 327*  464 339*  376 274* 424 592 600 464 339* 464 339*  328 239*  320 234* 720 1360 1408 984  344 251* 720 1360 1408 984  285 208* 408 298* 357 261* 728 1360 1408 984  416 304*  20% 80% 10% 30% 60% 100% 100% 100%  333 243* 448 327*  376 274* 424 584 592 421 307*  400 292* 728 1360 1408 984  400 292* 728 1360 1408 984  400 292* 736 1400 1456 1024  Table 6.6 - The product mix and the market structure of Company 3. Note: Prices of products destined to US markets (*) were used only in the US/Canada Policy presented in Section 5.4.3. Otherwise, the products destined to US markets had the same prices as those destined to domestic markets.  163  Appendix 2 - The Multi-criteria Timber Allocation Model Data  •  frm_Run_Allocalion_pld: Form  lll.l s ! t  a.  £  !1  Treatment Volumes Treatment  Volume  CC PC  i  Record:  3.998,529.24 1,470.76  l<l < 11  1  • l>l|>'lof  2  Rim E m p l o y m e n t L P  Period | Sawmill ID j Total Volume (m3)Total Profit (Million!) | Total Employment (pers hours) j Total Visual 1 Total Wildlife j Tota 1 1 350,000 $34.011942 624 000 0.00 200.000 $18.116068 139 0.00 0.00 i) 2 250.000 $37.289562 566 0.00 0.00 1! 3 1,400,000 0.04 2j 1 (117 817908 2,323 0.00 800,000 158.426689 21 2 548 0.00 0.00 t 3 1,000,000 (114.951100 0.00 0.00 2J7B _lj Record: l<l < ll 1 • * | of 6 <l 1 Achievment Leve5 ID | Objectives Targets | Ww+ B I B Objectives Achievment _•_ 1 Profit 407.04 1 _•_ Employment 6.376 11 2 Employment 6,483.001 Profit 380 61 o l 14U.UU 3AMIdlife Recreation 123 01 145.00 4 Visual Visual 119 24 5 Recreation 133.00 Wildlife 126 00 0 (AutoNumberl 0.00  mm  Record;  rfJ5tart|  M I « IT  •H  > l n l > » l of 5  B]MyThi!as_vl.DOC-Her... | [Eg Microsoft PowerPoint  Micromft  ton  Figure 6.1 - The Multi-criteria Timber Allocation model - The input-output data form.  164  *  _ m  * * m ;• jr  IIII I I  R w E m p l o y m e n t LP  «D •  120 •  J ««**  ID I Otjectiras T«rg«t | W- 1 2 Employment 6573 00 81 1 Pit* 266,00 100 5 Recreatian 133 00 20 4 Visual 14500 50 3WildM 140 00 SO ~» >er) 000 0  *m*.  i«[ < II  W+ 1 1 \ 1I >' 1 0  ,  r.  1  ' •  i  -1|  - •• -• .; r  1 » l>l|..|of 5  ;® 6:iim  Figure 6.2 - The Multi-criteria Timber Allocation Model - The main form.  165  I Company I Period SU No. Volume (m3) No.  Profit (Million $)  (Pers-years)  28 92 99 130 143 189 208 235 251 265  85,015 5,849 12,936 10,278 45,641 19,254 31,567 10,952 14,428  290 310 318 323 351  10,633 4,823 267 10,800 13,855 4,478  0.563928 0.184892 0.012422 0.646743 0.817548  382 388  4,525 169  0.211370  401 419 429 504  13,990 15,877 18,158 4,674  0.959924 1.022716 1.144844  43 44 78 90 101 123 128 143 178 224 233 249 317 318 328 339 342 343 344 356 357 363 379 392 398 407  81,335 99,886 49,901 50,273 33,975 71,628 62,891 7,634 84,757 19,257 12,089 19,268 32,108 12,851 17,153 3,375 15,685 37,154 31,253 16,061 15,961 15,002 14,014 28,415 21,460 24,029  4.536789 5.717424 2.477326 2.314370 1.595091 2.855200 3.511832 0.417955 3.694852 1.074390 0.656730 1.049649 1.732768 0.531529 0.997389 0.180069 0.621430 1.681484 1.431220 0.785221 0.914587 0.726491 0.818962 1.363016 0.943101  421 424 427 468 473 478 483  13,592 14,703 20,289 13,523 15,572 20,932 2,790  0.639964 0.865705 0.913171 0.644316 0.869215 1.061103  497 499 501  5,796 7,571  0.293197  8.92  0.437694 0.947433  11.65  m  11,831  21,026  5.519215 0.281739 0.544753 0.567328 2.623664 0.911419 2.272955 0.629687 0.601219 0.519898  Employment Visual Wildlife Recreation  0.261278 0.011370  0.332209  1.067868  0.120868  524 386,788 19.931931  145.20 11.98 23.67 18.81 83.85 35.23 53.92 20.04 26.40 21.65 19.46 8.92 0.49 21.26 25.35 7.66 8.37 0.28  0.360 0.600 0.600 0.480  0.600 0.600 0.600 0.600 0.600  0.240 0.012 0.240  0.600 0.600  0.240 0.240  23.38 26.53 31.35 7.55 132.30 162.47 81.17 87.96 57.65 125.33 102.30 13.36 148.30 30.31 19.03 30.32 56.18 21.13 28.20 5.55 25.79 65.01 54.68 27.26 26.24 23.87 23.04 49.72 36.42 40.78 22.35 24.17 34.43 21.52 26.70 38.10 4.78  36.79 629.15  Table 6.7 - The Multi-criteria Timber Allocation model • The allocation results in the Equal Weights Scenario. (Continues on next page)  166  Company No.  SU No. Volume  (m3)  Profit Employment Visual Wildlife (Million $) (Pers-years) 0.588452 7.56 1.098402 12.33 10.37 0.942035 2.832510 38.07 4.986051 48.75 0.220566 4.97 0.212 0.062364 0.85 0.046 0.583217 7.08 0.757806 8.75  60 10,925 70 17,806 82 15,193 132 52,053 237 67,557 336 6,628 406 1,139 434 10,090 484 13,009 508 5,599 0.354491 39 63,520 2.617810 45 19,741 0.977749 60 1,787 0.091657 36,544 1.558152 75 51,284 2.382228 85 87 28,897 1.089386 114 1,000 0.033527 117 17,482 0744185 118 52,496 1.979974 134 8,739 0.443649 135 10,744 0.391777 151 10705 0.272919 154 10,925 0.440211 173 3,030 0.096236 179 25,002 1.015020 190 1,260 0.046611 196 20,175 0.798644 197 1,438 0.020904 206 15,454 0.650995 212 300 0.001025 218 29,154 1.230070 871 0.021066 220 247 50,615 2.224299 252 42,330 1.866771 253 288 0.005956 259 101,588 2.452939 269 18,705 0.639277 280 616 0.012756 288 1,119 0.028909 334 20,288 0.612022 364 18,265 0.927192 368 17,591 0.722029 390 18,119 0.904759 395 109 0.001016 397 8,591 