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Knowledge-based approaches to forest operations scheduling problems Brack, Christopher Leigh 1992

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KNOWLEDGE-BASED APPROACHES TO FOREST OPERATIONS SCHEDULING PROBLEMS by CRISTOPHER LEIGH BRACK B.Sc. (For) (Hons) A THESIS SUBMIYfED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy  In  THE FACULTY OF GRADUATE STUDIES FORESTRY  We accept this thesis as conforming to the required standard  Signature(s) removed to protect privacy  THE UNIVERSITY OF BRITISH COLUMBIA November 1991 ©Cristopher Brack, 1991  In presenting this thesis  in  partial fulfilment of the requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Signature(s) removed to protect privacy  -  Department of The University of British Columbia Vancouver, Canada  Date  DE-6 (2188)  22 d 17  h€,-  //  (Signature)  ABSTRACT Operation scheduling in fast growing, intensively managed forest plantations is characterized by diverse qualitative and quantitative goals and constraints. These goals and constraints may be temporal or spatial, and may interact in complex ways. Traditional linear programming approaches to forest operations scheduling generally require significant simplifications to the problem statement before they can be solved and do not provide managers with easily understandable solutions except in simple cases. A series of knowledge-based models was developed to assist forest managers in operations scheduling problems. These knowledge-based models included random and heuristic search models using different knowledge amounts, and expert systems. The models used silvicultural knowledge deilved from plantation management plans of the Forestry Commission of New South Wales to construct practical and feasible thinning and harvesting regimes for each stand in a plantation. Other knowledge was derived from game and puzzle soMng domains and human experts in operations scheduling to help construct forest operations schedules that simultaneously considered some stand and forest management and environmental considerations. Operations schedules produced for two intensively managed and rapidly growing plantation forests by the knowledge-based models were evaluated for timber flow, stand health, scenic beauty, and water quality. Schedules were found that were within 5% of the optimal timber flow found by (integer) linear programming approaches. The knowledge-based model solutions were superior to the linear programming solutions for at least one of the health, beauty or water quality considerations, and were at least as good as solutions produced by human operations scheduling experts.  II  Abstract The knowledge-based models were used to explore the relationships between the various goals and objectives. The knowledge-based approach was also used to develop robust strategies in the presence of uncertainty in the growth models. Important stand I regime combinations were isolated to allow management to reduce the impact of uncertainty. The quality of the knowledge-based model solutions depended upon the specific knowledge included, and the forest structure. However, more knowledge did not necessarily lead to a better solution. In the larger plantation forest examined, additional knowledge did not lead to a better solution relative to the solution generated by a model using little knowledge. This was because the additional knowledge lacked key information about the forest age class distribution and problem size. Without this information, the additional knowledge was incomplete and directed the model- solution inappropriately. The knowledge-based models developed are simple and easy to understand. They can be used to integrate silvicultural knowledge with other forestry domain knowledge to produce plans that can be understood and defended. They can also serve to integrate future knowledge development and show the potential advantages of research.  III  TABLE OF CONTENTS Abstract  .H  Table of Contents  iv  List of Tables  Vi  List of Figures  VII  Acknowledgements  Viii  1. Introduction 1.1 Problem Statement 1.2 Objectives 1.3 Overview  1 1 4 5  2. Literature Review 2.1 Operations Scheduling System Requirements 2.2 Mathematical Programming 22.1 Problem Size 2.2.2 Solution Space 2.2.3 Risk and Uncertainty 2.2.4 Specifying the Objective Function 2.2.5 Solution Type 2.2.6 Applicability 2.3 Knowledge-Based Models 2.3.1 Random Search 2.3.2 Blind Search 2.3.3 Expert Systems 2.3.4 Applicability  7 7 10 11 14 15 17 18 19 21 23 26 29 .32  3. Methods 3.1 Introduction 3.2 Terminology 3.3 Data 3.4 Test Criteria 3.4.1 Whatto Test’? Timber Yields Scenic Beauty Stand Health Water Quality 3.4.2 What to Test With’ 3.4.3 What to Test Against’ 3.4.4 Do the Models Pass’?  34 34 35 36 38 39 40 41 43 43 44 45 47  4. Development of the Search Models  49  .-  iv  Table of Contents 4.1 4.2 4.3 4.4 4.5  Introduction An Exhaustive Search Introducing Domain Knowledge: StratSearch-1 More Domain Knowledge: StratSearch-2 Ordering Stands: StratSearch-3  .  49 50 51 58 61  5. Development of the Expert Models 5.1 Introduction 5.2 An Expert System Toolbox 5.3 An Expert System Approach to Risk 5.4 Expert Systems  63 63 64 65 66  6. Testing and Results 6.1 LINDO 6.2 PINEPLAN 6.3 StratSearch-1 6.4 StratSearch-2 6.5 StratSearch-3 6.6 Expert System 6.7 Risk  70 70 72 73 86 94 96 99  7. Discussion 7.1 Introduction 7.2 StratSearch Models 7.3 The Expert System 7.4 Strategy Scores 7.5 Knowledge in the Regime Formulation 7.6 Knowledge in the Linear Evaluation Function 7.7Risk  102 102 103 105 107 109 111 116  8. Conclusions and Future Research  118  9. Literature Cited  122  V  LIST OF TABLES  Table 2.1 Disadvantages of mathematical programming approaches in forestry  20  Table 2.2 Advantages of knowledge-based models  33  Table 3.1 Scenic beauty scores  42  Table 6.1 LINDO solution scores  70  Table 6.2 Coolangubra test case scores for PINEPLAN  72  Table 6.3 Coolangubra test case scores for StratSearch-1  74  Table 6.4 Coolangubra test case best strategy comparisons for StratSearch-1 (random stand order) 78 Table 6.4 (Continued)  79  Table 6.5 Coolangubra test case best strategy comparisons for StratSearch-1 (area weighted random stand oider) 83 Table 6.6 Bombala best strategy comparisons for StratSearch-1 (random stand order)  85  Table 6.7 Coolangubra test case scores for StratSearch-2  89  Table 6.8 Coolangubra best strategy comparisons for StratSearch-2  91  Table 6.9 Bombala best strategy comparisons for StratSearch-2  .94  Table 6.10 Coolangubra strategy comparisons for StratSearch-3  95  Table 6.11 Bombala strategy for StratSearch-3  96  Table 6.12(a) Coolangubra strategy improvements for ES-i  97  Table 6.12(b) Bombala strategy improvements for ES-i  .98  Table 6.13 Strategy improvements for ES-2  99  Table 6.14 Timber flow scores under risk for Coolangubra  vi  101  LIST OF FIGURES Figure 3.1 Plantation management areas  .36  Figure 3.2 Coolangubra S.F. Age Class area distribution  44  Figure 3.3 Bombala District exotic conifer plantation age class area distribution  45  Figure 4.1 Example thin_rule database  54  Figure 4.2 Ordered list of regimes produced by example thin_rules database  55  Figure 4.3 Thin_rule database for standard regimes  56  Figure 6.1 Coolangubra StratSearch-1 exploratory search with random stand order all scores 75 -  Figure 6.2 Coolangubra StratSearch-1 exploratory search optimal scores  76  Figure 6.3 StratSearch-1 Timber flow scores (sorted) using upper limit of 60,000m3/yr and random ordering of stands  77  Figure 6.4 Coolangubra StratSearch-1 exploratory search with area weighted random stand order all scores  .81  Figure 6.5 StratSearch-1 exploratory (area weighted random) search optimal scores  82  Figure 6.6 Bombala StratSearch-1 exploratory upper limit search all scores  84  -  -  -  -  Figure 6.7 StratSearch-2 exploratory search all scores -  Figure 6.8 StratSearch-2 exploratory search optimal scores -  Figure 7.1 Potential linear evaluation function  90 115  vi’  ACKNOWLEDGEMENTS I would like to thank my supervisor, Dr Peter Marshall, for his assistance and enthusiasm throughout my stay in Canada. I would also like to thank the rest of my supervisory committee, Drs Tom Hall, John Nelson, Richard Rosenberg and David Taft, and others in the Faculty of Forestry, notably Drs Tony Kozak and Valerie LeMay, for their support and teachings on forestry and life. An acknowledgement is also clearly due to the Forestry Commission of New South Wales for their financial support and provision of data. I also acknowledge the financial support offered by the Institute of Foresters of Australia, the Donald S. McPhee Fellowship Fund, and the University of British Columbia through their Graduate Fellowship. -  I would also like to acknowledge the comradeship of the “Hut 6ers, some of wham have  shown me the way to the end of a Ph.D. program, and others who helped push me along that way. I would especially like to thank Bill Riel for the regular and required “Coffee and Philosophy” sessions that kept me sane when my Artificial Intelligence programs were acting unintelligently. I would also like to thank my family for their support and encouragement. Thanks especially to Jacquie, who sat through more about forestry and computers than anyone should need to bear, and yet continued to be patient, and interested, and helpful whenever she could. Finally, I want to acknowledge the influence of my Dad who wasn’t able to see the conclusion of this part of my life. His pride in his children was not coupled with any demand but only with love, and it strengthened and allowed us to reach out to achieve so much. Thanks for your strength and for teaching me to see the good in people. To God’s glory....  viii  1. INTRODUCTION  1.1 PROBLEM STA TEMENT Foresters share with all managers the problem of planning the efficient allocation of the resources under their control. Forest managers also face the dilemma of efficiently generating both politically and technically feasible plans that provide for a wide variety of forest uses and conditions (Fox et a!. 1988). They must solve this dilemma in a decision-making environment characterized by (1) increased public demands and scrutiny, (2) conditions of limited time and limited funds, (3) production processes of a long-term nature which are not predictable with absolute precision, and (4) knowledge that is complicated and difficult to incorporate into the -  decision process. In forestry, allocation is the decision on where, when, and how much to thin, fertilize, clear or otherwise treat the forest. This action, called operations scheduling, has been undertaken by foresters since the profession began (Wilson 1971). The desired objectives of operations scheduling can vary widely. These objectives also vary over time as product demand, and the relative value the company and society places on various resources, change (Dykstra 1990). Public demands and desires for the various resources produced by forests (e.g., timber, range, water, recreation, wildlife) continue to expand. These demands lead to objectives that may be qualitative or quantitative at stand or forest levels. The forest itself is not static; it grows, decays and otherwise changes significantly over time. Forest management must be able to generate a framework for action which permits swift adaptation to changing circumstances. Operations schedules and plans must be able to keep  1  Introduction pace with, or anticipate these changes (Dykstra 1990). Foresters must provide good 1 plans for the immediate planning period which do not compromise future flexibility (Nelson and Brodie 1990). Plantations and intensively managed forests have a large capital investment and inefficient management can be very expensive. Legal and moral restrictions may lead to the development of prescriptions designed to protect specific values and thus enforce good management in a wider perspective. The increasing complexity of forest management is accompanied by a more intense public scrutiny of governmental and private management decisions (Fox et aL 1988). “There is no doubt that the job of the forester has become much more difficult in recent years” (Jeffers 1989).  -  Much of the current forest management planning is based upon large-scale mathematical models of the linear or nonlinear programming type (Casti 1983). MAXMILLION (Ware and Clutter 1971), Timber RAM (Navon 1971; Chappelle eta!. 1976), MUSYC (Johnson and Jones 1979), FORPLAN (lverson and Alston 1986) and RADHOP (Brack 1983) are examples of mathematical programming models that have been used. Mathematical programming models are an elegant approach to forest management planning. However, there are non-trivial difficulties with structuring forestry management problems as mathematical programming models. These stem from the basic system theoretic structure (Casti 1983). The constraints of real life situations are also often too large for the computers available to practicing management foresters to handle (Gadow 1988, Hoganson and Rose 1984).  1  A good plan is defined for this dissertation as one that meets the objectives and priorities of the landholder. Different people may classify different plans as good.  2  Introduction The Forestry Commission of New South Wales manages over 170,000 ha of exotic conifer plantations. Pinus radiata (D.Don) is the dominant species, chosen because it is suitable to a wide range of soils and climate, produces excellent all-purpose wood fibre, and responds to economic investment (Home 1986). In the 1970’s, the Forestry Commission adopted a mathematical programming approach to the scheduling of its extensive plantation operations. The plantations are roaded at establishment, dividing the estate into about 3,500 compartments of approximately 50 ha each. The compartments are planted with nursery seedling stock at densities of between 1200 and 1800 stems/ha. Many of the seedlings receive starter and booster fertilizer treatment to enhance the short and long term potential of the plantation estate. Competition from unwanted species may be controlled by physical site  preparation, annual chemical weed suppression, and judicious placement of fertilizer (Home 1986). Competition between the planted trees is manipulated by thinning operations. In general, Commission employees mark trees for removal or retention in commercial operations. These plantations represent a large capital investment. There are also a large number of potential management strategies that can be applied to the forests. Furthermore, the plantations are a public resource, open to public scrutiny. Thus, the operations scheduling is an important and complex task. The mathematical programming approach used for these plantations was based on the work pioneered by Clutter (1968) and was named RADHOP (RADiata Harvesting OPtimisation). However by 1985, RADHOP had been discredited by solutions that were impractical, complex and contained errors. A simulation model, PINEPLAN (Brack 1988) subsequently replaced RADHOP, primarily due to the desire for local (field or District) control and ease of understanding. However, this model was also unsatisfactory because a lot of professional time was needed to find a solution, which then had no guarantee of being very good. The simulations also use the  3  Introduction solution bases provided by the last RADHOP runs to provide a starting point. As the old RADHOP bases becomes less applicable, the simulation solutions become potentially less good arid more difficult to achieve. A better operations scheduling approach is required for the efficient allocation of the substantial plantation resources controlled by the Forestry Commission. The Timber Industry Strategy (developed for the state government of Victoria, Australia) directs that procedures be developed for integrated planning for multiple-use of forests (McKenney 1990). This implicitly assumes that the current techniques are insufficient for the complex task of multiple-use forest operations scheduling and that new approaches are needed.  i.2 OBJECTIVES  -  The objectives of this dissertation are threefold: a)  to demonstrate that the explicit incorporation of spatial constraints, flexibility, stand arid forest level goals, and qualitative objectives can be achieved through a generalized model that uses a knowledge-based approach;  b)  to develop an operations scheduling support system for finding good, realistic solutions to an operations scheduling problem in the presence of operational constraints and management goals;  C)  to examine the effect of introducing risk and realistic qualitative objectives in addition to the traditional goal of maximizing volume from a forest.  4  introduction 1.3 OVERWEW This dissertation initially describes the requirements of an effective operations scheduling support system. It will be shown that the traditional mathematical programming approaches are unable to meet all the needs of a decision support system in a complex plantation environment. The potential for a knowledge-based or artificial intelligence system is also examined. It  is shown that the application of artificial intelligence tools and knowledge about the management problem has the potential to significantly assist the forest manager. Using a small plantation forest, a series of knowledge-based operations scheduling support systems are developed. These systems apply knowledge gained from the procedures used in game and puzzle solving, as well as forestry domain knowledge. The domain knowledge is derived from published management p1ansand from my experience with operations scheduling in Australian plantations. The systems developed include random, weak, and heuristically controlled search models and expert systems. The types of systems developed are unique in the forestry literature. No published system has attempted to apply knowledge-based models to solve complex operations scheduling problems at both the stand and forest level. The systems developed are shown to provide significant assistance in solving the operations scheduling problem. Using the developed models to solve problems for a test plantation as well as a larger plantation enabled the effects of risk and inclusion of qualitative goals to be examined. New ways of examining and dealing with muftiple goals and risk in forest management are introduced as a result of these analyses.  5  introduction The models developed can be used as prototypes for general operations scheduNng systems. The growth equations and the stand and forest knowledge-bases may be easily changed. Such changes will allow the models to be used in a variety of forest types and management environments.  6  2. LITERATURE REVIEW  2.1 OPERATIONS SCHEDULING SYSTEM REQUIREMENTS Planning in most forest operations is a complex task that can result in major financial losses if done improperly (Robak 1989). Forest planning systems in the 1990’s and beyond will need sophisticated computer information processing and knowledge-based management systems to access data for decisions. Assuming that the manager can get these data, the systems must be integrated in a way that permits forest managers to visualize the multi-resource tradeoffs associated with management decisions, and then brought into the decision process to produce schedules that are sound and defensible (Fox etaL 1988; Dykstra 1990). Success or failure of a support system lies not in having the latest technology, so much as in ideifng the mind processes of the users who will use the system when it is in place, and in providing information in a form compatible with those processes (Gordon et al. 1987, Baskerville and Moore 1988). However, most systems that have been developed to help managers plan their operations fail in a number of important areas. They are not helpful in considering the whole scope of the problem, often concentrating on specific, narrow parts of the larger planning tasks. Integrated planning of the entire operation is not facilitated. This integration must extend at least to the stand and forest levels, and Johnson (1989) believed it should extend to the growing and ulitization of the resource. It must also extend to include the various objectives that management must consider, both quantitative and qualitative. Erdle and Frame (1990) suggested that forest management planning should extend beyond the design of management to include the identification of limitations and useful guidelines  7  Literature Review for research and development. A decision support system should reveal impending management problems and potential opportunities. Often the users do not want to know just the answer, they want to know the details involved in a good answer. Some of the existing systems may answer simple questions, but these are often not sufficient. Kidd (1989) condemned the rigid dialog and user interlace of many information systems. Managers need to know more than even most Expert Systems are designed to provide. The types of questions and control that people want when dealing with a management support system are similar to those asked of a consultant. These include: 1.  the user volunteers constraints on the solution space at an early stage in the problem evaluation.  2.  a negotiation of-asolution between theuser andthe-consultant. Early first approximate solutions should be generated and then negotiations over their acceptability may lead to improvements.  3.  explanations that enhance the user’s understanding of the domain. The user does not want just a sensitivity analysis, or a list of the mles used by an expert in arriving at a solution.  4.  the user wants a comparative answer. For example, which is better X, Y or Z?  Mendoza (1987) believed that effective planning and information systems must be interactive (i.e., involve periodic feedback from the decision maker). He stated that it is apparent that an analyst-decision maker interaction is essential, particularly in complex planning problems such as multiple-use forest management. Amell et a!. (1991) also found that many forest managers wanted computer assistance in their decision-making, but they wanted to retain control by using tools that were specifically designed to interact with the user.  8  Literature Review  Bramer (1983), while discussing look-up tables that determine the moves a computer would recommend, stated that certificates of humanoid morphology should be demanded before responsible tasks of high complexity are entrusted to machines. That is, the manner in which the recommendation is arrived at should be understandable by a human. People are afraid of computers making the decisions (Saarenmaa 1989). But, according to Saarenmaa, the real dangers of decision support systems are that computer-made decisions can be less good than man-made and nobody will take responsibility for them. This may be particularly the case it the managers do not understand how the solution was developed. However, models can contain too much detail and resolution (Brand and Penner 1990). They become too sophisticated in equipment and operator experience to be of any use. Very sophisticated models may also need powerful-computers that are only available at central locations that are remote from the user. Thus, the user may be isolated from the model and treat the model answers with suspicion. A decision support model must find the balance between too little and too much detail. In summary, a forest management system must not simply provide more information. The goal is better information use in forest management decision making (Baskerville 1988). The system must support and enhance the managers judgement and improve effectiveness of management rather than efficiency (Guariso and Werther 1989). The management system must enhance the foresters view of the whole problem, spatially and temporally. It must be responsive to the quantitative and qualitative objectives and users needs, allowing consultant-like control and explanation. Finally, it must produce understandable results and be user-friendly.  9  Literature Review 2.2 MATHEMATICAL PROGRAMMING  Theoretically, mathematical programming (MP) approaches meet many of the requirements of a good management support system. However, a number of basic problem areas reduce the usefulness of a MP approach to operations scheduling. Some of these problems may be ameliorated with the introduction of more powerful computers and more efficient models. Other problems appear to be inherent in the need for adaptation of the approach to account for complex operations scheduling problems. Several authors conclude that MP approaches could, at best, only be a part of the operations scheduling solution. Hoganson and Rose (1984) concluded that mathematical programming models cannot sufficiently capture the reality of the management problem, and that their only use can be to provide the managers with additional data. For example, Paredes et aL (1988) used the allocation-evaluation aspect of MP to determine the cost or value of non-market resources. Allen (1986) used MP to find a true non-inferior set of solutions to aid in objective preference determination. Brodie and Haight (1985) praised the advances made in MP software and their potential use for studying (but not soMng) integrated management concerns. Garcia (1984) thought that MP tools should be used in conjunction with search models. This complementary approach would allow the mathematical programming tool to evaluate all possible combinations of a simplified problem while the search model could evaluate a small proportion of the possible alternatives and answer the users questions about sensitivity. The following five sections will discuss the difficulties of solving complex operation scheduling problems with MP.  10  Literature Review 2.2.1 PROBLEM SIZE Mathematical programming approaches traditionally solve operations scheduling problems by aggregating forest stands into homogeneous classes and developing a set of management regimes for each class (Hokans 1984). An estimate of costs per unit area and responses for each combination of class and regime is then used as the basis for allocating area by land class to each regime. Development of all the feasible and worthwhile management regimes is an increasing problem. The new forestry ethic, or ecophilosophy, is calling for knowledge-intensive, natural management. More emphasis must be placed on stand level decisions in forest management (Bullard et aL 1985). That is, management regimes must be related to the specific area and  consider factors like soil, topogfaphy, neighbors, cultural and spiritual significance. Chief Roger Jimmie (Jimmie 1990) believes management should consider the whollistic (sic) forest, including “Maybe squirrel he climb that tree  ....“  Simplistic management regimes, (e.g., clear the oldest  stands first) are not acceptable. The number of possible management regimes that can be applied has also increased due to a willingness to invest more money in forest operations. When there is no investment money available, many treatments, otherwise economically sound, cannot be applied and hence do not need to be considered by management. Governments and industry seem to be getting the mandate to spend more money on intensive management (Reed 1990). Intensive management allows many silvicultural tools and treatments to be applied. In Canada, these treatments may include enrichment plantings and thinning. In New South Wales, additional treatments may include post-thinning fertilizer and multiple lift pruning. Marshall (1988) notes the best management strategy for a forest may not be composed of the optimal treatments for each of its stands. Planners must simultaneously consider the stand  11  Literature Review  and the forest in their planning and this is the most demanding task in modern forest management planning (Gadow 1988). Thus sub-optimal stand treatments may need to be included in an analysis in order to find the optimal forest management. Eriksson (1983) noted that unless all the necessary conceivable columns (stand treatments) are included, an optimal solution will not be found by a mathematical programming algorithm. He developed a column generation model to efficiently include extra columns in a mathematical programming model, but still notes that the solutions may not be optimal. The effectiveness of FORPLAN’s linear programming matrix generation is very sensitive to the number of columns (Johnson and Crim 1986). Without data aggregation, the number of stands and the number of regimes that can be applied to each of these stands can cause a mathematical programming model to be very large. The analyst must determine which regimes are reasonable (Jamnick 1990), and unless the problem is already well bounded and known, this is not a trivial task. The quality of the solution will depend on how well the analyst was able to include important regimes. The number of constraints or rows can also cause size problems in a mathematical programming formulation. Johnson and Crim (1986) concluded that the FORPLAN linear programming solution is very sensitive to the number of constraints. In a plantation, these constraints typically include limits on the volume produced each year in various size classes, clearfall areas, seasonal constraints, road usage limits, etc. Again, the constraints cannot be aggregated over years without introducing a bias in the solution and the loss of valuable information. Spatial and adjacency constraints are often excessive. Torres-Rojo and Brodie (1990) developed a heuristic to develop the smallest number of adjacency constraints. Complicated constraints may also need to be added to the model formation to allow non quantitative factors to be considered in the solution. For example, it may be necessary to specify  12  Literature Review  that a regime be applied to either one or another unit in order to meet some specific management goal. This either/or constraint can be included in a mathematical programming model through the addition of two constraints and an integer variable thus increasing both the number of rows and columns in the model formulation. If stand identity is not important, the linear program can be formulated as a model II problem (after the classification of Johnson and Sheurman 1977). Such a formulation may decrease the number of columns (at the expense of a slight increase in the number of rows) and hence make the matrix generator solution algorithm more effective. FORPLAN can use model I or model II formulations (Johnson and Stuart 1986). However, in the plantation situation, model II formulations are not very effective because spatial information is important and should not be lost and the potentially large variety of cultural and thinning operations makes the collection of shnllar land units unlikely. Other methods to overcome the size problem with mathematical programming include decomposition algorithms. Dantzig and Wolf (1960) and Hoganson and Rose (1984) decomposed the problem into a series of subproblems which were tied together by dual values. Williams (1976) divided the problem into two phases. A linear program model handled the linear allocation problem at the forest level, while the linked stand level problem was solved through a network formulation. Decomposition approaches can handle more complex models, however there is still a limit on the number of forest wide constraints. O’Hara (1987) considered that decomposition approaches were still unable to handle realistic operations scheduling problems because there are an enormous number of constraints that need to be considered, especially when spatial considerations were important.  13  Literature Review Finally, Paredes and Brodie (1988) reported an increasing consensus among staff and practitioners that the size of linear programming solutions is beyond their capabilities to fully and readily interpret and analyze. Thus, operations scheduling problems are too big to be effectively solved by mathematical programming techniques, and even if they could be solved, the solution may not be acceptable to the managers. The mathematical guarantee of convergence to an optimal solution in a finite number of steps can amount to a warrantee that a solution will be obtained one day before doomsday (Glover 1978). Generally the time for a linear programming solution increases proportionally with the number of variables times the square of the number of constraints. However, the solution time may dramatically increase as the number of integer variables increases (Schrage 1986).  2.2.2 SOLUTION SPACE The regimes and constraints imposed in a model formulation bind the feasible solution space in a mathematical programming problem. However, uncertainty surrounds the desired output, market and non-market values, future management options, costs, growth predictions, etc. and it is clear that practical feasibility cannot be defined precisely (Hoganson and Rose 1984). The space within which the mathematical model will search may be unnecessarily small or restricted, and the optimal answer found may be highly inferior to a solution that was barely excluded by the constraints. A search of the dual values and right-hand side sensitivity analysis provided by most mathematical programming implementations may help to show where constraints have been excessively restrictive. These constraints may be eased and the problem resolved, thus reducing the effect of an unnecessarily tight restriction. However, practical problems may have too many constraints and interactions to allow this sort of sensitivity analysis to be profitably pursued.  14  Literature Review Mendoza (1986) provides a heuristic model to help determine goal programming target levels and this approach may also be used in constraint setting. In their decomposition algorithm, Hoganson and Rose (1984) only required that yield constraints be approximately met so the solution space was not so rigidly defined. Their approach was inherently integer, and strict flow equality could not be met (as in continuous decomposition approaches). Approximate constraint satisfaction was defined as being within 5% of the set volume constraint. This meant that their solution was much faster than the Dantzig Wolf (1960) decomposition which ensured that the constraints were always met. However, their algorithm was still restricted in the number of constraints that could be considered. Paradoxically, another problem with a solution space is that it may be too large, especially in formulations that include iritegervariables. Most mathematical programming tools  use a Branch and Bound approach to solve for integer solutions. This is essentially an intelligent search of possible ways of rounding the variables to integer values. By rounding to integer variables, the optimal solution may move from the boundary of the solution space to the interior of the hyper-dimensionally enclosed space. Constraints that are unnecessarily loose may cause a larger space than necessary to be searched.  2.2.3 RISKAND UNCERTAINlY In forest management, decisions are rarely made in an environment of certainty, but under risk (multiple outcomes with known probability) , or even more commonly under 2 uncertainty (outcome probabilities unknown) (Kao 1984). Dixon and Howitt (1979) identify three categories of uncertainty: 2  Statistical decision theory, on the other hand, defines risk in terms of a loss function, not as a measure of how much is known about outcomes.  15  Literature Review 1.  forest dynamics or growth,  2.  forest inventory or stock levels,  3.  preference function or objective.  Marshall (1987), on the other hand, classified uncertainty as coming from sources internal or external to the timber supply models: 1.  internal sources included simplifications required by the models, inaccuracies in the database, imprecisions in yield projections.  2.  external sources included the changing nature of the desired forest state, improper specifications of the returns, potential changes in political or policy decisions.  In-all but the most special eases, optimal decisions change when risk or uncertainty is explicitly recognized in formulating a problem (e.g., Lohmander 1990, Reed and Errico 1986). A mathematical programming solution is open loop, i.e., it data change unexpectedly there is no way to modify the decision variables to account for such changes (Casti 1983). The optimal solution is valid for the initial input data; if any part changes beyond a very restricted range, the solution must be recomputed with the new data set. Even in the intensively managed plantations of New South Wales, internal sources of error may be significant (e.g., height and basal area inventories are known within 3% and 5% error intervals respectively (x=0.05) (Brack 1988)). The effect of these uncertainties on the value of the mathematical programming solution is difficult to determine. Sensitivity analyses may be used to determine the effect of uncertainty on solutions. The values for predicted yields can be systematically changed, the matrix regenerated and solved (McKenney 1990). Uncertainty from external sources has to be treated similarly. The  16  Literature Review interpretation of the mass of results from these multiple runs would be beyond the ability of most practitioners. Casti (1983) outlined a method to determine which features of a solution are important and how great a change is allowable before a full recomputation of the problem is warranted. However, this method requires a dynamic programming model which probably could not handle the large model formulations needed in operation scheduling problems.  2.2.4 SPECIFYING THE OBJECTIVE FUNCTION In mathematical programming models, the contribution of each action is quantified through the objective function. In simple cases, the objective function may be defined as the sum -  of volumes produced or-the net-discounted revenue. However, these simple cases are very rare and management is increasingly forced to deal with objective functions that are not linear, actions producing non-tangible products, and contributions that are not easily quantified. At the cost of additional rows and integer constraints, linear programming models can include non-linear contributions in the objective function or even be turned into quadratic programming models (e.g., Schrage 1986). Model size and understandability is again a limitation. Dynamic and goal programming also extend the linear programming model to consider several goals simultaneously. They attempt to incorporate tangible and non-tangible contributions by providing a pseudo-quantification where necessary and then deriving a weighting strategy to provide for tradeoffs. Hotvedt et aL (1982) for example ranked non-inferior solutions for problems with multiple goals and then derived a weighting structure. Mendoza (1987) used an interactive approach with the decision maker periodically re-evaluating preferences.  17  Literature Review The contribution of an action to the objective may be related to the action applied to other units. For example, five adjacent stands cleared in one year produce a visually poor forest, whereas spacing out these operations over a number of years produces a varied and more attractive forest. The inclusion of such a contribution to beauty in the objective function is possible at the cost of increasing the number of rows and columns, including an integer definition and introducing a scalar variable (Schrage 1986). An added complication is that the value of the scalar is important; if it is too large, a solution may not be found, but it it is too small the objective function may give incorrect values. These types of spatial and non-linear contributions are generally either ignored in MP’s, or included as constraints. A large number of rows are needed to include spatial constraints, and -the problem of the- level of -these constraints remains. MUltiple runs with different constraint Levels may show the trade-off with the objective function value.  2.2.5 SOLUTION TYPE If a mathematical programming algorithm is provided with the proper model formulation, data tree of internal uncertainty and has sufficient time and computer memory, it is guaranteed to (eventually) obtain an optimal solution. However, the time spent in arriving at this solution is wasted if the solution is ignored by the manager. D’Avignon and Winkels (1986) felt that managers “do not believe in mathematics”, and thus the presentation of a mathematically guaranteed optimal will be met with little enthusiasm. They believed that managers prefer to obtain a set of reasonable and well explained proposals that they can understand and accept. The final decision is made by the managers own reasoning or intuition.  18  Literature Review Managers may not even be interested in a solution that optimizes any quantifiable goal, but rather one that is robust (Arrow and Fisher 1974, Henry 1974, Elton 1986). When commitments are made, a manager may prefer to make a small sacrifice in expected value in order to choose a robust solution. Warner (1983) concluded that the solution emphasis should be satisfaction rather than optimization. Bare and Mendoza (1988) conclude that traditional MP5 solve the wrong problem: optimizing a given system rather than designing an optimal system. They use a series of soft right-hand-side constraints and de novo programming to design systems of better performance. However, their test examples are small and relatively simple problems and the method is still limited by the problems mentioned in the previous sections.  2.2.6 APPLICABILITY Except for simple scheduling problems, MP’s are not effective operations scheduling  tools. This is the result of five basic problems (Table 2.1). Microcomputers are still limited in the size of MP problem that they handle, although the size has grown markedly in recent years (Johnson 1991). Thus, practicing management foresters will still be isolated from the model and may remain suspicious of the solutions provided by remote technicaI experts”. The number of columns in a MP may be very large if there are numerous possible management actions. The columns and rows are also very large if complex constraints or objectives are included. However, the size problem may be more related to interpreting the results than specifying the problem. The analysis of the reports generated by MP’s is not easy or trivial, especially when integer and accounting variables have been included.  19  Literature Review  Table 2.1 Disadvantages of mathematical programming approaches in forestry Problem  Description  References  Size  Large areas of forest with significantly different types of terrain and conditions may be involved in a problem. The potential regimes and constraints are numerous and variable, leading to a combinatorial explosion. Data aggregation leads to information loss and potential bias. Regimes for a stand are often mutually exclusive and affect neighboring units.  O’Hara 1987; Paredes and Brodie 1988; Hokans 1984; Barber 1985; For. Corn. 1984; Dantzig and Wolf 1960; Williams 1976;  Solution Space  Results are sensitive to the allowed solution space. Extrapolation is difficult. Uncertainty does not allow the solution -space to be definitely assigned.  Hoganson and Rose 1984; Casti 1979  Uncertainty  Risk or uncertainty is involved in the prediction of growth, yields, inventory, values, future management, etc. MP’s are essentially open loop, and there is no simple mechanism for understanding how the resufts change.  Casti 1983; Reed and Erico 1986; Marshall 1987; Marshall 1988; Kao 1984;  Objective Function  It is difficult to put a value on many aspects of a forest. Ranking is often the only option, and it is difficult to use this in MP approaches.  Hotvedt et aL 1982; Mendoza 1987; Paredes and Brodie 1988;  Solution Types  Solutions are often very complex, and cannot be easily understood by managers. They are often not robust, nor ‘friendly’.  Glover 1978; Elton 1986; D’Avignon and Winkels 1986; Dixon and Howitt 1979.  Control of the MP problem is limited to setting constraints and selecting regimes, but the effects of these controls are not obvious and can only be determined through multiple runs.  20  Literature Review Jamnick (1990) asserts that matrix generators and report writers essentially make MP’s easy to run and analyze. However, his problem was relatively trivial, with a simple maximize volume objective and no spatial or qualitative constraints. The MP model simply provides more information for the forest manager. It does not allow better information use in a complex forest problem; the user is unable to easily understand the solution, nor easily see the interaction between qualitative and quantitative goals. Therefore, MP’s are not very useful as decision support tools for operations scheduling in complex forest problems.  2.3 KNOWLEDGE-BASED MODELS -  Due to the diffkuity of finding the optimal solution to large problems with MP-techniques,  work has been devoted to the use of search techniques (Dannenbring 1977). Operations scheduling problems may be considered as a search through possible combinations of forest units and regimes. The problem may thus be formulated as a state space search and use some Artificial Intelligence (Al) tools. State space search is not clearly circumscribed and does not abide by the mathematical etiquette of proof, theorems, convergence, or optimality. However, search may be more desirable than mathematical programming when (based on Zanakis and Evans 1981): 1.  inexact or limited data are used to estimate model parameters or starting points.  2.  the problem uses a simplified model. This model will already be an inaccurate representation of the real problem, thus making an optimal solution only academic.  21  Literature Review 3.  a reliable exact method is not available, or is computationally unattractive.  4.  the results from the heuristic solution are better than the results from methods now used.  5.  simplicity is important so users can understand the process and are therefore more likely to implement the results.  6.  other limitations of computer resources, money, time, etc. apply. Large problems may be studied without encountering the “combinatorial explosion” problem because searches only need to deal with a limited sub-set of the combinations at any time (Firebaugh 1988)-.  -  Search approaches are also being used to simplify some mathematical programming packages. Glover (1978) for example, concluded that the usefulness of a particular integer programming algorithm can depend on its heuristic content. These rules are often used to prune the decision tree at an early stage (ignoring many possible avenues) and thus reduce the area that needs to be searched. Bradley (1971), Cooper and Drebes (1967), and Glover (1977) discussed the application of heuristics in mathematical programming. The commercial packages LINDO (Schrage 1986) and SAS (SAS Institute 1985) use a range of intelligent search heuristics to solve integer programming problems. In the forestry literature, search techniques have also been called simulation approaches, heuristic programming, heuristic procedures, heuristic algorithms, or heuristic optimization. Crookston and Stage (1989), Goforth and Floris (1991), Kourtz (1987), and Rauscher et  al. (1990) describe knowledge-based forest systems that may be considered to be complex decision trees.  22  Literature Review 2.3.1 RANDOM SEARCH  Random search may be used when the rules or heuristics to direct the search are not known and the systematic app’ication of arbitrary rules is not sufficient. A range of possible directions are known, but it is often too large to enumerate and test to determine how the search should be directed. Random searches randomly generate many search patterns. The results from these searches are evaluated and the best selected. The success of a random search in providing near-optimal solutions depends on three factors: 1.  the magnitude of the objective function values for a problem;  2.  the shape of the right-hand tail of the probability density of oecve vues  -  3.  