0.304021 406 8,752 0.433223 409 17,011 0.676207 412 10,546 0.429301 435 3,009 0.104362 1,407 0.059897 442 444 5,322 0.223357 455 677 0.024740 456 7,483 0.312013 458 839 0.028600 461 1,826 0.036507 475 155 0.004673 476 556 0.003957 461 1,042 0.035345 485 1,276 0.012902 494 505 509 511 525  4,326 1,814 15,753 8,947 486  0.201652 0.072391 0.769017 0.339450 0.019754  Recreation  3.55  44.24 12.83 1.18 25.45 35.72  20.13 0.62  11.37  36.57 5.36 6.98  7.06  7.10 1.86 17.65 0.81 14.05 0.87 10.19 0.18 20.31 0.54 34.79 29.48 0.18 70.76 12.33 0.37 0.69 14.51 11.87 11.76 12.28 0.07 5.43 5.93 11.38 7.05 1.90 0.89 3.41 0.43 4.52 0.55 1.15 0.10  0.35 0.67 0.83  2.65 1.15 10.24 5.40  0.31  Table 6.7 - The Multi-criteria Timber Allocation model - The allocation results in the Equal Weights Scenario. (Continues on next page)  167  Company No.  Period SU No. Volume  (m3)  Profit  (Million $)  Employment (Pers-years)  Visual  11 21 24 27 35 46 48 71 84 88  10,594 39,885 8,533 19,669 15,653 9,529 8,033 20,042 5,174 20,075  0.831435 3.250295 0.785404 1.741709 1.208890 0.806411 0.679098 1.991425 0.370491 1.459917  25.89 98.11 21.39 48.38 39.24 23.44 19.76 50.24 12.73 49.38  107 147 263 291 366  13,863 12,757 10,953 13,413 2,789 4,195  0.996596 1.371287 0.847633 0.989656 0.216437  34.10 31.18 27.29 32.99 6.95  6,201  0.553317  13.41  0.252  2,907 6,212 4,510 10,825 4,188  0.371228  5.65  0.252  0.552940 0.438375 1.090866 0.428786  13.53 9.96 26.97 9.25  0.252 0.252  21,657 1.291278 3 29 154,697 13.015122 27,924 2.430744 40 63 103,573 8.140838 64 12,184 0.653561 77 47,107 3.746296 81 36,745 2.743630 84 17,197 1.084868 144 12,888 0.755721 14,264 0.790284 161 171 40,945 3.145738 172 35,286 3.548630 187 9,859 0.563559 198 33,603 3.697028 202 24,455 1.352175 214 31,795 2.207245 222 21,558 1.697799 225 21,326 1.048002 231 21,567 1.437492 236 20,249 1.569524 264 59,210 3.639816 340 6,484 0.392740 350 27,345 2.858702 355 28,601 2.643117 360 22,166 2.151668 362 27,935 2.186393  46.93 341.62 60.12 224.43 26.40 102.08 81.14 37.26 27.93 30.91 90.42 77.92 21.36 72.81 52.99 69.77 46.71 46.21 46.73 43.88 128.30 12.71 58.50 63.16 47.42  0.504  384 425 432 437 471 487 492  0.352366  14,141 10,616 16,636 20,206 16,152 12,693  0.966637 1.055530 1.589148 1.857445 1.549222 0.775312  6,996 13,546  0.415686  457  516  6,395  0.427264  366 370 400 405 422 426 433  1.493826  Wildlife  0.504  0.630 0.630  0.504 0.378  0.630 0.630  Recreation  0.630 0.630  0.630 0.378 0.378  0.630 0.146  0.376  0.630 0.630 0.630  0.378 0.630 0.088  9.20 0.252  0.630 0.252 0.630  0.504  0.484 0.630 0.630  0.630 0.630  0.504  0.630  0.630  0.252  60.15 31.03 20.66 32.60 43.50 31.43 24.88 12.07 26.36 18.42  0.378  Table 6.7 - The Multi-criteria Timber Allocation model - The allocation results in the Equal Weights Scenario.  168  SU No. Volume Profit Employment Visual I Company Period I (Million $) (Pers-years) (m3) No.  1  1 5 13 16 28 33 52  14,659 14,281 10,325 4,982  78 83 90 96  19,960 12,450 20,109 3,249  101 107 111 112 119  13,590 14,987 6,217 7,212 13,263  0.717791 0.853829 0.347526  130  10,278  0.567328  18.81  141 159 160 165 176 177 193 214  18,947 1,187  1.240825 0.081713 0.208225 0.350942 0.433583 0.053236 0.174338 0.704168 0.183598 0.451190 0.223781 0.304641 0.273632  30.26 1.89 6.86 11.24  1,211 1,742 9,341  215 240 254  3,961 6,078 7,407 913 2,619 12,718 3,328 8,136 3,887  258 278 289  5,557 5,063 6,238  290 291 309 321 344  10,633 14,501 1,662  0.073727 0.103313 0.507460  2.10 3.02 16.54  0.965523 0.927143 0.559056  22.60 24.39 18.89 8.82  0.281140 1.114797 0.721188 1.041466 0.192169  0.397499 0.723331  36.53 22.78 39.58 5.37 25.94 27.42 11.01 12.34 24.27  14.73 1.58 4.04 24.28 5.50 14.89 6.65 9.95 9.37  Wildlife  0.360 0.360 0.480  0.600  0.600  0.600 0.600  0.480 0.360 0.600  0.600 0.600  0.600 0.480 0.480 0.480  0.600 0.600 0.600  0.600 0.360 0.480 0.360 0.360  0.600  0.600  0.360 0.600 0.600 0.600 0.360  11.05  0.600 0.600  0.563928 0.804041  19.46 26.54  0.600 0.600  356  0.094270 0.103042 0.644049 0.353349  2.98 3.13 24.61 12.26  0.240  1,805 12,501 6,425  363 371  6,001 984  0.326921 0.055567  10.74 1.70  0.240 0.240  380  1,609  0.091869  2.79  0.240  388 411  169 2,176 7,435 5,437 3,088 8,373 1,730 1,576  0.011370 0.132744 0.396304 0.287984 0.174943 0.477497 0.096785 0.089670  0.28 3.59  0.240  13.75 10.06 4.92 17.14 2.86 2.73  0.600  0.360  0.366847  420 421 445 478 494 497  Recreation  0.600  0.240 0.240 0.240  0.600 0.600  0.240 0.360  Table 6.8 - The Multi-criteria Timber Allocation model - The allocation results in the Profit M A X Scenario. (Continues on next page)  Company Period SU No. Volume Profit Employment Visual No. (m3) (Million $) (Pers-years) 1  2  21 107,798 28 70,734 37 10,246 44 99,886 45 19,741 46 25,755 47 15,860 48 21,710 53 26,759 3,282 58 63 103,573 68 19,105 79 7,248 25,885 105 125 17,234 126 62,891  5.775613 4.373403 0.544719 5.717424 1.047609 1.435506 0.953196 1.175327 1.500903 0.191692 6.053280 1.160475 0.407439 1.384888 1.015380 3.511832  175.34 115.06 16.13 162.47 30.03 41.89 24.96 35.31 43.53 4.99 168.47 28.05 10.26 42.10 26.21  132  52,053  2.906075  84.67  134 8,739 136 21,574 162 11,880 169 10,020 171 40,945 216 11,316 221 7,293 222 21,558 224 19,257 230 22,334 233 12,089 236 20,249 249 19,268 328 17,153 351 34,637 424 14,703 473 15,572 484 13,009 497 1,857 524 386,788  0.476856 1.222350 0.677505 0.553028 2.248535 0.668342 0.422770 1.232628 1.074390 1.225383 0.656730 1.182463 1.049649 0.997389 1.816774 0.865705 0.869215 0.770996 0.093930  12.83 36.61 18.07 15.95 71.64 16.62 10.71 35.07 30.31 35.15 19.03 32.94 30.32 28.20 56.34 24.17 26.70 19.10 2.86  19.931931  629.15  Wildlife  Recreation  102.30  Table 6.8 - The Multi-criteria Timber Allocation model - The allocation results in the Profit M A X Scenario. (Continues on next page)  170  Company No.  