the ability to model a large number of random solutions (i.e., fast computer algorithms).  If the objective function values are large, or the right-hand tail of the probability density function is skewed, any solution that is not the optimal may be significantly lower in value. If the objective values are small, or the density function sharply truncated, a large number of solutions will be very close to the optimal. The random search is not disciplined and the expansion of nodes or the direction of the search is not structured. The goal is to obtain at least one solution yielding an objective value within a specified subregion of the optimum or extreme. The theory behind its use relies on the premise: Given a finite number of [random] solutions, the relative frequency distribution of objective function values is bounded on the right by the maximum (Bullard et aL 1985).  23  literature Review  For any problem, the probability that at least one random solution yields an objective value within a sub-region of a probability density relation is given by: 1 -(1 -a)”. where: denotes the relative size of the sub-region (as a fraction). denotes the number of random solutions tried.  a n  This equation does not depend on the total number of possible solutions to a problem. This is important because the number of possible solutions may be finite but astronomical, particularly for operations of interest (Dannenbring 1977). Ills also possible to estimate the average time needed to find an optimal solution. If the optimal value is not known, and there are N possible states, then you must search all N states. If the optimal value-is known, you only need to search an average of 0.5*14 states if the states are  randomly ordered. However, if you onlywant to find a state that is close to the maximum, you would search an average of: 1 P(x,Q) where: P(x,Q) denotes the probability that state x is within Q of the maximum. This relationship again does not rely on the total number of possible elements, but does require knowledge about the true maximum. Cooke (1979) proposed a model that would estimate the true optimum for a random search. Using an ordered set of values (Z ,Z 1 , 2 Optimal Z  =  ) (e-1) 1 (2*Z -  *  .  .  .  1*e Z  Z  where e denotes the Naperian constant. Alternatively, if the shape of the objective function density curve is known, an estimate of the optimal value confidence limit can be made. For example, the minima can be estimated from  24  Literature Review  an ordered list [Z 1 ,Z ,. .,Z,J, using the following confidence limit formula for a Weibell 2 .  distribution (Golden and Alt 1979): confidence limit alpha = 100 * (1  -  e)  1 >Z SothatZ 1 > 0 Z -b where: denotes the estimated minimum value 1 ) a=Z 1 2 -(Z Z b  =  Z[Q 63*n+1] a -  n denotes the number of iterations.  [1 denotes rounding down of the result. Golden and AlL (1979) refined their estimates of a and b, but Zanakis and Evans (1981) and O’Hara (1987) suggested that this is unnecessary. Bullard et a!. (1985) described a model to determine the optimal residual stocking in an uneven-aged forest. A practical range of residual stocking was determined. Random numbers of trees to cut from all classes recognized were generated and yield flows modelled. Cutting combinations not meeting volume or other constraints were rejected. For multiple growth period problems, the random solutions were generated sequentially, period by period. The objective value was calculated for each valid combination and compared with the incumbent. The higher value and associated thinning regime was stored. With a fast computer, thousands of regimes could be modelled. SCRAM (Spatially Constrained Resource Allocation Model OHara 1987; O’Hara eta!. -  1989) determined the thinning schedule where constraints on logging areas adjacent to units logged in the previous one, two or three periods applied. This model randomly selected an available stand for harvest, checked the volume constraints, and then flagged the adjacent units  25  Literature Review as not available until the corresponding time period had elapsed. The process was repeated until all units were harvested or an infeasible solution found. One hundred solutions were generated and the best schedule and an estimate of the true optimal value obtained. The random selection of the available units could be biased by different weighting attributes. However, O’Hara lamented that SCRAM did not take advantage of the growth characteristics of the stands. He noted that rapidly growing stands should be allowed to grow (i.e., harvested in later periods), while slower growing stands could be harvested in earlier periods. Clements eta!. (1990) and Nelson and Brodie (1990) also developed search models that used a random ordering of the units. Nelson and Brodie found that the search models arrived at conclusions that were very close to the optimal solution found by mixed integer programming.  2.3.2 BLIND SEARCH Some search examples used in forestry involve weak or blind searches and have no information to estimate the value of going through any particular state space path (Le., they use no domain knowledge). Simple rules select a decision (i.e., which operator will be applied in which order). The results of following this path are modelled. Revised rules may alter the proposed path, and the new results are modelled. This process may be repeated until some goal or limit is reached. Blind searches examine some or all possible combinations of units within the feasible solution space. The search is normally directed by the systematic application of a simple rule (e.g. clearfall the next largest volume stand in the current period until some constraint is met). The objective function for the terminal state using this simple rule and the validity of constraints may then be assessed. The simple search rule may then be altered and the search repeated from the initial state. The wood supply model FORMAN (Wang eta!. 1987) for example aflows  26  Literature Review  the user to select from a list of systematic search rules. The search is made, then the model may be rerun using a ditferent rule for the search. There are advantages to using a blind, non-random approach. Pearl (1984) considers that the major advantage is that the problem can be split into subsets of potential solutions. This allows an enormously efficient split-and-prune method to be used. Pearl used a game called the 8-queens puzzle to demonstrate the advantage of splitand-prune. To win this game, eight queens must be legally placed on a chess board. A legal position is where no queen can attack any other queen (i.e., two queens cannot occupy the same vertical, horizontal or diagonal row). A partially filled board (i.e., part of a potential solution) can be examined. If it fails (i.e., two queens can-attack), then all the-potential solutions that include this part can be pruned and not examined. If it does not fail, the potential solution can be further refined by adding another queen anywhere on the board. The resulting potential solutions can be examined, rejected ones pruned and successful ones further split. This method guarantees that subsequent refinements will not generate potential solutions that have already been rejected (Le., it is not wasteful). The method also guarantees that no potential solution will be overlooked. The approach is basically a breadth-first search which can efficiently prune itself. Assuming that no board can be repeated, there are a total of 64*63*62*...*57 or 1.8*1014 possible boards that can be generated. If there are 100 winning positions, then a randomly generated board has a probability of 1.8*1012 of being a winning board. On average, you would need to examine over 200 million randomly generated boards before there was a 50% chance of finding a winning board. The split-and-prune method has an initial 64 boards, but by eliminating the column, row and diagonal of the initial piece, each refinement has only 42 legal boards left. Add another piece, eliminate the illegal options, and each refinement has a maximum of 32 legal  27  Literature Review  boards and so on down to smaller legal refinements. Thus, the total number of boards examined is about 9 million and a solution is guaranteed. The random approach does not prune sub-sets of potential solutions. Certain search algorithms will model every possible path. These exhaustive searches can find a true optimum (Le., the largest objective function). Other search algorithms may use the split-and-prune method to search every legal board refinement, thus finding an optimal solution more effectively. OHara (1987; O’Hara eta!. 1989) developed an exhaustive search model that could deal with a maximum of 25 cutting units over five time periods. It scheduled the optimal felling iii the presence of spatial constraints that excluded the logging of stands adjacent to a stand logged in the previous one, two or three periods.  -  -  PIN EPLAN (Brack 1988) is a simple search model. PINEPLAN is used by the Forestry Commission of New South Wales for scheduling the yields from its exotic conifer plantations. This package simulates the growth and yield of a cutting unit using a silvicultural regime provided by the user. Simple tables present the yields, by product type, from all the cutting units. The user may then aLter any of the regimes for any cutting unit to try to improve the yield flow. Hence, a solution is found and then the user may search for an improved solution by changing selected unit I regime combinations. The user is basically searching the state space. The package has some simple rules to stop ridiculous regimes, but basically the forester using the package must use his/her own knowledge to define the appropriate regimes and search for better combinations. Other examples of the use of search routines in operations scheduling include the Economic Harvest Optimization (ECHO Sessions 1977, Walker 1971) model and Timber -  Resource Economic Estimation System (TREES Tedder eta!. 1979) model. These systems -  assume a harvest priority for the cutting units. This priority is, in effect, the control heuristic. The  28  Literature Review search will systematically apply the operators to the next stand on the priority list. The priority may be set by policy decisions. However, an inappropriate priority may easily lead to sub-optimal solutions. There do not appear to be any examples of more sophisticated structured searches in the forestry literature.  2.3.3 EXPERT SYSTEMS The formal definition of an expert system is not clear. Often it is defined in terms of what it should accomplish and how it should behave. Rauscher and Cooney (1986) simply state that an expert system should organize and store the logical intelligence of one or more people on a -  -  particular subject. Moore (1989) states that an expert system should  1.  beeasyto use.  2.  eliminate routine decisions by inexperienced users.  3.  incorporate knowledge by experts in the form of the program flow and access to quality software.  Firebaugh (1988) gives a general definition of expert systems as: a class of computer programs that can advise, analyze, categorize, communicate, consult, design, diagnose, explain, explore, forecast, form concepts, identity, interpret, justify, learn, manage, monitor, plan, present, retrieve, schedule, test, and tutor. They address problems normally thought to require human specialists for their solution.” “.  .  .  Schank (1988) believes that Al systems are not defined by their methodologies, but what problems these methodologies attack. He considers that the most important problem is learning. An Al program that does not learn is not an intelligent program (Schank 1988).  29  Literature Review  An expert system differs from a search system in five ways: 1.  the heuristics can be more sophisticated, (e.g., qualitative rules, quantitative rules and probabilities).  2.  the expert system should be able to explain or justify the decision. Firebaugh (1988) considered this aspect to be one of the major distinguishing characteristics.  3.  a search system is normally based on only one or two simple systematic rules, while expert systems have databases which can exceed 500 rules.  4.  the algorithms in the search systems tend to be imbedded into the computer program aflowing no flexibility. Expert systems tend to have rule or knowledge databases which can be updated easily without affecting the program. The knowledge database is separate and may be improved (i.e., new knowledge may be added or learnt).  5.  knowledge about the unsearched portion of the domain is used in determining the direction of the search.  Walters and Nielson (1988) give as prerequisites for the successful development and use of an expert system: 1.  no known or acceptable algorithmic solution.  2.  an human expert’s solution is satisfactory, but problems arise. For example, the solution may be too costly or untimely.  30  Literature Review  3.  decisions made by other than an expert are likely to be different. These differences will have a significant impact on financial cost, resource consumption, delay, risk, etc.  Schmoldt and Martin (1986) developed an expert system to help diagnose pest problems in red pine (Pinus resinosa, Aft) stands. The system, named PREDICT, recognized 28 different symptom causes and used over 400 rules. The system can monitor and identify an insect pest. It can also diagnose pests that are most likely to attack a stand and suggest controls. They developed this system because keeping abreast of current research and development in all the relevant fields is virtually impossible and some assistance is necessary. As forest pest management problems are based on judgement and experience and do not lend themselves to precise quantification, mathematical programming tools cannot provide this assistance. However, they believed that an expert system could effectively deal with incomplete and uncertain information and thus be a very useful system. CHAMPS is a sophisticated forest managers decision support tool (Rauscher and Cooney 1986). An expert system component helps select cultural practices for stand management. The system recommends a practice to achieve management goals. The rules in  its database are derived from the following sources: 1.  a series of managers handbooks published by the USDA Forest Service (timber management related rules).  2.  published work from John Mathisen, a wildlife biologist (wildlife management related rules).  3.  work from the USDA Forest Service’s “Watershed Management Project” (watershed management related rules).  31  Literature Review 4.  discussions with foresters of the Itasca County Land Department (local management related rules).  Hokans (1984) used an Al approach to improve the effectiveness of a linear program solution to forest management. The forest had to be aggregated into homogeneous classes to make the solution space small enough for the linear programming tool to solve. After the regimes were optimally allocated to these classes by the linear program, the area of each class needed to be made up by forest units. A discriminate function ‘learned’ how a forester selected units to make up the area required in each management class by recording selections made by the forester and then finding common attributes (e.g. average distance from each other). Other examples of expert systems in forest management include Schmoldt and Martin (1986), Power(1988), Rauscher andHacker (1989>, Reinhardt eta!. (1989), Jamnick (1990),  Johnston eta!. (1990), O’Hara eta!. (1990), Yang (1990) and Berry eta!. (1991). Davis and Clark (1989) and Lamberl and Wood (1989) also gave a number of references to expert systems being applied in the natural resource management field. They concluded that natural resource management is only lagging about three years behind the expert system trend setters. However, none of these systems deal with the detail or the complex interactions needed when scheduling a variety of operations over a whole forest.  2.3.4 APPLICABILITY Knowledge-based models clearly have a potential for use in operations scheduling problems. They can produce useful solutions and may not be restricted by the theoretical and practical problems associated with mathematical programming models (Table 2.2).  32  literature Review Table 2.2 Advantages of knowledge-based models Problem  Comment  Size  Excepting exhaustive searches, the problem size has little effect on the solution. Very large problems may require overnight (or longer) periods to generate enough random solutions to ensure a good solution is found.  Solution Space  Limited only by the control heuristics. Can be altered interactively by the decision maker.  Uncertainty  Stochastic modelling and probability based rules may be used to incorporate risk and uncertainty.  Objective Function  Can be very flexible. Can easily include qualitative measures and the contribution of groups of actions.  Solution  Potentially very good solutions available. Solutions are understandable and easily revised. Search models are simple and easily understood by the manager, while expert system  approaches generally include explanation features that can enhance the usefs understanding of the solution process. The user can have direct control of the problem solution, and generally the models are very fast allowing multiple runs to show quickly the effects of changing parameters.  33  3 METHODS  3.1 INTRODUCTION The basic tenet of this research is that incorporating more knowledge into a model will lead to a better operation scheduling solution. Initial models were developed which used little knowledge. As shortcomings in these models were observed, domain and procedural knowledge were added to improve the model efficiency and accuracy. Hence model development was incremental as the amount of knowledge used by the model increased. A sequence of models was developed, ranging from simple disciplined search models to an expert system. The remainder of Chapter 3 describes the data used in model development and testing. Chapter 4 describes the development of the knowledge-based search models. Art exhaustive search algorithm is discussed but not tested, then three search models are developed. The first two models use both random and heuristic approaches, differing only in the amount of knowledge used in their control. The final search model is a non-random model. Chapter 5 describes the development and use of an expert system toolbox, and two expert system models. The models were developed to run on an IBM (or compatible) microcomputer (under MicroSoft DOS) so that they could be used by foresters at the local level. The computer used was a Toshiba T520011 00 running with 2Mb RAM at 20MHz with a 30386 and 30387 math coprocessor chip. Most of the model speed estimates are based on this machine running under Microsoft Windows, Version 3.0. This was a practical consideration as some of the runs required several hours of searching; the multi-tasking Windows environment meant that the computer would not be tied up all day. The models were developed using the PROLOG programming language. PROLOG is suited to developing state space search and puzzle-like programs because it is recursive and  34  Model Development uses declarative or logic programming. Turbo-PROLOG (Borland International 1988) is a DOS microcomputer version of PROLOG, and was used for the model development.  3.2 TERMINOLOGY Regime will be used to denote a particular sequence of thinning operations applied to one stand or unit. Strategy refers to a particular combination of regimes that are applied to the forest. A stand is a geographically distinct and contiguous area of forest that shares a common history and will treated by a common regime. It may be part of an age class or forest unit and is often a compartment or a small number of neighboring compartments. -  PROLOG programs are essentially a database of facts and clauses. Facts declare  something as true (e.g., compartment 1 is classified as a good site). This fact may be coded as: classification(good_site,compartment_1). Clauses are made up of two parts, the conclusion and the antecedent (or head and body). The antecedent may be made up of one or more premises. For example a clause may conclude that fertilizer should be added to a stand if the stand is on a good site and money is available. This could be coded as: action(fertilise,X):classification(good_site,X), money(available).  premise premise  conclusion antecedent  PROLOG programs are driven by a GOAL. The program proceeds by attempting to match any tact or conclusion in the database (program) with the GOAL premises. If a matching conclusion is found, it becomes a new GOAL and PROLOG searches to match its premises. A  35  Mode! Development GOAL succeeds when all its premises are matched. If any premise fails because a match cannot be found, PROLOG backtracks and tries to solve the preceding premise. Sometimes backtracking to preceding premises is undesirable. Backtracking can therefore be stopped by a cut. When the program logic passes a cut, backtracking to the preceding premises is disabled.  3.3 DATA Facts, rules, and expert guesses are the basic data requirements in knowledge-based models. For the models described in the next two Chapters, basic data were collected from the Plantation Management Areas of the Forestry Commission of New South Wales (Figure 3.1). -  These plantations essentially contain only one species of exotic conifer, Pinus radiats (DDon), and cover a range of marketing, environmental and historical conditions. Figure 3.1 Plantation management areas  athurst Llbury ombal a  AUSTRALI A  36  Model Development  Management Plans are prepared for each management area. These plans provide most of the domain rules used in the models developed. Where facts are related to specific management areas, the models allow those facts to be conditionally asserted. PIN EPLAN yield scheduling solutions and experiences were also used in the development of rules. I have been using and developing PINEPLAN for a number of years. My last scheduling problem was in 1988 when the operations on over 70,000 ha of plantation were scheduled in a tightly constrained market in the Albury region. That project took approximately five professional-months to arrive at a satisfactory solution. Most of the domain rules relate to the timing and intensity of thinning operations. This is because thinning operations are the most important and versatile tool in fast growing, intensively managed plantations. They can influence the qua[ityand quantity of most plantation products from fibre through to water and scenic beauty. Without carefully devised thinning regimes, other management tools may be ineffective. For example, fertilizer application may be economically justifiable if it is applied after thinning a well-developed mature stand, but uneconomic otherwise. The health of a plantation also relies on regular thinning because the initial stocking density is high. If the density remains high, stands may easily become stressed and subject to insect attack. Finally, thinning can produce a marketable product and hence a financial return that can immediately offset some of the cost of treatment.  37  Model Development The growth models used to predict volume in the search and expert systems were copied from PINEPLAN, which in turn were developed from RADHOP. Growth was estimated using the following models: Vi=MDHi*BARi*kj MDHi  =  (1.97*i 2 0.01286*i 1.1128) -  -  Scale  5 BAi BAR  BARi  =  1 BA  e*lnj)  =  *  -  +  4.189O8*(1A)  +  O.033759*(1A)*MDH o 2 )  where: V 1 MDHi BARi 1 BA BARs  Scale A BAj  denotes the volume removed at age i in m lha. 3 denotes the mean dominant height m) of the stand at age i denotes the basal area removed (m /ha) in an operation at age i. denotes the basal area at age i. denotes the residual basal area scheduled (m /ha) in an operation at age i. 2 denotes a volume conversion factor between 0.1 and 0.33. In PINEPLAN this is provided by the user based on experience with the unit and operation type. Average k values by age and operation were derived from the PIN EPLAN solutions denotes a ratio of known MDH at age j against an unscaled estimate of MDH at agej. is the ratio of age j I age i. denotes the basal area at an earlier age j.  