Period  SU No. 3 17  76 82 84 85  88 131 185 263 271 331 392  393 426 433 468  18 27 35 43 59 60 61 67 70 74 82 84 143 146 148 167  Volume (m3)  Profit Employment (Million $) (Pers-years)  27,510 1.359679 8,143 0.432043 6,202 0.334380 1,379 0.085532 22,458 1.184887 24,103 1.238759 25,501 13,177 4,534 13,914 5,353 13,483 13,355  1.308991 0.682073 0.240635 0.704592 0.276065 0.712002 0.685042  5,279 0.278549 5,966 0.301194 3,289 0.159564  6,356 0.324993  21.20 5.86 4.52 0.94  17.31 18.58  19.65 10.15 3.12  11.01 3.91 10.81 10.70 3.74 4.47 2.33  4.70  17,734 53,158 42,305 81,335 24,279 12,712 7,839 14,995 17,806 18,422 13,814 12,677 53,276 4,789 15,849 13,546 18,265  0.905557 3.013282 2.039159 4.302252 1.358241 0.652087 0.453880 0.763975 1.046098 1.021708 0.815717 0.604556 2.777193 0.260023 0.802000 0.716823 0.911020 7,796 0.433059 21,567 1.023517 27,379 1.340741  11.53 37.03 30.65 56.65 16.91 8.38 4.81 9.75 11.74  323 325 339  32,108 1.660510 26,999 1.367711 25,228 1.233420 3,375 0.171623  23.26 19.56 17.57 2.19  376 377 378  11,141 0.550228 11,373 0.625053 11,195 0.557095  7.14 7.71 7.28  181 210  231 235 317  357 364  384  15,961 0.884745 18,265 0.927192  11,338 0.608690  387  21,078 1.152571  429 430  18,158 1.049701 30,221 1.486183 10,090 0.555445  390 394 406  434 509  0.424 0.424  Wildlife Recreation 0.530 0.530  0.419 0.318  0.318 0.212 0.212  0.530 0.530 0.530  0.530 0.530  0.530 0.530  0.530  0.212  0.212  12.15 8.98 8.83 38.59 2.98 10.30 8.81 12.04 4.85 15.02  19.07  10.82 11.87  7.48 15.07  18,119 0.904759 28,878 1.452436 11,175 0.553154  12.28 20.65 7.58  15,753  10.24  0.769017  Visual  12.31 21.61 6.75  Table 6.8 - The Multi-criteria Timber Allocation model - The allocation results in the Profit M A X Scenario. (Continues on next page)  171  Company No.  Period  SU No. Volume Profit E m p l o y m e n t V i s u a l Wildlife Recreation (m3) (Million $) (Pers-years) 10,594 11 0.831435 25.89 0.630 14 1,920 0.172048 3.64 0.378 0.630 0.162094 0.630 23 1,796 3.43 0.378 0.630 50 2,381 0.179451 4.55 9,344 0.792007 23.42 0.260 81 198 33,603 3.881879 76.45 4,683 0.392805 10.27 0.630 199 31,567 3.509474 71.82 208 237 67,557 8.322115 152.73 242 1.966344 16,227 32.45 6,484 0.445812 14.42 0.252 340 366 8,021 0.622425 19.98 0.252 367 19,965 2.247894 40.22 432 14.12 7,856 0.928069 457 13,546 1.568517 27.68 490 14,454 1.594403 29.11  5  24 25 29 30 32 40 51 71 77 81 103 126 147 152 172 182 188 257 333 350 355 360 362 370 375 379 400 401 405 414 419 422 425 437 449 452 465  471  487 490 492 499 503 504 508  16,313  1.543751  23,062 1.870011 38,201 3.992193 154,697 13.015122 27,141 2.167391 1.351675 16,235 27,924 2.430744 7,490 0.724314 54,167 4.741488 47,107 3.746296 11,490 0.857900 34,187 3.012078 2.758887 32,280 3.264968 34,480 31,963 3.219521 35,286 3.548630 7,814 0.780298 18,565 1.920360 2,263 0.208742 10,235 0.895870 27,345 2.858702 28,601 2.643117 22,166 2.151668 27,935 2.186393 10,616 1.055530 6,664 0.640989 14,014 1.162723 16,636 1.589148 1.244772 13,990 20,206 1.857445 6,287 0.588828 15,877 1.372239 16,152 1.549222 16,758 1.317420 1.316523 16,789 9,943 0.949761 6,692 0.598193 17,054 1.478533 12,169 1.043751 29,257 2.597301 182 0.019091 11,320 1.020919 7,571 0.611508 4,583 0.396348 4,674 0.431396 0.488069 5,599  31.75  50.93 82.25 341.62 58.81 31.15 60.12 12.72 119.62 102.08 25.37 73.61 69.95 74.24 69.26 77.92 13.05 35.36 3.81 19.64 58.50 63.16 47.42 60.15 20.66 11.13 27.46 32.60 27.23 43.50 10.76 30.90 31.43 31.92 32.21 17.15 11.73 33.66 23.72 64.21 0.35 22.03 12.96 7.84 8.00 9.35  Table 6.8 - The Multi-criteria Timber Allocation model - The allocation results in the Profit M A X Scenario.  