These models were based on data collected from the plantations in New South Wales. The data represent a wide range of site quality, but thinning regimes were restricted to thinnings from below.  3.4 TEST CRITERIA There are two aspects that determine the success of the operations scheduling models developed: the model and the strategies produced as solutions. The evaluation of the models would require the assessment of a number of factors like usability, efficiency and understandability (Barreto et al. 1989, Schmoldt 1988, Slagle and Wick 1989); however, as this  38  Mode! Development research will only involve the development of working prototypes, only the potential for the model will be discussed. To evaluate the strategies generated by the operations scheduling models, three decisions must be made: what to test, what to test with, and what to test against (O’Keefe et a!. 1988). These are not trivial decisions, especially when it is difficult to classify a decision as right or wrong.  3.4.1 WHATTO TEST? The models developed in this research were designed to suggest good forest operation scheduling strategies in the presence of constraints. A good forest wide strategy must meet forest and stand constraints and produce acceptable levels of all the relevant forest products. These products include not only different qualities of timber volume, but also scenic, wildlife and environmental values. A forest strategy needs to be scored in terms of all these aspects. The scores for each model can then be compared and evaluated. To provide for comparisons, I developed a series of algorithms to score the strategies. These scores were designed to provide a quantitative value for qualitative factors and are used as indicators only. It is important that these algorithms are fast. For example, I tried to include a wildlife corridor criteria. With few exceptions, native animals do not extensively use plantations of exotic conifer in New South Wales. However, the plantations are often surrounded by habitat preferred by the native animals. If corridors exist through the plantation to these habitats, island ecology suggests that the wildlife will benefit. I assumed that a corridor would be provided where an animal could trace a path across the plantation using neighboring compartments that had recently been thinned or cleartelled. However, although this was a trivial programming task in PROLOG,  39  Model Development  paths needed to be evaluated every year and the potential number of routes was very large. One of the operations scheduling search routines only took 20 seconds to model a forest-wide strategy, but it took more than twice that long to determine it corridors were open every year. Thus the main requirement of a random search (Le., speed) was violated by including this scoring function. Including a Geographic Information System may have allowed better scoring functions to be used, but there was little spatial data and an appropriate system was unavailable. Timber Yields The value of a scheduled volume flow lies not only in the total volume produced, but also in how this flow varies between years. If the flow changes significantly between years, potential losses to the producer or manufacturer may result. It the yield drops significantly in one year, the manufacturer may have under-utilized mill capacity. If the yield rises significantly in one year, there may not be a market and the operation specified to produce that yield may become infeasible. The effects of missing that operation may be significant over time if it invalidates future scheduling operations or results in an over-stocked and unhealthy stand. A variety of timber products may be produced from a plantation (e.g., pulpwood, sawlog, veneer quality peelers). However for simplicity, in this dissertation only total wood volume will be considered. The following equation was used to quantify the timber yield flow for the 21 year planning horizon:  Timber=  1 21  2010 E  -  1=1990  where:  40  Model Development  1 x  denotes the volume produced in year i.  1 a  denotes a significant deviation to the mean volume for year i. If the difference is less than, 10,000, then 1 a  =  0, otherwise  11 a =UI-x 1 - 10000.  denotes the 21 year mean volume production. A high value indicates that the average yearly volume is high and that there is little deviation from year to year. If there is no significant deviation, the score equals .t. By squaring , a large difference is weighted much more than two or three small differences. 1 a The significant deviation is set at 1 0,000m 3 for this dissertation. Different values may be  appropriate for different industries and different forest scales; however, 10,000m 3 would be appropriate for many small industries and larger industries could easily cope with such a deviation. This dissertation also does not consider changing the volume limits during the planning horizon (e.g., 50,000m 3 for the first 10 years then rising to 1 00,000m 3 for the rest of the period). This change could have been easily incorporated into all models used, but would have made the comparisons between answers more complex. Scenic Beauty Scenic beauty is difficult to quantify, however a plantation site may be qualified as scenically attractive or less attractive (Forestry Commission of N.S.W. 1984). In a plantation, a poor rating may be due to an extensive area of clearfall or an extensive area of overstocked 4  Management Plan for Bombala Exotic Forests Management Area. Hereafter referred to as the Bombala MP.  41  Model Development forest. A good rating may result from a view of well stocked compartments in a variety of developmental stages. A selected road-side site may be classified in any year as poor, acceptable or good using a scheme such as that shown in Table 3.1. Table 3.1 Scenic beauty scores Category Poor  Value -1  Description Extensive recent clear fall area. Over 50 ha visible clearfallen in the last 5 years.  Poor  -1  Extensive overstocked areas. Over 50 ha of delayed thinning visible.  Good  +1  An area with a low occurrence of clearfall and overstocking. Less that 25% of visible area is clearfallen or overstocked and all visible area is over 20 years of age.  Average  None of the above categories.  0  A scenic beauty score for the first 21 years may be calculated as: 2010  Scenic-Beauty-Value  =  E  PV21.  ..1990  where: Pi  denotes the score of selected forest sites that are classified as good, average and poor in year i.  A fixed number of sites were selected in the forest and classified every year. The sites were along tourist roads or at prominent locations. A high value would indicate that the strategy  42  Model Development has produced a relatively attractive forest. If every selected site was attractive, the score would equal the sum of the number of sites. However, some sites could not be ranked as good, regardless of strategy, simply because they are too young. Stand Health Stand health is closely related to thinning and stocking levels. The Bombala MP states that well-thinned stands are less susceptible to snow damage (Section while areas overdue for thinning may have a greater problem with water stress (Section, windthrow (Section 1 .4.3.2), and fungal diseases (Section The Management Plans for the Bathurst and Albury Regions give similar outlines. -  The hectare-years of stands overdue for thinning was-used as an indicator of potential  stand health. This was multiplied by minus one for consistency with the previous scores (Le., larger scores (smaller negative) are better than smaller scores (larger negative)). A large negative value would indicate a potentially unhealthy forest. A value of zero would indicate that the plantation is well thinned. Water Quality Forestry operations near water courses may impact on water quality. In New South Wales, this impact may not be great because of the stringent controls on logging in wet weather. However, some loss of quality may result as runoff moves dirt into the river system. An undisturbed stand may act as a buffer and filter out the dirt if it lies between a water course and a stand in which an operation is carried out. Clearlall operations would probably have a greater effect on dirty runoff than thinning because there is more ground disturbance and probably less slash left. Therefore, the total  43  Mode! Development volume removed from operations on stands that are not buffered by undisturbed stands, multiplied by minus one, was used as an indicator of water quality. A large negative value, say more than the equivalent of a 10% clean all of the watershed basin, may indicate a potential low water quality (Brandt eta!. 1988).  3.4.2 WHAT TO TEST WITH? The models must be tested with a set of input data or test cases. Ideally a number of well documented cases from a complete range of problems would be used in the testing. However, the issue is not the number of cases, but rather the coverage or range of cases. Initial test data were taken from a small plantation called Coolangubra State Forest. This  plantation- contains 60 stands, -covers about 4,000 ha and has a very uneven age class  -  -  distribution (Figure 3.2). The mean annual increment is about 15.5m lhalyr, which would yield 3 62,000m / 3 yr in a perfectly normal forest. Figure 3.2 Coolangubra S.F. Age Class area distribution  33D  —  —.-—  ——..  1.._—  0.  ,  ---—  __-_-.-—  -__—  , ,  —  ‘  —..  ---  _  -  -.  8’ J’  4  6  Yer AcrteJ (rrk,s 193D)  44  -  Model Development Figure 3.3 Bombala District exotic conifer plantation age class area distribution  Fb±fl (lhmrth)  Yer Ra-tei (ni-LB 1I)) Gxkng±ra  Bnhxia  The Coolangubra data were used to test the essential soundness of the models for fine calibration of the algorithms. Once the models were calibrated, they were tested against a larger, independent data set. This data set included all the Bombala District plantations and covers about 40,000 ha with 200 stands (Figure 3.3).  3.4.3 WHAT TO TESTAGAINST? The models must be tested against some standard (e.g., a known solution or an expert solution). These standards were provided by the two generally used operations scheduling tools; mathematical programming and simulation by expert users.  45  Model Development New South Wales Forestry Commission experts have used PINEPLAN to schedule yields for the Bombala Plantation District. These PINEPLAN schedules were carried out in 1990 and took about one month. The Coolangubra State Forest had not been scheduled by Commission experts. An experiment was therefore designed where three forestry and computer literate PIN EPLAN novices tried to arrive at a yield scheduling solution. These volunteers were informed of the different scores that would be applied in evaluating their strategies (although they were not given the actual algorithms). Their solutions were used as standards for comparison and also to illustrate the range of strategies and resulting scores that could be scheduled. PINEPLAN solutions may give good answers, but within the constraints mentioned in Section 22, a mathematical programming technique may find an optimal strategy. The computer package LINDO (Schrage 1986) was used to provide an optimal standard. As mentioned in Section 2.2, it is difficult to include anything but quantifiable, additive values in the objective function. The quadratic nature of the timber flow score, interaction of units for the beauty and water quality scores, and lack of an objective way to weight the various scores meant that a comprehensive objective function would be difficult to derive. The maximization of volume in the planning period was the simple objective function selected for the comparison LINDO runs: 2  E  2010 2  1=1  j=1  k=199O  m  MaxZ  VI.k  where V jk denotes the volume produced by stand i, using regime j in year k. 1 Constraints were included to force the yearly yield to keep within a small percentage of the 21 year average, thus making the timber flow score equal the average volume, e.g. n  0.90  *  m  E  E  1=1  j=1  VIk  -  Z 21  46  <  0  Model Development n  m  i=1  J=l  1.10*  E  VIk  -  Z  >  0  21  All regimes for each forest stand were generated by a modified version of one of the  search models. This allowed every regime that could be considered by the search models to be included in the input matrix. The regimes suggested in the Bombala MP were defined as standard regimes. First thinning could only occur between 13 and 21 years and subsequent operations had at least a five year interval. The residual basal areas were specified according to the All Experts Thinning Guide (Bombala MP, Appendix 10), and early clearfalls (an anathema to most Commission experts) were excluded. By generating every regime used in the comparable search models, the strategies were directly comparable (Le., there was no biasing of the answer by leaving out necessary columns). The Coolangubra plantation was small enough to not require any stand data aggregation for LINDO. There were about 9000 standard regime/stand combinations or columns in this problem, and the LINDO version used could handle just over 10,000 columns. However, the Bombala District was too big to solve without aggregation of the stand or regime data. Spatial information was therefore lost and LINDO may not provide a practically feasible solution with the Bombala data.  3.4.400 THE MODELS PASS? The operations scheduling models developed in this research were developed to find good feasible schedules, as judged against multiple objectives and constraints, rather that a rigidly defined optimum solution. The user may then select the best schedule according to his or  47  Model Development her own judgement. By the judicious selection of constraints, the user may be able to find an optimal solution, but this is not guaranteed and may require a lot of searching. it is unfair to expect a knowledge based (satisfaction) model to perform at levels close to optimal results when existing systems cannot perform at these levels (O’Keefe etah 1988). If the models developed in the course of this research can produce strategies that are consistently close to, or better than the strategies produced by existing techniques then they may be considered as successful. It would be possible to do pseudo-Turing test (Firebaugh 1988) to determine if the strategies produced by the model are comparatively good. This test would be based on the premise: If a forest manager consistently selects the strategies produced by the developed models as poorer than the strategies produced by existing systems, then the developed models areunsatisfactoiy. Conversely, if the manager cannot choose between the strategies, or selects the model produced strategies as better than the existing system produced strategies, then the developed models are satisfactory.  48  4. DEVELOPMENT OF THE SEARCH MODELS  4.1 INTRODUCTION It has been said that all great inventions begin as toys or games (Townsend 1987). I chose to begin my model development by using the paradigm of the 8-queens puzzle. The board was a hypothetical three dimensional space. The X dimension represented stands, the Y dimension was time, and the Z dimension volume of timber output. Other units could have been used for the Z dimension (e.g., value of timber or forage volume available), however the methodology would remain consistent. Legal moves were acceptable regimes applied to a forest stand, that did not conflict with  specific neighbors. For example,-a move may be tG clearfalt stand I in yearj to produce X 1 output. This may be represented as  [Xj].  An alternative regime may be to thin at year jto  produce X 11 output, followed by a clearfall in year k with Xik output [X , Xik]. These are 2 11 -  mutually exclusive regimes, akin to placing a queen in the left corner or the right corner in the 8queens puzzle. A conflict would occur for neighbors X 1 and X if there exists  and X . and 1  their output sum exceeds some limit (e.g., the neighbors are cleared in the year j and the total cleared exceeds prescribed limits). The winning condition is when: Klower.I  1 X <  <  Kupperj  .  for every specified year i and where Kiower and Kupper denote minimum and maximum bounds.  49  Development of the Search Models 4.2 AN EXHAUSTIVE SEARCH The first strategy search model used very little domain knowledge. Its basic control was provided by the procedural knowledge contained in the split-and-prune technique of state space search. It was driven by: GOAL access_data, get_next_unit(X), generate_regime_list(X,Strat_list), update_boards(Strat_list, Boards), test_for_winning_condition(Boards). access_data gets KIower and Kupper for the years 1990 to 2010, and reads the area and inventory database for the relevant stands. -  getnext_unit is-the equivalent to picking up a quee generate_regime_list generates a list of all the possible regimes that can be applied to  stand X. This is equivalent to finding all the squares on the chess board that are not currently occupied by a queen. In an intensively managed plantation, the number of possible regimes would be very large. Even restricting these regimes to the standard ones (as defined in Section 3.3.3) resulted in over 700 regimes. update_boards refines the list of boards by adding the new regimes. Any illegal boards are pruned from the list of potential solutions. test_for_winning_condition tests to see if any of the refined boards meet the winning conditions, If the conditions are met, the goal is successful and the program stops. If not met, the program backtracks to get_next_unit, selects another stand and further refines the potential solutions. If there are no more units, the program fails and it can be concluded that the puzzle cannot be solved.  50  Development of the Search Models As with the exhaustive search models discussed in the Section 2.3, this model is severely limited. If there are an average of 700 possible regimes per stand, placement of the first stand on the board creates 700 potential partial solutions. Placing the next stand on the board, creates a total of 7002 or 490,000 partial solutions. Unless these potential solutions can be significantly pruned, it is impractical to add even a third stand and refine the potential partial solutions to 343,000,000 (700) boards. The small Coolangubra test plantation could have up to 70060 or 5.1*10170 potential partial solutions. If only clearfall between the ages of 20 and 40 years is considered, the number of potential partial solutions may still be 2060 or 1.1*1078. OHara’s (1987) exhaustive search model was limited to a maximum of 525 or 3*1017 potential solutions. Thus, unless there are very few forest units, regimes, or the restrictions are very severe and allow -significant pruning, this exhaustive approach is not practicaf forthe development of arroperations scheduling strategy. The exhaustive search was however useful in refining strategies in the Expert System models (Section 5.2).  4.3 INTRODUCING DOMAIN KNOWLEDGE: STRATSEARCH-1 It can be seen from the previous section that finding all the potential partial solutions is not a satisfactory way to solve an operations scheduling problem in an intensively managed forest. However, if the best potential board could be identified after each refinement and the rest disregarded, the problem would be much simpler. It may be possible to identity the best potential board by the introduction of domain knowledge through heuristics. A simple heuristic for the 8-queens problem was given by Peail (1984) as: a candidate placement is preferred if it leaves the highest number of unattacked cells in the remaining portion of the board.  51  Development of the Search Models  Thus to refine a board, determine all the legal placements for the next queen and select the best refinement using the heuristic. Further refine that board until the winning conditions are met. If the heuristic is perfect, the problem will be solved in a minimum number of steps. However, if the heuristic is not perfect and a winning combination is not found, it may be possible to backtrack to an earlier refinement and choose the next best partial board. In the worse case, the problem reverts to an exhaustive search. A search model (StratSearch-1) was developed to select the preferred refinement based on the premise: every stand can be assigned an a priori preferred regime and assigning preferred and legal regimes to stands will tend to produce a good forest-wide strategy. The preferred regime would be selected by a heuristic. Barber and Brodie (1989) must have used a similar premise when they generated a wide range of regimes for a stand and ranked them on the basis of net present worth. The regime with the greatest net present worth was the preferred regime; however, if it could not be applied due to constraints, the next greatest value regime would be preferred. StratSearch-l’s preferred regime was a compromise between severaltactors and not just net present worth. For example, the Bombala MP (page 54) prescribed that a preferred regime would first thin at 13 years, with subsequent thinning at 18, 23, and 28 years, and a clearfall at 35 years. The other plantation management areas have similar preferred regime descriptions. The preferred regime is a compromise between many factors (e.g., risk of damage, recreation values, potential for future markets, biological, and economic considerations) . If this preferred regime 5 could not be applied, there would be a second best regime. The second best regime may be to  5  See pages 23, 24, 29 and 42 of the Bombala MP (Forestry Commission of N.S.W. 1984).  52  Development of the Search Models delay clearfall by one year. There would also be a third best regime, and so on. The heuristic thus contains stand level knowledge. This heuristic was incorporated into the Stratsearch-1 model by the goal: GOAL: access_data, get_next_unit(X), generate_best_legal_regime(X,Strat), update_boards(Strat,Board), test_for_winning_conditions(Board). The generate_best_legal_regime clause would generate the (next) preferred regime until tests for legal placement succeed. A regime is legal where the years scheduled for harvest did not previously exceed the KIower level, and the output produced did not cause the Kupper level to be exceeded.  -  Once the preferred legal regime is returned, update_boards assigns that regime to the stand and the board is tested for a winning condition. If there is no winning condition, the program backtracks to get_next_unit to place the next stand on the board. Unlike the 8-queens problem, this program is potentially too big to allow extensive backtracking. Once a legal regime is assigned to a stand, backtracking to allow examination of another regime for that stand is cut. The model can only backtrack to pick another stand. This is a practical necessity caused by Turbo-PROLOG’s inability to handle large numbers of backtracking points. The failure to allow backtracking does not a create a problem in finding the goal if the puzzle is decomposable and the heuristic does find the best regime for each stand independently. Unfortunately, the operations scheduling problem is rarely decomposable. Thus, if the first regime that succeeds with generate_best_legal_regime is not on a winning path, the model will fail it is not guaranteed to find a winning solution if one exists. -  53  Development of the Search Models The a priori regime ordering was based on the Bombala MP prescriptions . It was 6 inferred that on time first thinnings were a first priority, timely clearfalls a secondary priority, and numerous mature thinnings a third priority. This knowledge was captured in the get_strat clause, which was called during generate_best_legal_regime: get_strat([thin(9,_,O) LJ[]). get_strat(History,[NextThin P]) thin_rules(NextThin,Conditions), meet_conditions(Conditions,History,NextThin), get_strat([NextThinHistoryj, P). Get_strat is a recursive clause, building up a regime until the final operation is a thin(9,_,O) (Le., a clearfall). Types of re-establishement and regimes for the subsequent rotation could be included in an extended knowledge-base, but were not considered in this research. Get_strat uses a thin_rules database which specifies operations that can take place if certain conditions are met. These conditions are tested in the meet_conditions clause. A thin_rule database may consist of several rules, such as those given in Figure 4.1 for example. Figure 4.1 Example thin_rule database thin_rules(thin(1 ,1 3,1 6),[nothin(1 ,O,O)]). thin_rules(thin(1 ,1 5,1 8),[nothin(1 ,O,O)]). thin_rules(thin(2,20 ,22),[nothin(2,O,O),thin( 1 ,O,O),int_limit(min,6)]). thin_rules(thin(2,25 ,25),[nothin(2,O,O),thin( 1 ,O,O),int_limit(min,6)]). thin_rules(thin(9,35 ,O) ,[nothin(9,O,O) ,thin(1 ,O,O),int_limit(min,5)]). thin_rules(thin(9,40,O),[nothin(9,O,O),thin(1 ,O,O),int_limit(min,5)]).  