172  Appendix 3 - The D E A Timber Allocation Model Data  DMU  S1_B1 S1 B2 S1_B3 S1_B4  B5 S1_B6 S1_B7 B8 S1_B9 S1_B10 S1 B11 S1 B12 S1_B13 S1 B14 S1 B15 S1 B16 S1 B17 S1 B18 S1_B19 S1_B20 S1_B21 S1_B22 S1_B23 S1_B24 S1 B25 S1 B26 S1_B27 S1_B28 B29 S1 B30 S1 B31 S1 B32 S1_B33 S1 B34 S1 B35 S1 B36 S1 B37 B38 S1_B39 S1_B40 S1 B41 S1 B42 S1 B43 S1 B44 S1 B45 S1_B46 S1_B47 B48 S1 B49 S1 B50 S1 B51 S1 B52 S1_B53 S1 B54 S1 B55 S1 B56 B57 S1 B58 S 1  S 1  S 1  S 1  S 1  S 1  Volume Small D B H  Thous. m3 0.198 9.532 1.502 6.650 0.899 3.902 1.347 1.479 4.386 3.219 0.265 2.550 0.757 0.046 0.133 1.132 0.149 0.848 1.945 0.048 4.329 0.804 0.072 1.516 0.293 1.728 1.521 0.698 1.522 2.081 1.498 0.471 0.359 0.258 0.287 0.483 0.778 4.623 2.346 1.283 1.179 3.532 0.707 1.554 0.796 1.163 1.855 4.558 2.582 2.986 2.464 1.401 1.215 0.266 1.270 1.662 0.245 1.485  INPUTS Volume Medium D B H  Thous. m3 4.289 6.743 4.339 11.302 9.279 11.402 0.920 1.371 6.258 2.101 0.423 4.320 9.432 5.661 1.501 8.417 2.535 3.347 24.146 2.012 9.341 3.161 3.146 2.605 3.715 9.458 11.602 3.696 11.224 3.429 6.313 1.555 0.859 1.293 1.475 2.448 1.836 2.614 5.197 1.258 4.276 5.255 2.071 2.771 1.971 3.212 4.400 4.524 4.973 7.146 10.962 3.005 7.894 8.000 6.527 12.098 0.615 2.704  Volume Large D B H  OUTPUTS Revenue Employment  Thous. Thous. Thous $ m3 Pers. Hours 0.705 214.49 783 0.371 274.37 6186 0.949 255.08 1320 0.715 522.42 5273 0.687 407.84 1875 0.000 410.89 4114 0.000 32.65 861 0.030 50.00 1000 0.000 215.50 3546 0.000 67.80 2118 0.017 16.45 215 0.000 143.73 2210 0.392 409.66 1676 0.377 251.63 900 0.074 60.73 368 0.212 321.71 2043 0.136 94.26 603 0.624 162.86 989 1.582 1139.53 4159 0.000 74.33 358 0.197 413.59 3375 0.000 97.29 1163 1.741 204.96 704 0.000 84.33 1333 0.132 119.24 1111 0.122 382.57 2413 0.000 433.07 2755 0.266 146.60 1096 0.853 403.99 3163 0.000 114.45 1832 0.000 260.19 1713 0.000 48.52 597 0.000 13.42 519 0.352 59.07 454 0.087 61.78 402 0.000 80.90 763 0.000 50.28 892 0.000 85.22 3067 0.537 223.60 2217 0.000 29.64 1054 0.000 150.16 1498 0.000 122.80 3457 0.000 75.61 733 0.000 102.25 1309 0.000 83.19 694 0.101 138.56 1030 0.000 157.58 1803 0.000 164.83 3274 0.331 194.61 2297 0.000 249.11 2985 0.140 415.46 3264 0.265 146.19 1109 2.759 467.99 1976 11.906 1005.20 1934 2.070 419.99 1456 0.690 480.02 3002 0.000 19.24 255 0.049 98.90 1299  Table 6.9 - The DEA Timber Allocation model - The input data. (Continues on next page)  continued...  DMU S2_B1 S2 B2 S2 B3 S2 B4 S2 B5 S2 B6 S2_B7 S2 B8 S2 B9 S2 B10 S2_B11 S2 B12 S2_B13 S2 B14 S2 B15 S2_B16 S2_B17 S2 B18 S2 B19 S2_B20 S2_B21 S2_B22 S2_B23 S2_B24 S2 B25 S2_B26 S2_B27 S2_B28 S2_B29 S2_B30 S2_B31 S2 B32 S2 B33 S2 B34 S2_B35 S2 B36 S2_B37 S2 B38 S2_B39 S2 B40 S2_B41 S2 B42 S2 B43 S2_B44 S2_B45 S2 B46 S2 B47 S2_B48 S2 B49 S2 B50 S2 B51 S2 B52 S2 B53 S2 B54 S2 B55 S2_B56 S2 B57 S2 B58  INPUTS OUTPUTS Volume Volume Volume Revenue Employment Small D B H Medium D B H Large D B H Thous. Thous. Thous. Thous. Thous m3 m3 m3 Pers. Hours $ 149 0.198 4.289 0.705 179.81 9.532 6.743 0.371 354.94 1219 1.502 0.949 218.44 306 4.339 11.302 567.79 1024 6.650 0.715 0.687 387 0.899 9.279 460.03 3.902 11.402 0.000 550.40 818 1.347 0.000 56.63 175 0.920 1.479 1.371 0.030 66.80 198 299.57 705 4.386 6.258 0.000 3.219 2.101 118.95 431 0.000 0.265 0.017 21.38 45 0.423 479 2.550 4.320 O.OOO 201.32 0.757 9.432 0.392 454.74 394 237 0.377 236.07 0.046 5.661 0.074 59 0.133 1.501 67.30 1.132 8.417 0.212 386.38 433 127 0.149 2.535 0.136 106.76 204 3.347 0.624 161.75 0.848 967 1.945 24.146 1.582 1175.43 74 2.012 93.98 0.048 0.000 4.329 9.341 0.197 475.31 715 0.804 131.12 215 3.161 0.000 1.741 186 0.072 3.146 110.50 255 1.516 2.605 0.000 114.95 0.132 149.48 205 0.293 3.715 0.122 445.12 508 1.728 9.458 594 1.521 11.602 0.000 536.33 221 3.696 0.266 147.71 0.698 478.77 667 1.522 11.224 0.853 359 2.081 3.429 0.000 161.89 389 1.498 6.313 0.000 325.58 124 65.88 0.471 1.555 0.000 26.94 102 0.000 0.359 0.859 97 0.352 45.08 0.258 1.293 98 0.087 57.82 0.287 1.475 164 95.90 0.483 2.448 0.000 153 0.000 74.53 0.778 1.836 150.94 593 2.614 0.000 4.623 482 5.197 0.537 253.61 2.346 54.28 210 1.283 1.258 0.000 300 0.000 201.81 1.179 4.276 653 3.532 5.255 0.000 228.96 145 0.707 2.071 0.000 100.08 270 1.554 2.771 0.000 123.87 146 1.971 0.000 88.21 0.796 236 159.64 3.212 0.101 1.163 346 0.000 208.15 1.855 4.400 4.524 239.03 666 0.000 4.558 224.22 463 2.582 4.973 0.331 320.54 606 0.000 2.986 7.146 694 468.54 2.464 10.962 0.140 247 182.02 3.005 0.265 1.401 487 7.894 334.69 1.215 2.759 428 8.000 11.906 308.40 0.266 306.41 359 1.270 6.527 2.070 738 1.662 12.098 0.690 523.01 62 0.615 0.000 27.39 0.245 245 2.704 0.049 119.81 1.485  Table 6.9 - The DEA Timber Allocation model - The input data. (Continues on next page)  continued...  DMU S3_B1 S3 B2 S3 B3 S3 B4 S3_B5 S3_B6 S3 B7 S3 B8 S3 B9 S3_B10 S3 B11 S3 B12 S3_B13 S3 B14 S3_B15 S3 B16 S3 B17 S3 B18 S3 B19 S3 B20 S3 B21 S3 B22 S3 B23 S3_B24 S3 B25 S3 B26 S3 B27 S3 B28 S3 B29 S3 B30 S3_B31 S3 B32 S3_B33 S3 B34 S3 B35 S3 B36 S3 B37 S3_B38 S3 B39 S3 B40 S3 B41 S3 B42 S3 B43 S3 B44 S3 B45 S3_B46 S3_B47 S3 B48 S3 B49 S3 B50 S3_B51 S3 B52 S3 B53 S3 B54 S3 B55 S3_B56 S3 B57 S3 B58  Volunle Small D B H Thous. m3 O 198 9 532 1 502 6 650 O 899 3 902 1 347 1 479 4 386 3 219 O 265 2 550 O 757 O 046 o 133 1 132 o 149 o 848 1 945 o 048 4 329 O 804 O 072 1 516 O 293 1 728 1 521 O 698 1 522 2 081 1 498 O 471 O 359 o 258 o 287 o 483 o 778 4 623 2 346 1 283 1 179 3 532 O 707 1 554 O 796 1 163 1 855 4 558 2 582 2 986 2 464 1 401 1 215 O 266 1 270 1 662 245 o1 485  INPUTS O U T P U T S Volume Volunle Revenue Employment Medium D B H Large D B H Thous Thous. Thous. Thoi J S m3 m3 Pers. Hours $ 4 289 O 705 341 92 444 6 743 O 371 385 30 4197 4 339 O 949 396 oo 775 1 1 302 O 715 738 78 3155 9 279 O 687 606 81 1070 11 402 O OOO 561 82 2418 O 920 O ooo 46 92 591 1 371 O 030 73 18 663 6 258 O