The first rule in this example database declares that a first thinning can be scheduled at age 1310 a residual basal area of 1 6m 1 ha if the regime does not already schedule a first 2 thinning. The third rule declares that a second thinning can be scheduled at age 20 to a residual  6  Forestry Commission of N.S.W. 1984, Section page 54.  54  Development of the Search Models  basal area of 22m /ha if the regime does not already schedule a second thinning, a first thinning 2 has been scheduled, and there is a minimal interval of 6 years since the last scheduled operation. The last rule declares that a cleartall (to a residual basal area of 0) be scheduled at age 40 if a first thinning has been scheduled and at least five years have elapsed since the last thinning. Such a database would produce an ordered list of regimes (Figure 4.2). Figure 4.2 Ordered list of regimes produced by example thin_rules database  1 2 3 4 5 6 7 8 9 10  [thin(1 ,13,16),thin(2,20,22),thin(9,35,0)]. [thin(1 ,1 3,1 6),thin(2,20,22),thin(9,40,0)]. [thin(1 113,1 6),thin(2,25,25),thin(9,35,0)]. [thin(1 ,13,16),thin(2,25,25),thin(9,40,0)]. [thin(1,13,16),thin(9,35,0)]. -[thin(1,I3,I6),thin(9,40,O)J. thin(1 ,1 5,18) ,thin(2,25,25) ,thin(9 ,35,0)]. [thin(1 ,1 5,1 8),thin(2,25,25),thin(9,40,0)]. [thin(1 ,15,18),thin(9,35,0)]. [thin(1 ,15,18),thin(9,40,0)].  Changing the order of the rules in the database, or the constraints on those rules allows generating regimes in different orders. The constraints can also be extended to include other aspects of the problem. For example, the fertilizer history of the stand may influence the regime (e.g., fertilized stands may produce economic yields earlier). The overall problem situation may  influence the order as well. For example, when sawlog material is at a premium, four thinning operations are desirable; for pulp only markets, three or two thinnings may be more desirable. The standard regimes for the Coolangubra mathematical programming standards were generated using a thin_rules database of 35 rules (Figure 4.3). The standard regimes for Bombala included an option to cleariall unthinned stands between the ages of 30 to 34 years.  55  Development of the Search Models This was necessary as some stands had already exceeded the latest age where a first thinning could have been carried out. Figure 4.3 Thin_rule database for standard regimes thin_rules(thin(1 13,1 6),[nothin(1 ,O,O)]). thin_rules(thin(1 ,1 4,1 7),[nothin(1 ,O,O)]). thin_rules(thin(1 ,15,1 8),[nothin(1 ,O,O)]). thin_rules(thin(1 ,1 6,1 9),[nothin(1 ,O,O)]). thin_rules(thiri(1 ,17,23),[nothin(1 ,O,O)]). thin_rules(thin(1 ,18,23),[nothin(1 ,O,O)]). thin_rules(thin(1 ,19,24),[nothin(1 ,O,O)]). thin_rules(thin(1 ,20 ,24),[nothin(1 ,O,O)]). thin_rules(thin(1 ,2 1 ,25),[nothin(1 ,O,O)]). thin_rules(thin(2, 18,21 ),[nothin(2,O,O),thin(1 ,O,O) ,interval(min,5)]). thin_rules(thin(2, 19 ,22),[riothin(2,O,O),thin(1 ,O,O) ,interval(min,5)]). thin_rules(thin(2,20,22),[nothin(2,O,O),thin(1 ,O,O),interval(min,5)]). thin_rules(thin(2,21 ,23),[nothin(2,O,O),thin(1 ,O,O),interval(min,5)]). thinruIes(thin(2,22,24,1nothin(2,O,O),thin(1 ,O,O,interval(min;5)fl. thin_rules(thin(2,23,24),[nothin(2,O,O),thin(1 ,O,O),interval(min,5)]). thin_rules(thin(2,24,25),[nothin(2,O,O),thin(1 ,O,O),interval(min,5)]). thin_rules(thin(2,25,25),[nothin(2,O,O),thin(1 ,O,O),interval(min,5)]). thin_rules(thin(2,26,26),[nothin(2,O,O),thin( 1 ,O,O),interval(min,5)]). thin_rules(thin(2,27,26),[nothin(2,O,O),thin( 1 ,O,O),interval(min ,5)]). thin_rules(thin(3,24,25),[nothin(3,O,O),thin(2,O,O),interval(min,5)]). thin_rules(thin(3,25,25),[nothin(3,O,O),thin(2,O,O),interval(min,5)]). thin_rules(thin(3,26,26),[nothin(3,O,O),thin(2,O,O),interval(min,5)]). thin_rules(thin(3,27,26),[nothin(3,O,O),thin(2,O,O),interval(min,5)]). thin_rules(thin(3,28 ,27),[nothin(3,O,O),thin(2,O,O) ,interval(min,5)]). thin_rules(thin(3,29 ,27),[nothin(3,O,O),thin(2,O,O) ,interval(min,5)]). thin_rules(thin(3,30 ,28),[nothin(3,O,O),thin(2,O,O) ,interval(min,5)]). thin_rules(thin(3,3 1 ,28),[riothin(3,O,O),thin(2,O,O) ,interval(min,5)]). thin_rules(thin(3,32 ,28),[nothin(3,O,O),thiri(2,O,O) ,interval(min,5)]). thin_rules(thin(9,35,O),[nothin(9,O,O),thin(1 ,O,O),interval(min,5)]). thin_rules(thin(9,36,O),[nothin(9,O,O),thin(1 ,O,O),interval(min,5)]). thin_rules(thin(9,37,O),[nothin(9,O,O) ,thin(1 ,O,O),interval(min,5)]). thin_rules(thin(9,38,O),[nothin(9,O,O) ,thin(1 ,O,O),interval(min,5)]). thin_rules(thin(9,39,O),[nothin(9,O,O),thin(1 ,O,O),interval(min,5)]). thin_rules(thin(9,40 ,O),[nothin(9,O,O),thin(1 ,O,O), interval(min,5)]).  Using the above heuristic, regimes for each forest stand were generated in a disciplined manner. However, three factors affect the quality of the strategy produced:  56  Development of the Search Models 1.  the yield limits; Kiower and l<upper  2.  the order in which the stands appear, and  3.  the preferred order of the regimes.  The yield limits will determine which regimes are legal. S 1 ipper will set the maximum allowable yield. If this value is too low, the mean volume over the planning period will be low. If Kupper is too high, volumes may be inefficiently assigned. If  is set too low, regimes that  could improve the average volume without violating Kupper would be excluded. However, if Kiower is too high, regimes may be accepted which inefficiently direct volume away from the deficit years. StratSearch-1 was systematically run a number of times to find appropriate Klower and Kupper limits. The order in which the units are selected influences the regime assigned. The first stand selected would almost certainly be assigned its first preferred regime. The last stand would similarly almost certainly be assigned a much less preferred regime and unlike the 8-queens problem, all the units are not equal. An ad hoc order of the stands is unlikely to produce the best strategy and trying every possible order would be too slow. Coolangubra for example has 60! or 8.32*1081 possible ways to order the units. There are several intuitive ways of ordering the forest units: area, age, site quality or a combination of these. However, none of these approaches produced a clearly superior model. Without a dominant heuristic for ordering the units, several ad hoc and random stand orders were used in StratSearch-1. For ease of reference, each set of StratSearch-1 runs was identified by a code which denotes stand order, Klower and Kupper and the number of repetitions in the set. For example, 50 repetitions of a search with random stand ordering, KIower of 35,000 and 1 Sipper of 45,000 is identified as R-35-45-50. One run with the stands in order of age would be Age-35-45-1.  57  Development of the Search Models In the random stand order runs, optimal scores were predicted using Cooke’s (1979) and Golden and Alt’s (1979) algorithms to get an idea of how good the strategies were, and whether more repetitions were needed. However, the predicted optimal scores for each of the various types of forest output were independent. A strategy that could produce the optimal timber flow may not produce the optimal scenic beauty, or even the highest mean volume. The problem of regime ordering could not be addressed by the simple structured repetition described above. More domain knowledge was needed in the search model.  4.4 MORE DOMAIN KNOWLEDGE: STRATSEARCH-2 StratSearch-1 used a fixed approach to ordering the regimes for each stand. A particular regime-would always be examined first. However, because the lack of backtracking meant that the quality of this ordering heuristic will determine if the problem could be solved, better heuristics were sought. A better regime ordering would be related to the specific problem being examined and how closely the current potential solution was to meeting the winning conditions. Stratsearch-2 attempted to include knowledge about the problem solution to date and how experts tend to order their PIN EPLAN searches to order the regime preferences. This additional knowledge is related more to the forest level than to an individual stand. A heuristic was developed to score each regime for a forest stand. This heuristic incorporated details of the impact of the proposed regimes on the forest level targets and whether these targets were limiting. The regimes were ranked and tested in descending order until a legal one found.  58  Development of the Search Models A function similar to Samuel’s (1959) Linear Evaluation Function was used to rank the regimes. This function is of the general form: V(s,,)  =  E cxj  *  a(su)  where: denotes a coefficient V(Su)  denotes the score of applying regime s to stand u.  Oi(su)  denotes some attribute of the potential situation resultant from applying regime s to stand u.  To help keep this evaluation function understandable, the number of attributes included was restricted to six. Wickens (1984) stated that, even if more information is collected, only four to five pieces will be used in decision making by managers. Thus, using more than six pieces of information would probably make the evaluation function into a black box that a manager would not understand or trust. The attributes selected included small and large volume deficits and surpluses for the current forest situation, number of thinnings scheduled for the stand, and the total volume produced by the regime. The number of thinnings is closely related to the health and beauty of the stand as well as to flexibility. A stand that is well-thinned is more amenable to management changes to cope with different environments and markets. Geographic or spatial considerations were not included in this scoring function because often the neighbors to the stand would not have had any regime applied. The scores provided by the evaluation function were qualitative not quantitative. A score of 2 indicates that a regime is preferable to another with a score of 1, but not that it is twice as good. Therefore statistical tools like simple linear regression could not be used to derive the  59  Development of the Search Models coefficients for this function. Instead, an artificial intelligence model learnt the coefficients from given examples (Gordon 1989, Pearl 1984, Michalski et aL 1983, Saveland and Stock 1988). The learning model was driven by the following goal: GOAL get_model_coefficients(Coefficients), test_examples(Coefficients), print_model(Coefficients). get_model_coefficients assigned initial values to the model. test_examples accessed a database of selected examples to prove that the coefficients made a model that ranked all the examples correctly. If test_examples failed, the first example that failed was asserted to a failed database and the program backtracked. get_model_coefficients systemmatically incremented (deeremented) the coefficients of attributes that differrect to find a setthat made the example in the failed database tnje. These minimally changed coefficients were returned and tested. Once test_examples succeeded, a logically correct evaluation model was produced. Selection of the examples for the learning algorithm is important (Michalski et aL 1983, Schmoldt 1989). Examples were chosen to represent the following conditions: 1.  V(5)  <=  0 if the regime cannot be applied (e.g., all output  produced in years when 1 Sipper is exceeded). 2.  ) 1 V(s  >  V(s) if  1 S  produces an output in a year with a large  deficit while s 2 produces an output in a year with a smaller deficit. 3.  V(s.)  >  V(s) if s 1 produces a larger output in a deficit year than  >  ) 2 V(s  . 2 S  4.  ) 1 V(s  >  V(s) if s 1 has multiple thinning, s 2 a single  thinning and s 3 only has a clear fall.  60  Development of the Search Models  Once coefficients were selected which were logically true for all examples and appeared fairly robust, the Linear Evaluation Function was used to rank the regimes for each stand. StratSearch-2 thus had a potentially better regime ranking heuristic. The Kiower and Kupper limits were effectively incorporated into the Linear Evaluation Function (years significantly less than the guiding volume were large deficit years, i.e., less than Kiower, and years significantly above the guiding volume were large surplus years, he., greater than Kupper) and thus only the guiding volume needed setting (i.e., one setting rather than two as in StratSearch-1). The guiding volume, K, is used to direct the search. An attempt is made to produce at least as much as K without inefficiently scheduling too much more than K. However, the goal is not to produce K voh.xme.  A systematic search similar to StratSearch-1 was used to find an appropriate K, and different ad-hoc and random stand orders were tried. The runs are named using a similar format to StratSearch-1 (he., stand order K number of runs). For example, 50 random repetitions with -  -  a K value of 45,000 would be written as R-45-50. The thin_rules database was expanded in some runs to include heavier thinning and early clearlall options. Extra first and second thinning options allowed removal of an extra 2m / 2 ha basal area, provided the subsequent operations still returned operational yields. Clearfails could be scheduled after 25 years if the stand had not been previously thinned. Runs that include these extra options are identified by a + (e.g., R-45-50+).  4.5 ORDERING STANDS: STRATSEARCH-3 StratSearch-2 incorporated domain knowledge to improve the ordering of the regimes. Systematic searches allowed K to be set at a realistic value, but the ordering of the stands was  61  Development of the Search Models still a potential problem. Multiple runs with different random stand orders do not guarantee any good stand orders. Fixed orders (e.g., FORMAN’s largest volume first) also do not guarantee good solutions. StratSearch-3 applied the Linear Evaluation Function to the stands as well as the regimes to order the stands. Initially, every regime for all the stands was scored and the best score selected. The stand / regime combination corresponding to this score was asserted into the strategy database, then the remaining stands re-examined. The regime scores changed because the volume surpluses and deficits changed as stands are assigned regimes. The selection and re-examination of the remaining stands continued until no stands were left or all the regime scores were less than zero. At that point, the final strategy was evaluated. Once K was set, StratSearch—3 only required one run (Le, multiple random runs were not needed). However, multiple systematic runs were needed to find the best K value. StratSearch-3 runs only needed the K limit to identify them (e.g., SS3-45) as there were no repetitions and the stand order was determined by the K value.  62  5. DEVELOPMENT OF THE EXPERT MODELS  5.1 INTRODUCTION The 8-queens puzzle is no longer an appropriate paradigm when the queens have different values and may move differently. The combinatonal explosion is too great and even good heuristics are too slow to find a solution. StratSearch-2 was up to 30 times slower than StratSearch-1. StratSearch-3 tried to rank the stands as well as the regimes arid was orders of magnitude slower again. A more appropriate paradigm may be a game like chess. The game of chess is basically a spatial problem soMng game. From an initial board position, players may move a variety of differently valued pieces in-different legal moves to generate a winning position. Computers are still not powerful enough to generate every possible board and a lot of heuristic knowledge has been built into chess playing models. Much of this knowledge is procedural (e.g., the alpha-beta algorithm, Slagle and Dixon 1969). This is of little direct application to an operations scheduling system. However, human chess playing experts, or Masters, apparently do not solve their problems with simple search techniques or alpha-beta algorithms. Although a lot of work has gone into these techniques for computer games, and several computer Masters essentially just use brute force search approaches, other researchers have tried to duplicate the way humans think, and their experience may help in the operations scheduling environment. Botvinnik (1984) believes the strong chess players do not see the whole board but only those pieces that move through the area of interest. They do not have vast look-ahead or search trees in their head, but rather concentrate on the features of certain positions (Michie 1980). The  63  Development of the Expert Model area or features of interest may change with changing goals. Botvinnik (1984) discussed a conceptual system of multiple goal levels within a general goal. The players may also recognize key features in a game which allow them to compare the current board with previous games. If the previous game was successful, the player may try to make the current board like the previous game, and then simply use the previous game’s winning strategy. The task appears to be when to change the focus of attention (Clancey 1988). When should the concentration be shifted from one goal to another, and how does one recognize a position that is essentially similar to an advantageous position experienced in a previous (victorious) game?  5.2 AN EXPERT SYSTEM TOOLBOX Turbo-PROLOG provides an interactive and flexible programming environment, and the development of the earlier search models led to the production of a number of useful utilities. These circumstances allowed me to design a toolbox of expert system tools to explore and incrementally solve a number of operations scheduling problems. Using what Rogers (1978) termed the break-make solution approach, I generally tried to break the scheduling problem into simpler sub-problems. Starting with an initial strategy, a specific goal would be selected. This goal was identified after exploring the strengths and weaknesses of the initial strategy by a number of tools (e.g., generating a histogram of yields, listing stands included in critical scenic points or water quality areas). I could then focus attention on a selection of stands that would influence this goal. All other units were accepted as constraints and an exhaustive search, or one of the StratSearch models, could search for a new set of regimes which allowed the sub-set to meet the goal.  64  Development of the Expert Mode!  Alternatively, some general modification heuristics could be applied to some stands (e.g., reduce the interval between first and second thinnings to move some volume production from the distant to the near future). The modification heuristics were based on experience with operations scheduling using PINEPLAN. I explored different ways of ordering goals and selecting units for modification in the Coolangubra and some hypothetical plantations. Some of the more useful approaches found in the experiments were compiled into executable programs (Section 5.3). Gordon (1989) would define such programs as procedural expert systems, while the toolbox environment described above would be a domain general deep expert system.  5.3 AN EXPERT SYSTEM APPROACH TO RISK  -  Expert systems should ideally take advantage of all the information or knowledge that is  available and useful. lithe initial strategy used in an expert system was based on StratSearch-1 or StratSearch-2 runs, then there is knowledge contained in the other boards generated. The multiple runs could determine which stand / regime combinations occurred repeatedly in the best strategies. In chess, experience has shown that the control of center-board is one very important consideration in a game. Consistently occurring regime combinations may be the operation scheduling game’s equivalent to the chess center-board. These combinations could be fixed, and the remaining units re-combined for a better strategy. One reason that center-board is so valuable in chess is that it allows a great deal of flexibility in the players future attack and defense. A good center-board position in a scheduling problem would also provide for a flexible way of dealing with a changing position (e.g., changes due to internal or external uncertainties). To try to locate this position, I used good strategies produced by StratSearch-1 R-50-60-50. The yield flow from these strategies was then predicted  65  Development of the Expert Model using a stochastic version of the deterministic growth model normally used. The stochastic model introduced a random error (e.g., 1% raised to the number of years between operations) to account for the uncertainty in inventory and growth. For example, a stand that was inventoried in 1990 then had a thinning scheduled in 2000 and 2005 would have the volume predictions multiplied by (r) ° and (r) 1 5 respectively (0.99  <  r < 1.01). The strategies were then re-ordered  on the basis of timber yield score and any consistencies amongst the regimes of the best strategies were examined. Stand I regime combinations common to the best strategies were fixed, then an expert system was used to schedule the remaining stands. The resultant strategy was compared to strategies developed by other techniques.  5.4 EXPERT SYSTEMS  -  The simplest Expert System developed (ES-i) selected one stand from a given strategy, then exhaustively searched the regimes to find one regime for this stand that most improved the strategy score. ES-i selected another stand, searched for the best regime and repeated until there were no more improvements. A stand may be selected several times after intermediate changes allow new regimes to be tried. The most improved strategy was interactively selected. One option defined a new strategy as improved if: 1)  all the scores of the new strategy exceed the old, or  2)  there are less significant timber yield differences in the new strategy than the old, (i.e., mean volume timber yield score is -  less), and none of the remaining new strategy scores are more than 1% worse than the old strategy scores.  66  Development of the Expert Model  Other menu options replace 2) above with improvements in the other scores without degrading the remainder more than 1%. ES-i was driven by the goal: GOAL:get_strategy_information, type_of_goal_improvement, select_unit(X), select_improved_regime(X), more_improvements(Response), Response = no, report. get_strategy_information accessed a previously constwcted strategy or board configuration. type_of_goal_improvement evaluated the strategy and determined the appropriate goal that should be improved. Unless the user specified a particular goal in an interactive  session, ES-i assumed a goal of improving any score where this would not cause the other scores to be decreased. select_unit selected the next unit (ordered by area, age, or randomly) that the system would examine. The regime associated with the unit was deleted from the strategy. select_improved_regime determined regimes for the selected unit that improved the appropriate goal. more_improvements could either back-track to select_units to pick a new set of units as the area of interest, or back-track to type_of_goal_improvement to provide for a different objective. Once more_improvements was bound with no, the new strategy was saved and reported. A second expert system, (ES-2), was developed as a multiple stage ES-i model. By selecting only one stand at a time, ES-i could only find local optima. Regimes could not be swapped amongst units unless the intermediate strategies also had improved scores over the original strategy. For example, if stand V was thinned in year A and stand Z was thinned in year  67  Development of the Expert Model B, to swap the thinning years (e.g., to improve scenic beauty), at least one intermediate strategy would be generated: Initial:  Stand Y in year A and Stand Z in year B (score I),  Intermediate: Final:  Stand Y and Z in year B (score j where  j> i),  Stand Y in year B and stand Z in year A (score k where k > i> i).  