OOO 268 48 2369 1470 2 101 O ooo 95 17 137 O 423 O 017 21 49 4 320 O ooo 194 97 1531 9 432 O 392 621 35 1008 5 661 O 377 396 38 480 167 1 501 O 074 94 86 1194 8 417 O 212 465 08 2 535 O 136 141 14 392 3 347 O 624 241 53 599 24 146 1 582 1758 33 2365 2 012 O ooo 108 42 173 9 341 O 197 550 45 2108 3 161 O ooo 128 39 715 3 146 1 741 361 43 404 2 605 O ooo 100 65 908 3 715 O 132 180 71 600 9 458 O 122 509 93 1377 11 602 579 56 1611 o ooo 3 696 213 83 681 o 266 11 224 546 63 1897 o 853 3 429 147 24 1162 o ooo 6 313 1014 340 82 o OOO 1 555 370 0 ooo 62 14 O 859 19 45 359 o ooo 1 293 94 94 278 o 352 1 475 257 TOO 17 o 087 2 448 113 02 487 o ooo 1 836 545 73 47 o ooo 2 614 112 57 2056 o ooo 1343 5 197 0 537 325 51 1 258 708 48 10 o ooo 4 276 228 72 899 o ooo 198 15 2212 5 255 o ooo 2 071 430 0 ooo 93 71 2 771 132 71 831 o ooo 1 971 117 25 409 o ooo 3 212 178 96 663 o 101 4 400 1117 209 78 o ooo 4 524 219 05 2145 o ooo 4 973 261 36 1458 o 331 7 146 331 86 1832 o ooo 590 95 10 962 1886 o 140 3 005 213 89 663 o 265 2 759 1169 7 894 685 23 8 OOO 11 906 1760 78 1021 747 6 527 2 070 659 71 12 098 739 12 1852 o 690 OO 28 OO 177 O 615 oO 2 704 122 54 806 o 049  Table 6.9 - The DEA Timber Allocation model - The input data.  su 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  Sawmill 1 BCC BCC-SUP 73.68% 100.00% 78.88% 96.01% 74.33% 86.93% 93.67% 89.93% 92.34% 95.69% 100.00% 88.21% 72.57% 73.12% 82.53% 77.23% 78.72% 77.28% 100.00% 73.72% 83.70% 86.07% 71.85% 88.14% 85.23% 79.88% 79.14% 81.11% 81.09% 90.30% 79.66% 85.79% 100.00% 81.50% 79.90% 82.41% 90.61% 100.00% 85.30% 98.11% 85.23% 97.69% 82.69% 87.09% 82.94% 79.53% 85.64% 94.92% 85.73% 87.83% 83.76% 81.40% 75.37% 74.22% 74.26% 79.37% 92.24% 87.56%  73.69% 126.20% 78.88% 96.02% 74.33% 86.93% 93.67% 89.93% 92.34% 95.68% 156.91% 88.21% 72.57% 73.12% 82.53% 77.23% 78.72% 77.28% 102.91% 73.72% 83.70% 86.07% 71.85% 88.14% 85.23% 79.88% 79.15% 81.11% 81.09% 90.30% 79.66% 85.79% 115.59% 81.50% 79.90% 82.41% 90.61% 107.19% 85.30% 98.12% 85.23% 97.69% 82.69% 87.09% 82.94% 79.54% 85.65% 94.92% 85.73% 87.83% 83.76% 81.40% 75.36% 74.22% 74.26% 79.37% 92.24% 87.56%  Sawmill 2 BCC BCC-SUP 42.63% 37.87% 42.34% 43.13% 50.82% 47.96% 42.43% 38.27% 42.60% 39.76% 99.47% 44.53% 51.80% 48.27% 60.60% 49.80% 51.02% 43.63% 66.79% 65.94% 45.85% 45.60% 30.68% 41.47% 47.92% 49.68% 51.30% 42.61% 46.28% 43.67% 53.08% 48.56% 43.27% 36.49% 47.20% 46.21% 42.38% 38.39% 44.57% 39.15% 49.41% 42.15% 49.38% 42.33% 44.80% 47.91% 45.61% 42.21% 41.35% 44.85% 46.02% 51.38% 37.42% 20.67% 39.40% 47.71% 77.53% 41.00%  42.63% 37.87% 42.34% 43.13% 50.82% 47.96% 42.43% 38.27% 42.60% 39.76% 99.46% 44.53% 51.81% 48.27% 60.60% 49.80% 51.02% 43.63% 66.79% 65.94% 45.85% 45.60% 30.68% 41.47% 47.92% 49.68% 51.30% 42.61% 46.27% 43.67% 53.08% 48.56% 43.27% 36.49% 47.20% 46.21% 42.38% 38.39% 44.57% 39.15% 49.41% 42.15% 49.39% 42.33% 44.80% 47.91% 45.61% 42.21% 41.35% 44.86% 46.02% 51.38% 37.42% 20.67% 39.40% 47.71% 77.53% 41.00%  Sawmill 3 BCC BCC-SUP 85.84% 79.86% 83.50% 79.23% 77.69% 72.02% 75.41% 73.89% 73.11% 75.70% 100.00% 75.34% 79.98% 83.52% 86.01% 74.23% 80.94% 77.23% 100.00% 76.99% 73.21% 70.68% 92.70% 70.78% 74.87% 71.51% 70.92% 77.41% 70.85% 71.17% 71.69% 69.56% 78.96% 84.38% 88.00% 74.05% 72.13% 74.89% 75.81% 77.30% 77.21% 75.56% 66.73% 71.35% 74.29% 71.79% 71.47% 73.94% 72.35% 71.09% 74.06% 76.45% 79.63% 100.00% 84.26% 79.52% 88.40% 69.15%  85.84% 79.87% 83.51% 79.23% 77.69% 72.01% 75.41% 73.89% 73.10% 75.69% 112.30% 75.34% 79.98% 83.51% 86.01% 74.23% 80.94% 77.23% 113.43% 76.99% 73.21% 70.68% 92.70% 70.78% 74.87% 71.52% 70.92% 77.41% 70.85% 71.17% 71.69% 69.56% 78.96% 84.38% 88.00% 74.05% 72.12% 74.89% 75.81% 77.30% 77.21% 75.56% 66.73% 71.35% 74.29% 71.79% 71.46% 73.94% 72.35% 71.09% 74.06% 76.45% 79.63% 135.76% 84.26% 79.52% 88.40% 69.15%  Table 6.10 - The DEA Timber Allocation model - The efficiency scores generated by the BCC and the BCC with super-efficiency models.  176  Company 1 Volume Revenue  su 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  Company 3  Company 2 Empl.  Volume  Revenue  Empl.  Volume  Revenue  (Pers. (Pers. (Thous m3) (Thous $) hours) (Thous m3) (Thous $) hours) (Thous m3) (Thous $) 5.2 342 16.6 274 6186 6.8 396 18.7 522 5273 10.9 607 15.3 411 4114 2.3 57 175 1.6 38 113 10.6 300 705 5.3 119 431 0.7 16 215 6.9 201 479 10.6 621 6.1 252 900 1.7 95 9.8 386 433 2.8 141 4.8 242 27.7 1758 2.1 74 358 13.9 475 715 4.0 131 215 5.0 361 4.1  119  1111  13.1 4.7 13.6  433 147 404  2755 1096 3163  1.2 1.9  13 59  519 454  2.9  81  763  . 1-0  14  393  11.9  468  1976  0.9  19  255  11.3  445  508  5.5 7.8 2.0  162 326 66  359 389 124  7.2  151  593  5.5  202  300  2.8 4.3  100 124  145 270  4.5 6.3 9.1  160 208 239  236 346 666  10.1 13.6 4.7  321 469 182  606 694 247  Empl.  (Pers. hours) 444 775 1070  1008 167 392 599 2365 404  1.8  100  257  0.5  20  84  2.8  117  409  20.2 9.9 14.4  1761 660 739  1021 747 1852  Table 6.11- The DEA Timber Allocation model - The allocation results.  177  Appendix 4 - The Hierarchical Timber Allocation Model Data  Heal's Procedure Heal (1969) considered a series of n production facilities (lower planning level) that used j resources to produce Yi amount of output. Each facility produced the output according to a production function:  whereby was the amount of resource j allocated to facility / and satisfied two conditions: X  ij  > 0 for each i,j  (2)  El..<i?. u  i  (3)  J  Rj was an upper bound on the resource j available for allocation (i.e. the allocation of scarce resources). A n upper level (e.g. a central planning board) planned the allocation of resources to each facility. The goal of the upper level was to find an allocation X», which maximized Y Y —' i i  i  subject to (2), and (3). The proposed iterative process consisted of a quantity-guided routine, in which the center first sent out to the facilities an initial allocation (proposal) so that: X  > 0 and Y X  - R  for all /'. In response to the initial proposal, the facilities (the  tj y ij j lower level) reported to the upper level the marginal productivity for each resource. In turn, these productivities were used to assist the center to adjust the proposed allocation and generate a new one. The rate of adjustment had the following format: '/ X  y  -Av(K 0  =  for i g K  0  where K  )f  j  ={i:X  fori GK "  J  J  (4)  j  U  > 0 , orX  ij  = 0 but/  if  > Av(K  J  ) / . }, and  V  178  : The marginal productivity (shadow price) of resource j when allocated to facility i. A v(K.)/".. J V  : The average marginal productivity (shadow price) of resource j calculated with the productivities for the facility i included in the set Kj.  In other words, in subsequent allocations (iterations) the upper level increased the allocation of resource j to those facilities i where its marginal productivity was above the average and reduced it when it was below the average. The purpose of defining the set Rj was that the upper level needed also to apply the adjustments to those facilities where the allocation of resource j was zero, but their marginal productivity was above average. The iterative process designed by Heal using the adjustments (4) was proven to increase the function V y monotonically. I  i  Hof et al. Procedure Hof, Kent, and Baltic (1992) employed Heal's procedure to develop an allocation model in which a regional control iteratively adjusted the output targets of forest level models using the following expression : 24  Y  *  ij  =Y + U  S\(Av(K.)f..-f..)/Yf.-)l]Y. j v y ; v ; v  for all i and j  (5)  where Y  : The adjusted target of output j for firm /.  S  : A number between zero and one that increases/decreases the rate of adjustment.  A l l the other notations are identical to those presented in Heal's procedure. The algorithm was proven to generate proposals that monotonically decreased the total cost of forest level activities.  The notation was modified to be consistent with that of Heal (1969).  179  S e w ! * I:  C:V1<wn\<yj^«oonV5»>«n*.lB*™ll.«««>  1 [ III 1 1  Short t o g s : Long Log* M « V a f Executable: XA Command in*: Status M e :  X : V * o » « o f f c ^ W o o d H o - A r j l / i » r \ b « A O u t p u M \ » « » t Logs" "C V r o g r a m f « e s \ w o o d R o « A A a V w t b r > \ O u t p u t s \ L o n g  Legs'  ?  CV^ionWP.MocotaA  c  if m •  nf J 1 *  - M a » » » c e YES k t r c u t no Set V e * t » N o SET a i M O f f Set O n » * M « < » . Dec C:V<aian\<J_Alec«txr\CMoutFte;tgetus.tict  RUN ALLOCATION RunXA_PTt><« Number of  8  8  1  2  tter«t»sns: Run XA_L™p*oyment  0  8  8  i \  t I  ObjectiveValues  Reran*  Ml «  IT GP.vlS.Wetgh-  t:«FM  Figure 6.3 - The Hierarchical Timber Allocation model - The interactive form.  180  181  Company No.  Period No.  SU  1  1  81 143 171 317 328 357 370 379  36;745 53,276 40,945 32,108 17,153 8,280 10,616 14,014  67.51 97.88 75.22 58.99 29.61 14.30 17.74 24.19  388 400 401 419  169 16,636 13,990  0.28 28.72 23.38 26.53  422 424 429 473 478  16,152 14,703 18,158 15,572 20,932  2  Volume (m3)  15,877  Employment Visual Wildlife (Pers-years)  26.99 25.38 31.35 28.03 40.00 7.55  604  4,674  43 78 84 90 101 107 123 128 178  81,335 49,901 60,460 50,273 33,975 37,467 71,628 62,891 84,757 19,257  132.30 81.17 98.34 87.96 57.65 60.94 125.33 102.30 148.30  21,567 12,089 19,268 36,252 3,375 17,523 15,685 37,154 31,253 16,061 7,681 15,002 18,119 28,415 21,460 24,029 13,592 12,693 20,289 6,998 10,090 1,407 10,904 2,790 5,796 7,571 21,026 22,690 386,788 486  35.08 19.03 30.32 58.97 5.55 28.81 25.79 65.01 54.68 27.26 12.63 23.87 29.79 49.72 36.42 40.78 22.35 20.87 34.43 11.14 16.06 2.17 17.35 4.78 8.92 11.65 36.79 38.50 629.15 0.77  224 231 233 249 291 339 340 342 343 344 356 357 363 390 392 398 407 421 426 427 433 434 442 471 483 497 499 501  518 524 525  Recreation  30.31  0.042  Table 6.12 - The Hierarchical Timber Allocation model - The allocation results in the Equal Weights Scenario. (Continues on next page) 182  Company No.  