If ES-i were modified to select two units each time, then perform an exhaustive search, a better local optimum may be found because units could swap without the intermediate stages. However, in the Coolangubra example, there are 60!((2!(602)!)1) or 1770 ways that two units could be selected out of 60 units. There are then about 7002 stand / regime combinations that can be applied, or 8.6r1  strategies to be examined in an exhaustive search. Of course, three  or foururiits may be involved in an optimat swap ancithere are about 34,220 or 4B7,635 ways that these units can be selected. It is obviously impractical to systematically select every combination of units and exhaustively search for better strategies. ES-2 used the fact that not all units were equally important for each score to allow reasonable group stand selection. If scenic beauty improvement were the goal, the first stage selected the group of units that make up the poorest beauty point. New regimes for these units were then selected which improved the scenic beauty score without too large loss in the other scores. The second stage called ES-i to improve the new strategy by selecting the remaining units, one at a time, and searching the regimes to find an improved strategy. ES-2 also was used to examine the effects of new regimes. The first stage selected units that could have the new regimes applied, while the second stage adjusted the remaining units to improve the new strategy. For example, the effect of heavy early thinnings could be examined. Two PIN EPLAN strategies thinned about 2m Iha heavier than the All Experts Thinning Guide 2 recommended in some stands. The first stage of ES-2 selected units where this additional  68  Development of the Expert Model regime may be beneficial (in this case units where thinning took place in a year of below average volume) and the second stage adjusted the remaining units to take advantage of the new flow.  69  6. TESTING AND RESULTS  6.1 UNDO The linear programming models were solved using LINDO on an IBM (3081-K mainframe) computer. The Coolangubra plantation test case took approximately 100 cpu seconds and gave a solution with a mean annual volume of 60,857m 3 or a total of 1 ,278,008m 3 over 21 years (Table 6.1). The Bombala plantation model used aggregated data and took about 30 cpu seconds to solve. The Bombala model using standard regimes found a solution with a mean average volume of 288,495m 3 while the inclusion of non-standard regimes increased the solution by 18% to 341 ,052m /year. Because the problems were constrained to having the 3  yearly yields with 10% (Coongubra) and 2.5% (Bomba) of the mean,the timber flow scores (Section 4.1.1) were identical to the mean volumes (te., no significant deviations). Table 6.1 LINDO solution scores Name  Time (cpu)  Volume  Timber  93  60,857  60,857  58,997 35,470  25  Coolangubra: LINDO LINDO (Manual Integer) LINDO (Integer) Bombala: LINDO (Standard) LINDO (Manual Integer) LINDO (non-standard)  27  Beauty  Health  -  -  -  55,354  4.62  -368  -11,396  53,447  52,929  4.81  -5,271  -10,483  288,495  288,495  272,751  252,968  341,052  341,052  70  -  0.76  -  Water  -  -49,545 -104,225  Testing and Results  LINDO’s dual prices indicated the costs of meeting the model constraints. The most important yield flow constraints were the minimum constraints of 1990 to 1993 in Coolangubra and 1991 to 1994 in Bombala. For each cubic meter of wood that the yields in one of these years could drop beneath the flow constraint of the mean volume, the total volume produced could increase by about 4m . 3 The initial LINDO solutions were non-integer solutions. Assigning each Coolangubra stand to the nearest whole regime, dropped the mean annual volume by 3% to 58,997m 3 while the Timber Yield score dropped by 9% to 55,354 as significant deviations in yield flow were observed. Stands in the Bombala problem had been aggregated into age class units to make the problem smaH enough to solve. To approximate an integer solution, the units were de-  -  aggregated into their constituent stands which were then assigned integer regimes. The regimes were assigned systematically to reproduce the appropriate ratios assigned to the age class unit by LINDO (standard). The mean annual volume dropped by 5%, while the timber flow score dropped by 12% (Table 6.1). Due to time constraints, no attempt was made to manually optimize the distribution of regimes for the scenic or water quality scores. LINDO is theoretically capable of generating mixed integer solutions. If each stand can be assigned only one whole regime, approximately 9000 integer constraints are added to the Coolangubra problem. After numerous FATAL-OUT-OF-SPACE problems, increases in computer resources, constraint relaxation (i.e., yearly volumes within 25% of the mean), TITAN transformation, and other tricks, a solution that carried a warning that it may be non-optimal was produced. Because LINDO’s branch-and-bound algorithm searches the solution space in the order of the constraints given, different orders of the constraints may produce results more quickly. Constraints were ordered in decreasing order of the LP solution dual values, but this also  71  Testing and Results  failed to give a solution without a warning of non-optimality. The best run used over 35,400 cpu seconds (9 hours and 51 minutes) and gave a mean annual volume of 53,447m , a drop of over 3 12% from the non-integer solution and poorer than the manually integerized solution (Table 6.1).  6.2 PINEPLAN  The three users of PINEPLAN produced very different results for the Coolangubra test case (Table 6.2). PINEPLAN users 1 and 3 were able to find integer solutions with mean annual volumes 10.2% and 3.8% better than the LINDO integer programming solution. These results were within 3.5% and 8.8% of the linear programming solution respectively. Both users were also able to find their solutions without relaxing the flow constraints. However, both these users scheduled many thinning operations to lower residual basal areas than recommended in the All Experts Thinning Guide (i.e., not just standard regimes were scheduled). Table 6.2 Coolangubra test case scores for PINEPLAN Name  Time  Volume  Timber  Beauty  Health  Water  Coo langubra: User 1  15 hours  58,901  58,901  4.24  -140  -28,382  User 2  3 hours  56,175  48,955  5.19  -503  -35,313  User 3  6 hours  55,486  55,486  4.67  -365  -27,166  1 month  358,469  -1,584,469  2.23  -1923  -92,641  284,531  112,214  1.11  Bombala: 1990 Expert (1991-1999)  72  Testing and Results User 2 was unable to meet the timber flow constraints. He devoted the smallest amount of time to the problem, but also produced a strategy with the best scenic beauty score, more than 11% higher than the nearest PINEPLAN rival. Of the 60 stands in Coolangubra, only four were scheduled with the same regime by users 1 and 3. No stand / regime combination of user 2 was duplicated by the others. User 2 tended to schedule light, frequent thinnings. The Bombala plantation operations schedule produced in 1990 did not produce a very even flow of timber, hence a low timber flow score. There were no large scale industries using the resource at the time, and the schedule was developed to provide a guide to the volume that could be advertised for tender. A large effort was therefore not warranted in evening out yield flows in the latter part of the planning horizon. However, the schedulers did concentrate on the minimum flows generated during the early part of the horizon, and the timber yield flow score is much better during 1991  -  1999. They scheduled thinning operations to lower residual basal  areas than recommended by the All Experts Thinning Guide to fill in perceived gaps in the flow. After 1999, the experts tended to schedule thinning on time and in accordance with the All Experts Thinning Guide. This meant that the health and scenic beauty of the plantation was very good.  6.3 STRATSEARCH-1 An initial run of StratSearch-1 on the Coolangubra data did not set volume constraints and the first (preferred) regime generated by set_strat was always accepted. The yield flow was understandably highly variable around a high mean value and produced a negative timber flow score. Health scored a perfect 0, but beauty and water quality were low (Table 6.3).  73  Testing and Results Table 6.3 Coolangubra test case scores for StratSearch-1. Name  Time  Uncoristrained+  0.5m  Area-56-56-1 Area-60-60-1 Area-65-65-1  Volume  Timber  Beauty  Health  Water  nla b  71,801  -291,709  4.33  0  -29,968  0.5m 0.5m 0.5m  Area b Area b Area b  49,801 51,276 53,419  46,849 47,297 43,832  4.95 4.95 4.95  -316 -150 -100  -27,406 -29,070 -28,691  Age-56-56-1 Age-60-60-1 Age-65-65-1  0.5m 0.5m 0.5m  Age b Age b Age b  48,188 51,494 52,503  46,032 48,332 45,845  4.76 4.76 4.76  -4,535 -2,115 -2,115  -19,777 -22,442 -22,878  R-56-56-50  20m Random b c g  52,099 52,265 55,838  50,847 51,062 56,875  5.05 5.07 5.62  -1,687 -1,615 1,481  -13,481 -12,010 6,193  R-60-60-50  20m  Random b c g  54,549 54,906 59,312  50,475 50,782 54,996  5.00 5.00 5.05  -25 429 5,674  -13,614 -12,097 8,951  -  Sort  -  -  R-60-60-100  40m  Random b c g  54,200 54,237 56,623  50,796 50,909 54,574  5.10 5.12 5.53  -685 -596 1,950  -10,806 -9,249 10,125  R-60-60-300  120m  Random b c g  54,797 55,085 58,757  51,239 51,312 55,350  5.19 5.23 5.81  -161 -57 2,881  -14,463 -14,296 -964  R-65-65-50  20m  Random b c g  56,744 56,779 59,990  51,574 52,117 59,553  5.14 5.17 5.81  0 10 1,900  -19,959 -19,494 -4,711  A*R6Q6O5O  2Cm  Area* b Random c g  54,119 54,167 56,890  51,037 51,152 56,200  5.14 5.16 5.67  -118 -59 1,789  -21,014 -20,034 -9,092  Name describes Stand Order minimum volume maximum volume repetitions Volume limits in thousands of meters cubed b denotes the ‘best’ (maximum) observed c denotes the estimated optimal using Cooke’s (1979) algorithm g denotes the estimated upper boundary using Golden and Alt’s (1979) algorithm -  -  74  -  Testing and Results Subsequent searches required setting the volume limits. As there was no a priori way to set these limits, and the sensitivity of the model solution was unknown, a range of exploratory runs were made. Using a random ordering of stands, StratSearch-1 was run five times with a lower and upper limit of 50,000m Iyr. The limit was incremented by 1 000m 3 Iyr and another five 3 random runs made, and this was repeated until the upper limit reached 69,000m Iyr (Figure 6.1). 3 Figure 6.1 Coolangubra StratSearch-1 exploratory search with random stand order all scores -  (a) Timber and Volume  (b) Beauty  53 —9— -  Mean -  Annual Volume —  —  —  -  5€.-  I*! : 50 51 52 53 84 56 57 58 59 60 62 63 64 65 66 68 68 K-upper limit  I  S  — limber Flow Score  bkrLcVPMA-MP-  60 51  (c) Health -fl  52 53  54  56 57  cc K-upper limit  58 58  eq eq eq en en  eq  (d) Water Quality  1r  I  -21  ! -St  50 51  -Si  52 53 54 56 87 58 58 60 62 83 64 68 66 68 68 K-upper limit  z  50 51 52 53 54 56 a, an en be K-upper lieS  I  eq  eq  eq eq  eq eq  Note: Five random runs are plotted for each K-upper limit denoted. The five tick marks after Kupper 50 all refer to runs with a K-upper of 50. K-upper values are in thousands. The highest index score at each limit level was then plotted and the optimal index score estimated using Cooke’s (1979) function (Figures 6.2(a)-(d)). The timber yield score appeared  75  Testing and Results best with an upper limit of between 56,000m /yr and 3 3 60,000m I yr, while the scenic beauty appeared best between 56,000m /yr and 3 3 63,000m I yr. Stand health appeared to improve linearly until an upper limit of 3 65,000m I yr resulted in no delayed thinning areas. Water quality declined as the upper limit was increased; however, there were marked differences between runs which suggests more random runs at each level may find better solutions. It appeared that the optimal upper level lay between 56,000m /yr and 3 3 65,000m / yr depending upon the relative weighting of the scores. Figure 6.2 Coolangubra StratSearch-1 exploratory search optimal scores (a) Timber Flow  -  (b) Beauty  5051525354555657585960618283646568676889 K-perHrnI  5051 52532456565728596061 6265646568676889 K-upper Nndt  (c) Health  (d) Water Quality  41  5051 52535455595758596061 6265648566876869 K-upper Ihidt  505152535455565758596061 6283648566876889 K-tper 1mW  Note: Filled in squares denote observed optimal scores. Blank squares denote Cooke (1979) predicted optimum.  76  Testing and Results StratSearch-1 was rerun with 3 56,000m / yr, 3 60,000m / yr and 3 65,000m / yr upper limits and lower limits 0m /yr, 3 3 5,000m / /yr and 3 3 yr, 10,000m 15,000m I yr less, (i.e., twelve runs). Each  run used 50 randomly generated stand orders. The 60,000m /yr upper and lower limit setting 3 was also run with 100 and 300 random stand orders (Figure 6.3). Figure 6.3 StratSearch-1 Timber flow scores (sorted) using /yr and random ordering of stands 3 upper limit of 60,000m  52  R-B0-&UI  R-60-6U-1 00  I  R-60-60-300  -50  Strategies from each set of runs were selected and compared (Table 6.4). Strategies that were highest in at least one score were selected. As the volume limits increased, the mean annual volume tended to increase. The highest mean was found at a Kijpper of 65,000m /yr. As 3 the difference between KIower and Kupper increased, the mean annual volume decreased, but  77  Testing and Results  the timber flow score did not. When the difference was zero, there were always significant deviations in the timber flow. When Kiower was at least 10,000 below l<upper several cases appeared where there were no significant flow deviations. Health and beauty scores tended to follow the same trends as mean annual volume, while water quality tended to become poorer as the volume limits increased. Table 6.4 Coolangubra test case best strategy comparisons for StratSearch-1 (random stand order).  Name  Repetition  R-41-56-50  Type  Volume  29 22 35 32 20 43 18 42 49 40 12 8 9 12 16 29 34  t,v 48,018 45,058 b h 44,539 -w 46,037 R-46-56-50 t 50,067 v,b 50,131 h 49,377 w 49,194 R-51-56-50 t,v 51,621 48,853 b h 50,793 w 50,470 R-56-56-50 w 48,455 b 49,217 h 50,925 v 52,099 51,195 t b = best scenic beauty score; h = best health score; t = v = best mean annual volume; w = best water quality -  78  Timber  Beauty  Health  Water  48,018 2.05 -16,278 45,405 4.19 -15,923 44,338 3.43 -10,877 45,638 -0.29 16,693 50,067 4.33 -5,065 49,527 4.95 -4,283 49,377 4.67 -4,095 47,525 1.86 -9,878 51,329 4.81 -6,640 44,669 4.95 -3,936 49,742 4.62 -1,395 49,345 4.86 -3,770 45,642 4.38 -5,669 47,057 5.05 -3,860 48,169 4.86 -1,687 49,254 4.71 -1,887 50,847 4.71 -2,803 best timber flow score  -31,606 -32,062 -30,571 -26,214 -29,440 -28,969 -27,810 -26,262 -30,449 -30,857 -27,597 -26,237 -13,481 -20,673 -28,311 -25,331 -28,951  Testing and Results Table 6.4 (Continued).  Name R-45-60-50  R-50-60-50  R-55-60-50  R-60-60-50 R-50-65-50 R-55-65-50  R-60-65-50  R-65-65-50  Repetition  Type  Volume  Timber  Beauty  Heafth  Water  2 41 37 21 15 9 17 28 26 33 22 17 3 3 25 39 20 26 32 21 13 19 47 6 47 4 21 3 28 33 41 47  t,v b h w t,v b h w t v b h w t,v,h b w t,v,h b w t,v b h w t,v b h w h v w b t  51,694 47,199 49,220 47,874 53,146 51,363 51,826 49,726 53,765 54,209 52,324 52,541 52,070 54,549 52,833 49,857 53,578 52,487 51,373 55,358 54,084 53,866 54,568 56,941 56,778 54,751 55,627 55,579 56,744 53,261 55,552 56,701  51,694 46,817 48,296 47,373 53,146 49,140 50,514 47,439 51,179 51,135 48,358 47,899 48,291 50,475 48,861 44,773 53,085 50,272 49,284 50,712 49,549 47,424 50,504 51,913 51,074 48,215 50,158 46,112 50,482 45,094 47,838 51,574  3.19 5.00 4.81 4.14 4.81 5.00 4.67 4.67 4.52 4.76 5.14 4.71 4.90 4.81 5.00 4.33 4.67 5.10 4.67 4.67 5.14 4.81 4.90 4.86 5.14 4.76 4.81 4.67 4.62 4.67 5.14 4.76  -5,994 -8,930 -3,680 -9,817 -1,922 -2,643 -1,740 -5,390 -1,566 -2,858 -1,171 -125 -1,430 -25 -2,821 -4,751 -1,305 -1,619 -4,293 -1,545 -3,295 -1,088 -1,361 -255 -289 0 -157 0 -508 -2,140 -91 -182  -28,725 -31,541 -28,868 -26,332 -28,032 -27,410 -31,907 -25,863 -28,547 -26,561 -27,954 -29,457 -25,664 -29,923 -28,170 43,614 -28,702 -29,296 -25,826 -29,289 -26,959 -28,880 -25,765 -31,518 -26,963 -28,568 -25,867 -27,766 -28,344 -19,959 -29,414 -27,484  b = best scenic beauty score; h = best health score; t v = best mean annual volume; w = best water quality  =  best timber flow score  There were no major improvements in the scores when the number of random runs was increased from 50 to 100 and 300 (Table 6.3). Except for water quality, the optimal scores observed in R-60-60-50 were within 3% of the optimal scores for R-60-60-1 00 and R-60-60-300.  79  Testing and Results This indicated that 50 runs was sufficient to find a good solution if water quality was not the most important factor in the strategy. Except for water quality, the optimal scores observed in the three runs where Klower equalled Kupper were close to those estimated by Cooke’s (1979) equation from the exploratory runs (Figure 6.2 and Table 6.4). The observed optimal water quality score was better than the Cooke predictions in all three cases. The Cooke estimates for beauty and timber flow were only exceeded in R-65-65-50, and then by less than 3%. The optimal health estimate for R-60-60-50 was two orders of magnitude too large. The Cooke estimates using the 50 runs (Table 6.3) appear realistic. Only twice were the Cooke estimates clearly optimistic; estimating the optimal health score in R-60-60-50 and R-6565-50 as positive. The best possIe heIth score IsO, and positivevalues cannot- be achieved (by definition). However, the estimated optimal for timber flow, beauty and water quality based on R-60-60-50 were exceeded by observed values in R-60-60-1 00 or R-60-60-300 (by 0.9%, 3.8% and 10% respectively). It is also noted that the optimal estimates based on R-60-60-1 00 were exceeded by mean volume, timber flow, beauty, and health scores observed in R-60-60-300 (1.1%, 0.6%, 1.4%, and 72% respectively). Cooke’s (1979) formula for estimating optimal values gave estimates within about 4% of observed optima (based on 300 repetitions) for most scores except water quality. However the optimal values predicted by the Golden and Alt (1979) formula were often ,  unrealistic (Table 6.3). Estimates for health and water quality scores were often large positive values, and the timber flow score was greater than Kupper for R-56-56-50. Although it is true that one could be 100% confident that the optimal would be less than those values, they were so far away from realistic scores as to be useless in determining the quality of the random search score. The width of the confidence ranges is clearly conservative. Despite the conservative nature of  80  Testing and Results the estimates based on the Golden and Alt formula, the upper score for scenic beauty predicted in R-60-60-50 was exceeded in R-60-60-1 00 and R-60-60-300. This was the only time an upper score estimate from the Golden and Alt formula was exceeded by an observed value. If the larger stands have a greater probability of being earlier in the list, then it may be that they will be assigned better regimes, and hence the strategy will be better. Strict ordering by area (or age) did not produce an outstanding strategy (Table 6.3), and the earlier exploratory analysis was repeated using an area-weighted random stand order (Figure 6.4). Figure 6.4 Coolangubra StratSearch-1 exploratory search with area weighted random stand order all scores -  (a) Timber and Volume —*—  Mean Ar.iual Volume  ——  flmbet Flow Score  56  (b) Beauty  t  52  *--+-‘rf-.-  I.  aTF[L  o---.--1-.--..-.-  ..  -...-—.—-.—...-.-  —  ! ‘VL’1  42  50 51 52 53 54 56 57 58 59 60 83 83 64 68 66 68 69 K-upper  50 51  (c) Health  50 51 52 55 64 56  67  52 55  54  58  51  58 59 60 83 K-upper  83 84 65 88 68 89  (d) Water Quality  58 59 60 82 83 84 65 66 68 69 K-upper  50 51 52 53 54 56 51 58 69 60 82 83 84 68 66 68 66 K-upper  Note: Five random runs are plotted for each K-upper limit denoted. The five tick marks after Kupper 50 all refer to runs with a K-upper of 50. K-upper values are in thousands.  81  Testing and Results Figure 6.5 StratSearch-1 exploratory (area weighted random) search optimal scores -  (a) Timber Flow  (b) Beauty  a  \  K/A\ II  :  ..A  -.. -  ‘  -  ‘  4.’ ,...j..j 4.C----  v  —“  -  -  ET J ..  ..  -••••— -•--  4r  ..  -  ..  ..  -  4.C  -  ..  ..  -  ..  -  -  -  -  -  .  ..  ..  ..  ..  ..  ..  ..  ..  ..  -  -  ..  -  -  -  ..  ./ —.  ..  ..  ..  S 50  58  53  59 K-upper  62  65  68  50  3 K-uppe  (c) Health  .:  (d) Water Quality  —  —  -2000  —  ..  -2500  -  -  -  —  —  -  -  -  $000-3500 50  —  -  53 K-upper  ..  ..  -  ..  -  -  -  -  —  -  ..  -  -  -  _  -  I  53  6 K-uppei  Note: Filled in squares denote observed optimal scores. Blank squares denote Cooke (1979) predicted optimum. The major difference between the area-weighted and the random stand order was that the index scores were more tightly clustered with the area-weighted ordering. The best timber yield score probably lay between 55,000m /yr and 62,000m 3 /yr (Figure 6.5(a)), while the best 3 scenic beauty index may be between 51 ,000m Iyr and 67,000m 3 /yr (Figure 6.5(b)). The stand 3 health index indicated that no stand needed to be overstocked over an upper limit of /yr, and maybe as low as 56,000m 3 63,000m /yr (Figure 6.5(c)). Water quality was probably 3 worse until a limit of 61 ,000m /yr (Figure 6.5(d)) and then was comparable with the random 3 ordering. However, the marked differences between runs again suggests that more random  82  Testing and Results orderings may find better water quality scoring strategies. StratSearch-1 was rerun with an area weighted random stand ordering; however, the area weighted random runs did not show any consistent improvement over the random runs (Table 6.5). Table 6.5 Coolangubra test case best strategy comparisons for StratSearch-1 (area weighted random stand order).  Name A*R565650  A*R606050  A*R656550  Repetition  Type  Volume  Timber  Beauty  Health  Water  24 14 51 45 26 15 28 36 40 45 23 22 42 32 29  t v b h w b h t w v t v b h w  51,946 52,496 50,463 51,879 49,561 53,906 52,338 53,538 53,011 54,119 56,019 56,994 55,836 55,262 55,210  51,470 50,497 47,090 50,931 47,430 50,142 47,383 51,037 49,177 50,439 50,817 50,470 49,891 48,323 50,270  4.86 4.71 5.24 4.62 5.00 5.14 4.86 4.86 5.10 4.86 4.76 4.95 5.10 4.81 4.90  -1,397 -2,563 -1,263 -,763 -2,502 -464 -118 -755 -1,255 -755 -207 -248 -170 -25 -125  -27,149 -30,672 -28,198 -30,475 -25,804 -30,531 -28,047 2&,834 21,014 -26,834 -26,890 -30,077 -27,054 -28,939 -26,015  b = best scenic beauty score; h = best health score; t v = best mean annual volume; w = best water quality  =  best timber flow score  If the timber flow score was the most important characteristic of the operations schedule, run R-50-60-50, Repetition 15 was the best for Coolangubra (Table 6.4). The run took less than one hour, and this strategy was found in less than ten minutes. Repetition 15 was 11% and 5% poorer than PINEPLAN users 1 and 3 respectively, but 9% better than user 2. The scenic beauty scores were 12% and 3% better than users 1 and 3 but 7% poorer than user 2. The stand health score was poorer than all PIN EPLAN users, but the water quality score was better than users 1 and 2.  83  Testing and Results  Figure 6.6 Bombala StratSearch-1 exploratory upper limit search all scores -  (a) Timber and Volume —0--  Mean Annual Volume  —  -  20(  (b) Beauty  -  -.  .---  ---  0-a.a-.—  —  —  :: L  (  .e i  200  225  250  275  300  360  200  250  K-upper  (c) Health  200  228  260  275 Kupper  275  300  350  Kupper  (d) Water quality  300  380 Kupp.r  Note: Five random runs are plotted for each K-upper limit denoted. The five tick marks after Kupper 200 all refer to runs with a K-upper of 200. K-upper values are in thousands. While Repetition 15 was more than 12% lower in volume than the initial LINDO solution, it was only 5% lower than the manually integerized solution and actually 4% better than the (nonoptimal) integer solution given by LINDO. Repetition 15 is at least as attractive as the LINDO runs, with a health score better than LINDO (integer) but poorer than the manually integerized solution. The LINDO solutions had better water quality scores. Based on the above analyses with the Coolangubra plantation, it was decided to run an exploratory StratSearch with the Bombala plantation using ‘Sipper from 150,000m Iyr to 3 350,000m / 3 yr and KIower 1 0,000m /yr below Kupper (Figure 6.6). 3  84  Testing and Results Kupper values of 265,000 and 275,000 were selected and 100 random stand order searches made for each limit (Table 6.6). Table 6.6 Bombala best strategy comparisons for StratSearch-1 (random stand order).  Name R-265-275-100  R-285-295-100  Repetition  Type  Volume  Timber  Beauty  61 84 100 33 34 77 53 36 18  t v b h w t,v b h w  268,670 268,930 267,652 262,045 260,617 282,642 277,206 279,209 278,023  268,670 266,210 264,879 215,963 208,056 248,032 199,136 200,762 186,647  -1.95 -0.52 1.43 -2.14 -3.14 -1.71 2.14 -2.10 -0.81  b = best scenic beauty score; h = best health score; t v = best mean annual volume; w = best water quality  =  Health  Water  -136,668 -99,516 -148,478 -88,992 -125,252 -98,887 -94,408 -105,678 -143,784 -87,734 -117,448 -100,481 -117,078 -95,632 -91,279 -98,524 -112,317 -88,965  best timber flow score  Run R-265-275-1 00 Repetition 61 found the highest timber flow scoring strategy. This score was within 5% of the LINDO (standard) solution and 5% better than the manually integerized solution. The LINDO integerized solution was more scenically attractive and had a higher health score, but was poorer in water quality. Run R-265-275-1 00 Repetition 100 was 4% above the integerized solution in timber volume flow, as well as higher scoring in scenic beauty and water quality. However, the best StratSearch-1 strategy was over 20% poorer than the timber flow solution found by LINDO (non-standard). Adding the non-standard regimes to StratSearch-1 would make no difference if they were a priori ranked after the standard regimes. If these regimes were ranked before the standard regimes, then the majority of the plantation may be treated by the non-standard regimes to the detriment of the stands.  85  Testing and Results The PINEPLAN expert solution timber flow was much poorer than R-265-275-100 Repetition 61. However, the PINEPLAN solution mean volume, beauty, health and water quality were all better than Repetition 61. Repetition 100 had a higher timber flow and beauty score than PIN EPLAN for the 1991  -  1999 period and was found in much less time.  6.4 STRATSEARCH-2  6.4.1 LINEAR EVALUATION FUNCTION The regime evaluation function used in StratSearch-2 was of the form: V = 4*DefL  +  8 2*DefS 6*SurL 2*Sur -  -  +  400*Thin  +  1*VoI.  where: ) produced in a year where more than two times the timber 3 DefL denotes the volume (m yield significant deviation of Section 4.1.1(m ) are needed to reach the desired 3 mean limit. 5 denotes the volume (m Def ) produced in a year where less than two times the 3 significant deviation is needed to reach the desired mean limit. ) produced in a year where the desired mean has been met 3 Surs denotes the volume (m but not exceeded by more than the significant deviation. ) produced in a year where the desired mean has been 3 SUrL denotes the volume (m exceeded by more than the significant deviation. Thin denotes the number of thinnings. Vol denotes the total volume produced by the regime (m ). 3  86  Testing and Results These coefficients were the smallest found by the learning algorithm of Section 3.3.3 and were fairly robust. Different learning data-sets arrived at similar coefficients and many examples, not included in the learning data-set, were ranked in a rational order. The coefficient for the Thin parameter was much larger than the other coefficients. This was because Thin can only take on an integer value from 0 to 4, while the other parameters denote volumes produced in an operation and can vary between 50 and 620. The learning algorithm incremented the Thin coefficient by  +-  50, but the other coefficients by +- 1, when  searching for a logically correct evaluation function. Although an a priori best regime for StratSearch-1 would have an early first thinning, followed by two to three mature thinnings and a clear fall at around 35 years, the evaluation function tended to delay thinning with a clear fall at around 40 years when the incumbent partial solution had a large deficit in all years. This was found to produce the highest regime score because the number of thinnings could remain high and a higher volume was produced by delaying thinning. Therefore, the first stand selected was usually assigned this delayed thinning regime. The large negative coefficient associated with SurL had the tendency to delay some thinning past the planning horizon for stands selected later in the run.  6.4.2 TEST RUNS Tests for StratSearch-2 using the Coolangubra test data were carried out in a manner similar to StratSearch-1. The K limit was initially set very high to simulate an unconstrained problem, and then exploratory tests systematically searched for an appropriate K level (Figures 6.7 and 6.8(a)-(d), Table 6.7). These runs were much slower than StratSearch-1.  87  Testing and Results Figure 6.7 StratSearch-2 exploratory search all scores -  (a) Timber flow and Volume -—  ——  Mean i1M  (b) Beauty  :  Volume  Thnber Flow Scota  “,  Il U  4.  .—  4.4  -  -...-‘-  -  -  -  I  4  -  -  iii i i r 1 iii ii i Ii IL ii I U I  1 ii i  -  -—  .4  -.  44-.  4  -  6 45  46  47  48  49  51  52  53  54  55  57  58  59  60  45  61  46  47  48  49  51  Guiding K limit  (c) Health  52 83 54 55 Gukling K bmit  87  58  59  60  61  (d) Water Quality  45 46 47 48 Guking K Imi  49 51  52 53  54  55  57  58  59  60  81  Guiding K limit  Note: Five random runs are plotted for each K-upper limit denoted. The five tick marks after Kupper 45 all refer to runs with a K-upper of 45. K-upper values are in thousands. The timber flow score increased to a plateau of 55,000 as the K limit increased to 58,000m / 3 yr (Figure 6.8(a)). The low flow scores when K was less than 3 48,000m / yr are due to surplus volume production (Le., more than 1 0,000m 3 above the average volume). Despite the negative coefficients associated with surplus production, thinning operations were scheduled to produce volumes above the guiding K volume to enable more thinning to be carried out at later dates. Scenic beauty tended to decrease with an increase in the K volume. However, most of the exploratory strategies were more attractive than StratSearch-1 exploratory strategies. A K guide of 3 58,000m / yr produced one of the highest beauty scoring strategies (Figure 6.8(b)).  88  Testing and Results Stand health decreased with an increase in the K limit, but again was generally superior to StratSearch-1 (Figure 6.8(c)). Water quality decreased with an increase in the K limit (Figure 6.8(d)). Three StratSearch-2 runs were made with K limits of 3 55,000m / yr, 3 58,000m I yr and 60,000m / 3 yr and 50 repetitions (Table 6.8). Table 6.7 Coolangubra test case scores for StratSearch-2.  Name  Time  Unconstrained  23m  Area-55-1 Area-58-1 Area-60-1  Sort n/a b  23 mm 23 mm 23 mm  Volume  Timber  Beauty  Health  Water  109,982-6,398,113  0.62  -23,931  -33,787  Area b Area b Area b  50,637 53,531 55,329  49,543 52,584 54,785  5.24 5.00 5.14  -540 -703 -659  -28,883 -27,634 -29,326  25 hr Random b c g  54,1-6a 54,352 57,512  53,155 53,537 61,436  533 5.35 5.76  -223 -205 474  -26,755 -26,688 -23,670  R-58-50  27 hr Random b c g  57,066 57,160 59,712  56,023 56,174 60,236  5.24 5.25 5.81  -725 -719 134  -26,491 -26,314 -22,460  R-60-50  27 hr Random b c g  57,444 57,514 59,453  56,434 56,458 60,362  5.14 5.16 5.62  -638 -626 262  -26,270 -25,988 -21,370  R-50-50  -  Name describes Stand Order guiding volume repetitions b denotes the ‘best’ (maximum) observed c denotes the estimated optimal using Cooke’s (1979) algorithm g denotes the estimated upper boundary using Golden arid Alt’s (1979) algoiithm Volume limits in thousands of meters cubed -  -  The Cooke estimated optimal based on the exploratory search were again quite realistic. The estimated optima for the timber yield flow were close to, but not exceeded by any of the observed values from the later runs. Only R-60-50 had an observed scenic beauty score that exceeded Cooke’s estimate (by about 3%), while only R-50-50 exceeded the health and water  89  Testing and Results quality estimates. The Cooke estimates, based on the 50 random runs, also appeared quite realistic. The Golden and Alt estimates, gave values that could never be reached for all three health scores. Figure 6.8 StratSearch-2 exploratory search optimal scores -  (a) Timber Flow  -  (b) Beauty  45464748495051 52535455565758596061 62  4647484950515253545558578858606162  Guiding K limit  -  (c) Health  -141K’  45464748495051525354568857  Guln K mit  -  (d) Water Quality  859608162  45 464748 49 5051 525354 55565758 5960 61 62  Gudng K Imit  Guiding K hmlt  Note: Filled in squares denote observed optimal scores. Blank squares denote Cooke (1979) predicted optimum. Run R-60-50 Repetition 11, provided a solution that had no significant timber flow deviations, and had a timber flow score within 8% of the LINDO solution (Table 6.8). This Repetition scored higher than the two integer solutions in timber flow and beauty, but poorer in water quality. It was also higher scoring in every category, except water quality (water quality was only 3% lower), than StratSearch-1 R-50-60-50. Repetition 11 also had a higher timber flow  90  Testing and Results  score than PINEPLAN users 2 and 3, and lts beauty score was better than users 1 and 3 and within 1% of user 2. However, the health score was lower than all three PINEPLAN users. Table 6.8 Coolangubra best strategy comparisons for StratSearch-2  Name  Repetition  Type  Volume  Timber  Beauty  Health  Water  R-55-50  15 2 23 11 50  t v b h w  53,691 54,163 52,443 50,804 50,971  53,155 50,094 48,374 48,803 48,111  4.95 5.14 5.33 5.19 5.10  -418 -593 -722 -233 -260  -28,402 -27,878 -28,154 -26,972 -26,755  R-58-50  12 40 19 38 7  t v b w  56,137 57,066 55,363 54,555 55,442  56,023 53,984 52,937 53,322 53,471  4.95 4.00 5.24 5.14 4.43  -791 -1,619 -1,403 -725-1,356  -30,691 -30,448 -30,398 -29,1-56 -26,491  R-60-50  43 19 11 3 10  t v b h w  56,690 57,444 55,527 55,038 56,295  56,434 44,277 55,527 55,038 55,838  5.10 4.52 5.14 5.05 4.71  -1,416 -1,824 -1,203 -638 -695  -28,817 -27,752 -34,303 -32,527 -26,270  R-60-50+  47 22 46 17 33  t v b h w  59,991 58,259 57,416 56,404 56,261  56,826 51,048 53,920 55,678 56,261  4.90 5.00 5.10 4.95 4.95  -887 -1,536 -1,537 -683 -880  -28,590 -28,326 -27,621 -28,043 -26,209  b = best scenic beauty score; h = best health score; t v = best mean annual volume; w = best water quality  =  best timber flow score  The inclusion of non-standard regimes in R-60-50+ improved the best annual volume and timber yield scores, although the runs were slower. Run 33 of R-60-50+ was better than PINEPLAN user 2 and user 3 in all aspects except health, and was within 5% of PINEPLAN user 1 for timber flow score.  91  Testing and Results The major problem with StratSearch-2 was its speed; 50 repetitions required a complete day to run the Coolangubra data. The addition of the non-standard regimes caused StratSearch 2 to further slow by about 25%. If only the first 20 repetitions were evaluated in the Coolangubra tests, the best scores remained the same, or dropped by less than 2%. An initial search of the Bombala data immediately suggested difficulties with the scale of the problem. An exploratory run, R-290-5, found scores reasonably close to the Bombala PINEPLAN run, but had a large negative timber flow score and ran over seven hours (Table 6.9). The poor timber flow score was caused by yields in the period 2000 to 2005 averaging well above the guiding K limit, while the period 1990 to 1993 averaged well below the limit. The Linear Evaluation Function that ranked the regimes was designed to stop this sort of uneven distribution. However, the initial Function defined a small-deficit as being within two significant deviations of K  (he., within 3 20,000m ) , while a large deficit would be any year with more than 20,000m 3 below K currently scheduled. Thus, for Coolangubra, the value or importance of adding to a years volume would change after about 60% of the K volume had been achieved. Because the significant volume deviation for Bombala was also 1 0,000m 3 and the harvest level was much higher, the Linear Evaluation Function would not change the value of adding volume to a particular year until 95% of the K volume had been met (he., a large deficit occurred until 95% of the K volume had been scheduled). The model therefore kept assigning volume to a year that had nearly reached its K volume, when it could have been assigning it instead to another more deficit year. To overcome this problem, the Linear Evaluation Function was expanded to include another deficit term: huge deficit. Volumes produced in the small deficit range (i.e., K to K minus 20,000) were weighted as 2, volumes in the large deficit range (i.e., K minus 20,000 to K minus 100,000) were weighted as 4, and volumes in the huge deficit range (he., less than K minus 100,000) were weighted as 8. The huge deficit term would have no effect on the Coolangubra  92  Testing and Results analyses presented before. StratSearch-2 runs that included the expanded Linear Evaluation Function are denoted with an * (e.g., R2905*). Further exploratory tests on Bombala suggested that the inclusion of the huge deficit improved the timber flow scores, however these scores were still low. Because the Bombala data had many stands, I decided to make only 20 repetitions per run to keep the time reasonable (Table 6.9). Random, and area- and age-weighted random stand orders were tried. Ageweighted random stand orders (younger stands appearing earlier in list) tended to give higher timber flow and health scores. Area-weighted stand orders gave very poor scores and were not extensively examined or reported in Table 6.9. The optimal values estimated by Cooke’s formula, suggested that the best possible strategy could score more than 20% higherthan the best strategobserved in 20 runs. The  estimated optimal values provided by Golden and Alt’s formula suggested that the upper scores may be as much as 200 500% higher than the best observed scores. Thus, 20 runs were -  probably insufficient to find a strategy close to the optimal possible by applying StratSearch-2 to the Bombala data. However, it appeared obvious that too much time would be needed to find a strategy that would meet the timber flow constraints; further runs were not warranted. The best strategies produced by StratSearch-2 were generally inferior to those produced by StratSearch-1 for the Bombala data. As I watched the strategy being built, I often noticed that the stands appearing early in the stand order were not given an optimal regime. For example, if the first stand considered could be thinned between the years 1990 and 1999 (Le., ages 13 to 21), StratSearch-2 would select a thinning in 1995 (i.e., age 18). Thinning at age 18 allowed two further thinnings followed by a dean all and the production of the maximum volume within the planning period, but inefficiently directed volume away from 1990  -  1993 which were problem  years. Stands appearing later in the stand order were more likely to be assigned a regime that  93  Testing and Results concentrated on the 1990  -  1993 deficit period, but too much volume had been directed away  from these years and the timber flow could not be balanced. Table 6.9 Bombala best strategy comparisons for StratSearch-2.  Name  Repetition  Type  Volume  Timber  Beauty  Health  Water  R-290-5  1 4 2 5  t v b,w h  332,886 333,387 329,116 323,218  -45,4903 -45,4878 -72,7120 -46,9281  0.52 -0.85 0.85 0.38  -51,149 -52,046 -54,605 -49,373  -91,424 -93,804 -90,654 -92,172  R2905*  1 3 4  t v,b,h w  285,689 298,370 278,881  21,432 -2,200 8,809  -2.95 -99,450 1.24 -83,348 0.29 -108,871  -97,801 -88,856 -88,483  266,060 274,762 280,763 285,086  252,205 256,124 233,413 205,940  -0.76 -0.71 -0.76 -0.76  -95,042 -92-,39G -98,365 -93,635  272,989 287,329 276,435 274,580  167,222 39,995 82,892 -60,569  0.76 -103,960 -95,394 -1.43 -92,181 -102,655 -1.43 -81,791 -93,611 -1.05 -123,413 -92,019  Age2701* Age2801* Age2901* Age3001*  -  Age*R28020*  1 11 1 11 6 4 8  t,b v h w  b = best scenic beauty score; h = best health score; t v = best mean annual volume; w = best water quality  =  -55,169 -55,014 -56,349 -54,930  best timber flow score  6.5 STRATSEARCH-3 StratSearch-3 did not use random stand orders, and the only unknown was the guiding volume level. A systematic search for the best K level would find the best StratSearch-3 strategy (Table 6.10).  94  Testing and Results Table 6.10 Coolangubra strategy comparisons for StratSearch-3  Name  Time  Volume  Timber  Beauty  Health  Water  SS3-45  6 hours  (386)  51,808  51,048  5.24  -467  -29,466  SS3-47.5  6 hours  (386)  53,767  52,420  523  -515  -30,613  SS3-50  6 hours  (386)  55,444  53,416  5.09  -923  -28,147  SS3-52.5  6 hours  (386)  56,702  54,703  4.85  -1,326  -30,597  SS3-55  4 hours  (486)  53,538  51,865  5.23  -714  -27,157  SS3-60  14 hours  (W)  54,895  53,976  5.09  -841  -27,982  (386) denotes running under DOS with an 80386 chip (486) denotes running under DOS with an 80486 chip (W) denotes running under Microsoft Windows with an 80386 chip The StratSearch-3 runs for Coolangubra all failed to find a strategy without significant deviations in timber flow. Generally, the flows deviated with surplus volume production in years 2000 to 2005. The runs with a guiding K of 55,000m 3 and above, also had significant volume deficits in 1991 to 1993. SS3-45 was higher scoring in all attributes than PINEPLAN user 2. PINEPLAN users 1 and 3 had better timber flow and health scores, but poorer beauty scores than any of the StratSearch-3 runs. Several StratSearch-3 runs were better in every aspect except water quality than the LINDO (integer) solution. Every StratSearch-3 run exceeded the LINDO (manual integer) solution for beauty score, but were lower for all other aspects. The StratSearch-3 runs were higher scoring in beauty and health than R-50-60-50 repetition 15 (Table 6.4) and R-60-50 repetition 11 (Table 6.8).  95  Testing and Results  StratSearch-3 required four to fourteen hours to run using Coolangubra data (depending on the system). The Bombala data would be three to four times slower than Coolangubra because there are more stands. A single run using Bombala data could therefore take several days, and it was impractical to systematically search for the best guiding K value. The Bombala plantation was scheduled with StratSearch-3 using an arbitrarily selected guiding K of 280,000m 3 and the expanded Linear Evaluation Function (Table 6.11). Table 6.11 Bombala strategy for StratSearch-3  Name SS3280*  Time  Volume  Timber  6 days  280,771  271,162  Beauty  Health  Water  -2.52 -105,082  -94,254  SS3280* scored higher than LINQ (Manual Integer) in timber flow and water quality and higher than the PINEPLAN expert timber flow. It also scored higher than R-265-275-1 00 repetition 61 in all aspects except beauty (Table 6.6). StratSearch-2 runs generally bettered SS3280* in all aspects except timber flow (Table 6.9).  6.6 EXPERT SYSTEM The application of ES-i with a goal hierarchy favouring timber flow improvement to the StratSearch and PINEPLAN strategies led to an improvement of at least 4% in the timber yield score (Table 6.12). ES-i found several strategies that dominated or nearly dominated the LINDO or PINEPLAN solutions. Note that in Table 6.12, a score greater than 100% denotes improvements in volume, timber flow and beauty if the original scores were positive, but less than 100% denotes improvements in health and water quality (i.e., less thinning is delayed). Changes in the health  96  Testing and Results  score can appear very dramatic when looking at the percentage change. However, this is occasionally due to the denominator being close or equal to zero (e.g., SS1 unconstrained). Because ES-i was only accessing the standard regimes, many of the changes to PINEPLAN user 1 strategy replaced non-standard regimes with standard ones. The standard regimes are better silviculturally for the stand and thus these changes would improve the stand as well as improving timber flow and forest beauty. The goal hierarchy and initial condition determined how much ES-i could improve the strategy. Experimenting with different goal heirarchies lead to different scores being improved, occasionally at the cost of the remaining scores. It was generally easiest to achieve an increase in timber flow score without lowering the other scores by more than 5%. -  Table 6.12(a) Coolangubra strategy improvements for ES-i  New score (Percent of Original) Timber Beauty Health  Initial Strategy  Volume  PINEPLAN user 1  62,693 (106.4)  61,661 (104.7)  4.57 (107.8)  -286 (204.3)  -30,242 (106.6)  PIN EPLAN user 2  56,226 (100.1)  56,060 (114.5)  4.90 (94.4)  -452 (89.8)  -33,611 (95.2)  SS1 Unconstrained  62,570 (87.6)  61,759 (-21.2)  -1,642 3.95 (91.2) undefined  -31,297 (104.4)  SS2 Unconstrained  58,945 (53.6)  58,540 (-0.9)  4.52 (729.0)  -1,801 (7.5)  -32,070 (94.9)  R-50-60-50 Rep 15  57,379 (108.0)  57,379 (108.0)  4.76 (99.0)  -890 (46.3)  -29,810 (106.3)  SS3-60  59,572 (108.5)  58,604 (109.1)  4.86 (95.5)  -811 (96.4)  -30,976 (110.7)  SSi denotes StratSearch-1, SS2 denotes StratSearch-2, SS3 denotes StratSearch-3  97  Water  Testing and Results Table 6.12(b) Bombala strategy improvements for ES-i  New score (Percent of Original) Timber Beauty Health  Initial Strategy  Volume  R-265-275-i 00 Rep 61  272,934 (101.6)  272,934 (101.6)  Age-280-1  273,387 (96.1)  267,416 (104.4)  SS3-280  285,868 (101.8)  282,541 (104.2)  -1.43 -145,038 (73.3) (106.1) -0.76 (107.0)  Water -97,494 (98.0)  -57,795 -101,016 (105.1) (109.3)  -0.71 -100,209 (28.1) (95.4)  -94,394 (89.8)  SS3 denotes StratSearch-3 It is interesting that very different initial strategies were modified by ES-i to give final strategies with similar scores (e.g., PINEPLAN user 1 and SS1 unconstrained have mean volume and timber flow scores within 0.2% of each other). The regimes initially applied to each stand rarely coincided, but after modification by ES-i, several stands generally shared the same operation schedule. For example, no stands were initially scheduled by SS1 unconstrained with operations the same as PINEPLAN user 1, but after modification by ES-i, nine stands had common regimes scheduled. ES-i did not generally find strategies without significant deviations in timber flow unless there were no deviations in the initial strategy. ES-i also failed to find large improvements in beauty or water quality. This was due to ES-i’s inability to move or reschedule several stands at onetime. ES-2 overcame this problem (Table 6.13) by using rules which considered more than one stand at a time.  98  Testing and Results Table 6.13 Strategy improvements for ES-2  New score (Percent of Onginal) Timber Beauty Health  Initial Strategy  Volume  PINEPLAN user 1 (Coolangubra)  62,200 (105.6)  61,525 (104.5)  4.62 (109.0)  -100 (71.4)  -27,005 (95.1)  R-50-60-50 Rep 15 (Coolangubra)  58,771 (110.6)  57,773 (108.7)  4.81 (100.0)  -604 (31.4)  -24,991 (89.1)  R-265-275-1 00 Rep 61 (Bombala)  287,334 (106.9)  277,435 (103.3)  1.14 (-58.5)  -95,589 (69.9)  -76,161 (76.5)  Water  ES-2 found better scoring strategies than ES-i, and the revised strategies dominated the initial strategies for all scores. The improvements in beauty, health and water quality were generally greater than the improvements afforded by ES-i. Groups of stands were selected and modified and this allowed the spatial aspect of the forest to be adequately considered. ES-2 was slightly more difficult to run than ES-i. Scores not on the top of the objective hierarchy were allowed to decrease significantly in the first stage to hopefully be reclaimed in the second stage. The user needed to order the heirarchies for both stages as well as set the allowable drops in scores.  