Period S U Volume Employment Visual Wildlife Recreation (m3) ^Pers-years) No. 45 19,741 13.48 60 12,712 8.80 70 17,806 12.33 82 15,193 10.37 51,284 85 37.51 134 8,739 5.62 364 12.47 18,265 425 3.44 5,109 437 16,789 11.46 484 13,009 8.75 508 5,599 3.55 10.75 509 15,753 44.24 39 63,520 64 32,929 22.94 36,544 75 25.45 87 28,897 20.13 114 0.62 1,000 117 11.37 17,482 118 52,496 36.57 10,744 135 6.98 151 10,705 7.06 154 10,925 7.10 161 38,407 26.75 0.004 173 3,030 1.86 179 25,002 17.65 190 1,260 0.81 196 20,175 14.05 197 1,438 0.87 206 209 212 218 220 247 252 253 259 264 269 280 288 334 368 395 397 409 412 425 435 444 455 456 458 461 475 476 481  10.19 1.29 0.18 20.31 0.54 34.79 29.48 0.18 70.76 41.24 12.33 0.37 0.69 14.51 11.76 0.07 5.43 11.38 7.05 7.47 1.90 3.41 0.43 4.52 0.55 1.15 0.10 0.35 0.67  485  15,454 2,137 300 29,154 871 50,615 42,330 288 101,588 59,210 18,705 616 1,119 20,288 17,591 109 8,591 17,011 10,546 11,649 3,009 5,322 677 7,483 839 1,826 155 556 1,042 1,276  494 505  4,326 1,814  511  8,947  2.65 1.15 5.40  0.83  Table 6.12 - The Hierarchical Timber Allocation model - The allocation results in the Equal Weights Scenario. (Continues on next page)  183  Company No. 3  Period SU No. 1  172 198 208 237 350 355 360  457 2  21 28 29  40 44 48 63 71 77  132 147 214 222 236 263 355 362 366 405 487  Volume Employment (Pers-years) (m3) 35,286 81.82 33,603 76.45 31,567 71.82 67,557 152.73 61.42 27,345 18,930 43.89 22,166 49.79 27.68 13,546 107,798 233.59 85,015 184.22 154,697 341.62 60.12 27,924 216.44 99,886 47.04 21,710 103,573 224.43 54,167 119.62 47,107 102.08 52,053 112.79 34,480 31,795 21,558 20,249 29,604 9,671 27,935 21,679 20,206 28,895  Visual  Wildlife  Recreation  74.24 69.77 46.71 43.88 64.96 21.36 60.15 47.58 43.50  63.41  0.012  Table 6.12 - The Hierarchical Timber Allocation model - The allocation results in the Equal Weights Scenario.  184  Comapany No. 1  Period 1  SU  No. 16  (m3)  14,659  28  85,015  58  3,282  47  63  15,860  Employment (Pers-years)  5.24  17,234  141  18,947  27.53  193 216  2,619 11,316  29.46 30.26  4.04 17.45  221  518  0.80  236  20,249  34.58  17,153 169  29.61 0.28  2,740  4.22  388 424 508 1  5  11  14,703 5,599 4,356  28,633  25.38 8.32 6.70  107,798  175.34  43  81,335  132.30  45  99,886 19,741  162.47  25,755  41.89  21,710 26,759  35.31 43.53  46 48  53 67 79  105  128 132 134  14,995  7,248  25,885  22.81  10.26  42.10  102.30  52,053  84.67  136  21,574  143  53,276  162  30.03  62,891 8,739  12.83 36.61  93.22  11,880  18.07  165  15,194  24.98  171  40,945  71.64  169  176  181 221  222 224  10,020 18,518  18,265  15.95  32.73  28.75  6,775  9.95  21,558  35.07  19,257  30.31  230  22,334  233 249  12,089 19,268  19.03 30.32  323  26,999  47.24  351  34,637  56.34  473  15,572  478  20,932  26.70  445  494  497 509 524  7,720  4,326  0.057  45.06  21 44  Recreation  26.21  125  328  Wildlife  22.60  176.89  19,105  Visual  145.20  103,573  68  2  Volume  35.15  10.93  38.10 6.35  5,796  8.92  15,753 386,788  23.96 629.15  Table 6.13 - The Hierarchical Timber Allocation model - The allocation results in the Profit M A X Scenario. (Continues on next page)  Comapany No. 2  Period 1  2  SU No.  27 59 61 70 74 82 210 357 377 429 434 18 35 37 60 76 78 83 84 85 107 111 131 146 148 167 214 231 235 291 317 325 331 339 364 376 377 378 384 387 390 392 393 394 406 430  Volume  Employment  (Pers-years) (m3) 38.88 53,158 24,279 17.76 7,839 5.05 17,806 12.33 18,422 12.75 10.37 15,193 5.09 7,796 15,961 11.36 8.04 11,296 18,158 12.93 10,090 7.08 17,734 11.53 30.65 42,305 10,246 6.76 12,712 8.38 13,195 8.70 49,901 34.76 31,124 21.68 60,460 42.11 51,284 35.72 37,467 26.10 15,541 10.25 16,322 11.37 2.98 4,789 10.30 15,849 13,546 8.81 22.74 31,795 15.02 21,567 19.07 27,379 36,252 25.25 32,108 23.26 17.57 25,228 20.78 28,686 2.19 3,375 11.87 18,265 7.14 11,141 77 0.05 7.28 11,195 11,338 7.48 15.07 21,078 12.28 18,119 20.58 28,415 7.20 11,231 20.65 28,878 7.58 11,175 30,221 21.61  Visual  Wildlife  Recreation  0.418  Table 6.13 - The Hierarchical Timber Allocation model - The allocation results in the Profit M A X Scenario. (Continues on next page)  186  Comapany No.  Period  3  1  2  SU Volume (m3) No. 25 198 208 237 242 350 367 432 457 490 9 24 25 29 30 32  17,697 33,603 31,567 67,557 16,227 27,345 19,965 7,856 13,546 14,635  16,313  Employment (Pers-years)  Visual  Wildlife  Recreation  40.01 76.45 71.82 152.73 32.45 61.42 40.22 14.12 27.68 26.48 31.75  23,062 20,504 154,697 27,141 16,235  50.93 44.15 341.62 58.81  40 51 71 77 81 103 126 147 152 172 182 188 199 257 333 355 360 362 370 375 379 400 401 405 414 419 422 425 437 449  27,924 7,490 54,167 47,107 36,745 34,187 32,280 34,480 31,963 35,286 7,814 18,565 12,559 2,263 10,235 28,601 22,166 27,935 10,616 6,664 14,014 16,636 13,990 20,206 6,287 15,877 16,152 16,758 16,789  60.12 12.72 119.62 102.08 81.14 73.61 69.95 74.24 69.26 77.92 13.05 35.36 24.27 3.81 19.64 63.16 47.42 60.15 20.66 11.13 27.46 32.60 27.23 43.50 10.76 30.90 31.43 31.92 32.21  9.S43  17.15  452 465 471 484 487 492 499 503 504  6,692 17,054 12,189 13,009 29,257 11,320 7,571 4,583 4,674  11.73 33.66 23.72 24.78 64.21 22.03 12.96 7.84 8.00  31.15  0.008  Table 6.13 - The Hierarchical Timber Allocation model - The allocation results in the Profit M A X Scenario. (Continues on next page)  187  A p p e n d i x 5 - The P o l i c y Analysis D a t a  Equal Weights Scenario Wildlife Corridor Unconstrained Profit generated by:  Employment generated by:  Volume of timber harvested with: Area allocated to: Goal achievement for:  Volume harvested in corridor (m3): Number of SUs in corridor allocated to:  Sawmill 1 ( $ ) Sawmill 2 ($) Sawmill 3 ($) TOTAL ($) Sawmill 1 ( P e r s o n Y e a r s ) Sawmill 2 ( P e r s o n Y e a r s ) Sawmill 3 ( P e r s o n Y e a r s )  TOTAL ( P e r s o n Y e a r s ) Clearcut (m3) Partial cut (m3) Harvesting (ha) Reserve (ha) TOTAL (ha) Employment (%) Recreation (%) Visual (%) Wildlife (%)  $19,996,920  $20,140,932  $21,036,635  $10,164,961  $10,253,513  $11,334,175  $11,334,175  $26,765,286  $26,765,286  $27,584,652  $27,600,674  $56,927,167  $57,159,731  $59,955,461  $60,439,018  2,950  2,947  2,859  2,847  686 2,739  686 2,743  696 2,643  2,648  6,375 3,992,474  6376  6,199  $21,504,169  697 6192 3,977,392  7,526  3,998,529 1,471  3,897,379 102,621  17,918  17,848  17,055  16,344  27,895  27,965  28,758  29,469  22,608  45,813  45,813  45,813  45,813  98%  97%  96%  96%  94%  92%  62%  64%  83% 91%  82%  76%  74%  91%  73%  70%  32,929  82,810  180,982  -  Partial Cuts Clear Cuts Reserve  Profit MAX Scenario Wildlife Corridor Unconstrained  -  7 1  34  33  27  9 25  Table 6.14- The results of the Wildlife Corridor policy. Equal Weights Scenario Accessibility Unconstrained Profit generated by:  Employment generated by:  Volume of timber harvested with:  Area allocated to:  Goal achievement for:  Sawmill 1 ( $ ) Sawmill 2 ($) Sawmill 3 ($) TOTAL ($) Sawmill 1 ( P e r s o n Y e a r s ) Sawmill 2 ( P e r s o n Y e a r s ) Sawmill 3 ( P e r s o n Y e a r s )  TOTAL ( P e r s o n Y e a r s ) Clearcut (m3) Partial cut (m3) TOTAL (ha) Sawmill 1 ( m 3 ) Sawmill 2 (m3) Sawmill 3 (m3) Harvesting (ha) Reserve (ha) TOTAL (ha) Percent Reserve Employment (%) Recreation (%) Visual (%) Wildlife (%)  Profit MAX Scenario Accessibility Unconstrained  $19,644,100  $20,140,932  $20,519,075  $21,504,169  $1,591,628  $10,253,513  $10,166,322  $26,422,935  $26,765,286  $27,600,674  $11,334,175 $27,600,674  $47,658,664  $57,159,731  $58,286,071  $60,439,018  2,886  2,947  2,871  23  686  696  2,716  2,743  2,671  5,625 3,025,900 9,067  6376 3,998,529 1,471  6,239 3,970,030 29,970  2,847 697 2,648 6192 3,977,392 22,608  3,034,967  4,000,000  4,000,000  4,000,000  1,750,000  1,750,000  1.750,000  1,750,000  34,967  1,000,000  1,000,000  1,000,000  1,250,000  1,250,000  1,250,000  1,250,000  11,663  17,848  34,150  27,965  15,601 30.213  16,344 29,469  45,813  45,813  45,813  45,813  75%  61%  66%  64%  87%  97%  96%  96%  90%  92%  71%  64%  85% •91%  82%  78%  74%  91%  79%  70%  Table 6.15 - The results of the Accessibility policy.  188  Profit generated by:  Employment generated by:  Volume of timber harvested with: Area allocated to:  Goal achievement for:  Sawmill 1 ($) Sawmill 2 ($) Sawmill 3 ($) TOTAL ($) Sawmill 1 (Person Years) Sawmill 2 (Person Years) Sawmill 3 (Person Years) TOTAL (Person Years) Clearcut (m3) Partial cut (m3) Harvesting (ha) Reserve (ha) TOTAL (ha) Percent Reserve Employment (%) Recreation (%) Visual (%) Wildlife (%)  Equal Weights Scenario US/Canada Unconstrained $14,982,277 $20,140,932 $6,645,069 $10,253,513 $25,928,822 $26,765,286 $47,556,168 $57,159,731 2,947 2,952 681 686 2,733 2,743 6,367 6376 3,959,487 3,998,529 1,471 40,513 17,848 18,030 27,784 27,965 45,813 45,813 61% 61% 97% 97% 93% 92% 82% 82% 91% 91%  Profit MAX Scenario US/Canada Unconstrained $15,661,698 $21,504,169 $7,249,845 $11,334,175 $26,761,760 $27,600,674 $49,673,302 $60,439,018 2,847 2,868 695 697 2,648 2,648 6,210 6192 3,977,392 3,979,903 20,097 22,608 16,344 16,361 29,452 29,469 45,813 45,813 64% 64% 94% 96% 65% 64% 74% 75% 70% 70%  Table 6.16 - The results of the U.S./Canada Trade policy.  Profit generated by:  Employment generated by:  Volume of timber harvested with:  Area allocated to:  Goal achievement for:  Sawmill 1 ($) Sawmill 2 ($) Sawmill 3 ($) TOTAL ($) Sawmill 1 (Person Years) Sawmill 2 (Person Years) Sawmill 3 (Person Years) TOTAL (Person Years) Clearcut (m3) Partial cut (m3) TOTAL (ha) Sawmill 1 (m3) Sawmill 2 (rr>3) Sawmill 3 (m3) Harvesting (ha) Reserve (ha) TOTAL (ha) Percent Reserve Employment (%) Recreation (%) Visual (%) Wildlife (%)  Equal Weights Scenario Cumulative Unconstrained $20,140,932 $14,662,713 $0 $10,253,513 $25,603,527 $26,765,286 $40,266,239 $57,159,731 2,871 2,947 0 686 2,708 2,743 5,579 6376 2,843,584 3,998,529 155,159 1,471 2,998,744 4,000,000 1,748,744 1,750,000 0 1,000,000 1,250,000 1,250,000 12,397 17,848 27,965 33,416 45,813 45,813 73% 61% 86% 97% 90% 92% 85% 82% 91% 91%  Profit MAX Scenario Cumulative Unconstrained $15,139,114 $21,504,169 $7,119,777 $11,334,175 $27,600,674 $26,688,820 $48,947,712 $60,439,018 2,860 2,847 693 697 2,661 2,648 6,215 6192 3,931,476 3,977,392 68,524 22,608 4,000,000 4,000,000 1,750,000 1,750,000 1,000,000 1,000,000 1,250,000 1,250,000 16,922 16.344 28,891 29,469 45,813 45,813 64% 55% 96% 96% 71% 64% 77% 74% 78% 70%  Table 6.17 - The results of the cumulative case.  189  

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