6.7 RISK The expert system improvements to initial strategies indicated that there were certain stand I regime combinations that were common in good strategies. It was anticipated that some stand / regime combinations would also be common to strategies that scored best when risk was introduced into the growth models through stochastic modelling.  99  Testing and Results Using only timber flow score, the repetitions for StratSearch-i R-50-60-50 were ranked. Using a stochastic growth model, the yield flows for the best 10 strategies were recalculated and reranked. Each strategy was modelled five times with the stochastic growth model. Using the common stand I regime combinations and ES-i, a new strategy (common_base) was built up. Stand I regime combinations that were common to at least five of the 10 best scoring strategies were identified. These were fixed and ES-i could make little or no change to these. Combinations common to three or four strategies had a greater chance of having some operations rescheduled, while stands with fewer than three operations common in the ten best strategies where maniplulated by ES-i around the volumes already produced to find the best scoring strategy. The common base strategy produced had a beauty score of 4.62, a healthsccre of -302-and awater q alltyscoraof -2Z063. Under deterministic growth modelllng the timber flow score was 56,182. The timber flow score of the common_base strategy was calculated for 50 runs where the growth was again stochastically modelled. This was compared with the score from R-50-60-50 repetition 15 and LINDO under 50 stochastic runs (Table 6.14). Except for common_base, the mean timber flow scores for the stochastic runs were slightly lower than the deterministic scores. Common_base has stochastic score means above and below the deterministic score. The common_base had the lowest variance and range of timber flow scores, while the expert system had the highest variance and range. The expert system strategy was highest scoring for mean, minimum and maximum timber flow which means it would be ranked best by maximin, maximax or expected value criteria.  100  Testing and Results  Table 6.14 Timber flow scores under nsk for Coolangubra  Risk  Mean  Coefficient of Variation  Common_base 1% R-50-60-50 Rep 15 1% ES-i R-50-60-50 Rep 15 1% LINDO 1%  56,231 53,125 57,223 55,400  0.45 0.52 0.62 0.55  55,678 52,357 56,051 54,783  57,003 53,674 57,841 56,073  1,325 1,316 1,795 1,290  (2.3) (2.5) (3.1) (2.3)  Common_base 2% R-50-60-50 Rep 15 2% ES-i R-50-60-50 Rep 15 2% LINDO 2%  56,059 53,194 56,730 55,508  0.86 1.11 1.04 1.01  55,061 51,623 55,376 54,315  57,245 54,388 58,134 56,537  2,183 2,765 2,757 2,221  (3.9) (5.2) (4.8) (4.0)  Name  Minimum Maximum  Range  0 denotes the percentage of the mean value. Statistics based on 50 random runs. The (area-weighted) mean time interval between operations for the expert system strategy was 7.98 years. This was significantly greater than the average interval of the other strategies (p<0.05). The other strategies had a mean interval of about 6.7 years.  101  (%)  7. DISCUSSION  7.1 INTRODUCTION In many instances, the strategies produced by the models developed during this research were at least as good as the strategies produced by conventional operation scheduling techniques. StratSearch-1 was able to find strategies for both Coolangubra and Bombala data that were better in at least two strategy scores than the LINDO or PINEPLAN solutions. StratSearch-2 found strategies for Coolangubra that, except for water quality, dominated StratSearch-1 and some conventional strategies. However, StratSearch-2 was unable to perform as well as the other techniques for the Bombala plantation. In particular, the timber flow score  was very low.  The knpwledg Qoritatned Lii StratSearch-Z’s Liftear Evaluation Function apared  to be deficient or incomplete and unable to correctly direct regime allocation in a large plantation problem. StratSearch-2 appears to be a useful technique for small operations scheduling problems. StratSearch-1 may be more generally applicable but unable to produce as good strategies as StratSearch-2 in small plantation problems. StratSearch-3 was unable to find a strategy without a significant deviation in the timber flow. The Linear Evaluation Function appears to have deficiencies in ordering the stands. The expert systems were able to improve the strategies produced by any of the models for either of the plantations. The relative improvement in strategy was influenced by the userdirected goal hierarchy and the initial strategy. The following sub-sections discuss the strengths and weaknesses of the search and expert system models developed. The potential for the models, and the scoring functions, will also be examined.  102  Discussion 7.2 STRA TSEARCH MODELS StratSearch models 1 and 2 are a combination of random and well-disciplined components. In common with several other forest search models (e.g., O’Hara 1987, Clements et. aL 1990, O’Hara etah 1990, and Nelson and Brodie 1990), the ordering of the stands is not well disciplined, but random or weighted random. The assignment of regimes to stands is disciplined, although the StratSearch models consider a much larger domain of possible regimes than other models. In StratSearch-1, the regimes are systematically examined in an order independent of the current problem. This is similar to other models, and good solutions can be found. StratSearch-2 reorders the regimes depending upon the current problem and partial soIutin.  can thus apply domain knowledge to take advantage o the way in which the problem  is progressing. This is unlike other forest search models referred to in this dissertation. The SCRAM model (O’Hara 1987; O’Hara et al. 1989) for example, did not consider changes in value or volume over time for a stand. It simply scheduled a harvest in the next legal harvest period when the stand was encountered in the list of stands. Therefore SCRAM did not recognize that the next harvest period may not be the most advantageous harvest period in certain circumstances. If the next harvest period was not critical, and the stand was still growing well, then its harvest could profitably be delayed. StratSearch-2 was able to consider delaying the harvest of such stands. StratSearch-3 removed the random component from the search. It used the Linear Evaluation Function to become a well-disciplined, best-first search model (without backtracking). The stands were ordered by the linear evaluation score of their highest scoring regime. Large area stands with regimes that produced volumes in deficit years were thus ranked before smaller stands and stands that produced volumes in other years.  103  Discussion The StratSearch models use a conceptually simple approach and do not require a sophisticated explanation procedure. Foresters need only examine and approve the systematic way in which the regimes are examined to understand the model. Re-ordering or adding to the thin_rules database could change the systematic order of regime construction if desired. The coefficients for the Linear Evaluation Function of StratSearch-2 and StratSearch-3 could similarly easily be modified by the user. Regimes ranked by the Function could be displayed for the user’s approval. If the ranking was not approved, the new ranking could be asserted into the failed example database (Section 4.4), and new coefficients searched. The user could also examine the regimes and ranking as the model is running. If an incorrect assignment is made, the user could interrupt the search and directly change the Function coefficients. Thus, the Function could increasingly mimic the waythe human managerwould schedule the forest. By looking at the summaiy scores for each of the strategies constructed, the user may also gain an understanding of the whole problem (e.g., what years are likely to be limiting, what areas and years are critical for scenic beauty and water quality). Because all the strategies are stored, the manager can examine and rank them according to his I her own reasoning and intuition. Additional characteristics can be easily scored and added to the comparison. Some StratSearch runs can require several hours or days to run. For example, StratSearch-3 took six days to develop a schedule for the Bombala plantation. This would be reduced to one or two days if a 80486 chip microcomputer were used without the multitasking environment of Windows. Even six days is not excessive when human experts would require months of expensive professional time. A dedicated 80386 microcomputer could be purchased for a few thousand dollars.  104  Discussion The StratSearch models are user-friendly and easily run. The user has a great deal of control over the model, but can still easily understand it and its strategies. Once the stand and regime databases are accessed, the user simply needs to set the limits and the number of runs desired.  7.3 THE EXPERT SYSTEM O’Hara (1987) noted that it could be very difficult to reorganize stand regimes in a strategy because of the interaction with geographic constraints. He concluded his Ph.D. dissertation with the following paragraph: It would be desirable to be able to take the best solution found by SCRAM and use it as a good starting point in the search for the true optimum. No suitable technique was found in the course of this study, but such an approach seems at present to be the only potential means by which the true optimum can be found. The expert system developed in this research is a tool that could be used to find the strategy optimum, or at least get closer to it. Even the simple ES-i model, using a series of goals and an exhaustive search, could make important improvements to a strategy. However, ES-i did not need “the best” strategy as a starting point, it needed one that did not require too much swapping of regimes between stands. This sort of regime swapping is exactly what O’Hara (1987) had in mind to improve the strategies developed by SCRAM. ES-i performed very well when the initial strategy was provided by unconstrained StratSearch models. Many stands were initially in an a priori best regime and ES-i could reschedule one or more away from that regime to improve the forest-wide strategy. The much more difficult task of swapping one stand into a year and moving another out of that year was avoided. ES-2 was able to swap regimes amongst stands, but the initial strategy was still important. Different starting strategies still led to different final strategies. Also, the user’s goal  105  Discussion hierarchy was important and different heirarchies would emphasize different improvements in scores. The expert systems used Botvinnik’s (1984) idea of multiple goal levels and a general goal. Merging sub-goals to meet an optimal goal is difficult where there are interactions between goals (Yang et a!. 1990) and this is why ES-2 could produce different scoring strategies from the same initial strategy. Several methods may be used to improve the situation when the interactions are limited (Yang etah 1990). However, the interactions between goals in operations scheduling are highly correlated because each operation may affect all the products of the forest. One user of PINEPLAN equated yield scheduling with a huge electronic Rubic’s Cube putting -  one thing in place altered everything else! Often one goal can be attained in a variety of ways; different goal heirarchies can still cause a score to fall within a specified range. The ordering of the list of goals is important, as it was in the pioneering Artificial Intelligence systems GPS (Ernst and Newell 1969) and STRIPS (Fikes and Nilsson 1971). However, the attainment of one goal is not always antagonistic to other goals (e.g., all scores for SS2 unconstrained were dramatically improved by ES-i). The timber flow score could have been improved without the other scores showing marked improvement, especially if the other scores had been included as constraints. Because MP models often include these other goals as constraints, this non-optimal improvement would be common. However, the expert systems enhanced the score improvement through the inclusion of the general goal. The expert systems can remove a lot of the routine work from operations scheduling. When using PIN EPLAN, much of the work is routine. The initial strategy is provided by the application of routine rules and then operations are moved forward or backward one or two years to balance the flow. However these simple changes may take many hours and do not ensure a  106  Discussion balanced flow. The PIN EPLAN expert may then introduce a non-routine option and apply it to several select stands. The remaining stands are then readjusted. ES-i and ES-2 can do the routine adjustments very easily and competently as these adjustments are based on simple rules. However, the selection of an appropriate non-routine regime is often an inspired choice! Experts are unsure of how they select non-routine options and it may therefore be very difficult for an expert system to duplicate. It may not be necessary to try to duplicate these inspired guesses if user can easily enter them and then allow the expert system to adjust the flow to take the most advantage of the changed situation.  7.4 STRATEGY SCORES The strategy scores were designed to provide an estimate of the quality of the various aspects of the strategy. They provided numeric values that could be compared and contrasted. Low scoring strategies for a particular aspect were poorer in that aspect than higher scoring strategies, but the user must make the trade-offs between the different aspects. Because the scores provided numeric values and StratSearch-i and StratSearch-2 had random elements, algorithms were available to predict the range of scores possible. The Cooke (1979) algorithm was used to predict the optimal score possible if a very large number of random repetitions were made. Occasionally, the observed optimum score was greater than the Cooke estimate and sometimes the Cooke estimate was higher than the theoretical maximum score. However, it seemed to predict well, especially for the mean volume and timber flow scores, even with as little as five runs. Increasing to 50 or 100 runs did not seem to improve the estimate. The quality of the Cooke (1979) estimation procedure was due, in part, to the freedom from an assumed distribution. It was not necessary to generate enough runs to show a particular distribution pattern. Also, the StratSearch models tended to exclude strategies that would have  107  Discussion  very low volume, timber flow, beauty and health scores and hence the ranges of the scores were smaller than otherwise might have been encountered. The Golden and Alt (1979) algorithm did require assumptions about the distribution of the scores; the distribution must be modelled by a three parameter Weibull cumulative distribution. Sufficient points were needed to make reasonable estimates of the parameters before the distribution could be modelled. I did not test the score distributions to see if they met this characteristic, although the distributions shown in Figure 6.3 look as though they could be represented by a Weibull distribution. For small random samples, the Golden and Alt formula estimated a very wide confidence limit range to the scores. In only one case was the optimal observed value greater than the upper limit predicted by the Golden and Alt algorithm. The major use of the estimated optimum score would be to determine if further runs were justified to find a good strategy. StratSearch-2 for Bombala is an example where this was necessary. Each repetition required more than two hours and hence two days elapsed before R 28O20* was completed. The timber flow scores were low and a decision was necessary to either abandon any further runs, or seek a better score. The Cooke (1979) formula suggested that the best timber flow score produced by StratSearch-2 with a K of 280,000 and a large number of repetition would be less than 200,000 substantially less than Stratsearch-1 or LINDO solutions. -  The Golden and Alt (1979) algorithm however estimated that the true optima would lie between 167,222 and 461,675. The upper limit here is plainly infeasible, being 33% higher than even LINDO (non-standard). More repetitions would have doubtlessly brought the estimated upper limit down, but each repetition would have required two hours; if the estimate was refined to less than 250,000, then StratSearch-2 would be abandoned in favour of StratSearch-1 and all the additional repetitions would have been wasted.  108  Discussion Thus, if a large number of repetitions can be quickly produced, the Golden and Alt (1979) formula would be useful to show how close the observed best strategy is to the upper confidence limit. However, if repetitions are slow due to a large number of stands or possible strategies, the Cooke (1979) estimate would provide a good indication of the value of proceeding with the current search based on only a few strategies.  7.5 KNOWLEDGE IN THE REGIME FORMULATION The standard regimes discussed in this dissertation were developed by a model that used little knowledge about the scheduling problem. Essentially a regime was built operation by operation, and the only factors that went into the decision of operation timing were the age of the stand, time elapsed since last operation, and volume or area constraint violations. The models used the recommendations included in the Bombala MP to determine timing and age, while the user input the area and volume constraints. Thus, the regimes are based on silvicultural and operational knowledge. This type of knowledge caused the model to initially develop regimes with early and numerous thinnings and StratSearch-1 attempted to use these regimes first. Because both plantation datasets had uneven age class distributions which caused them to have deficit yield flows in the initial years, this bias towards early thinnings allowed good strategies to be developed. If the age class distribution had caused the deficits to appear towards the end of the planning period, early thinnings may not have been so appropriate and the knowledge included in the regime generation algorithms may have been insufficient to develop good strategies. However, many of the plantation estates in Australia have an age class distribution similar to those of Coolangubra or Bombala.  109  Discussion When the thin_rule database was incremented with non-standard regimes (Le., thinning to low basal areas and early clearfall options), the potential number of regimes increased dramatically. However, often these non-standard regime options should not even be considered by the model. The conditions listed in the thin_rule database should be expanded to allow the exclusion of regimes as appropriate. For example, StratSearch-1 could not effectively use the non-standard regimes. If they were placed at the end of the database, they could only be considered by the model if all the standard regimes had already been rejected. As the standard regimes could only be rejected because of too much volume production in a specified year, and the non-standard regimes generally produce more volume, then the non-standard regimes would also be rejected. If the non-standard regimes were however placed early in the thin_rule database, they would be applied as a priority. Thus some stands would be heavily thinned when unnecessary, while others would be unthinned and over-stocked because the volume for that year had already been provided. Similarly, StratSearch-2 was unable to effectively use the non standard regimes. The Coolangubra strategies developed with the non-standard regimes were not as good as PIN EPLAN user 1, nor much better than the StratSearch-2 runs which only used the standard regimes. The conditions in the thin_rule database should be expanded. For example, the non standard regimes should be excluded from model consideration if they produce extra volume in a year that will probably have a surplus volume produced by standard regimes. The factors and conditions that allow a potential surplus to be predicted would have to be isolated by the model from its database or from the user. Thus, the thin_rule database and get_strat clause could incorporate silvicultural, prediction, and planning knowledge in its regime construction. The database and get_strat algorithm could be used for the integration of knowledge derived from  110  Discussion stand research. Recommendations for fertilizer application, pruning, planting, etc. could be incorporated and new regimes developed. Examining the regimes developed and their usefulness could also indicate where research is needed. For example, the regimes developed in this dissertation generally were unable to produce large volumes at young ages. This was a significant drawback as deficits appeared early in the planning period and the only volume available was from the first thinnings of young stands. Research could properly be directed to finding ways of increasing this volume (e.g., non-commercial thinning and fertilizer application at age 10 years). Before spending large research resources, an estimate of the potential of this regime could be made by StratSearch. If the new regime did not improve the problem situation, research could be directed elsewhere. The StratSearch models could be improved in terms of strategy development and speed of operation as fewer, more sophisticated regimes are generated.  7.6 KNOWLEDGE IN THE LINEAR EVALUATION FUNCTION One of the fundamental concepts in this approach to operations scheduling is the inclusion and organization of non-procedural knowledge into the model. This knowledge has been abstracted from the plantation management plans, and from the PINEPLAN users. Section 6.2 shows how well PIN EPLAN users can schedule harvesting operations in a complex planning environment. In the Coolangubra data, foresters were able to arrive at strategies with timber flows that scored very close to the optimal given by linear programming. They were also able to balance the timber flow goal with health and scenic quality. The PIN EPLAN experts for Bombala were also able to schedule operations in a large plantation and arrive at a schedule which produced a scenically attractive and healthy forest, with a reasonably high timber flow. The major problem appeared to be time constraints. The three PINEPLAN  111  Discussion  users for Coolangubra would probably have the quality of their strategy ranked in order of the time spent on its derivation. Trying to duplicate the processes of PINEPLAN users obviously has potential and the Linear Evaluation Function was the basic tool of this attempt. The knowledge embodied in the Linear Evaluation Function improved the performance of the model in the Coolangubra forest (compare Table 6.4 with Table 6.8). However, the Bombala plantation was generally not as well scheduled with the use of the Linear Evaluation Function as StratSearch-1 (compare Table 6.7 and Table 6.9). StratSearch-3 was unable to find a solution that did not have significant timber yield deviations and its timber flow and volume solutions were inferior to StratSearch-1 and StratSearch-2 for Coolangubra. As opposed to the basic tenet stated in Section 3.1, the inclusion of some more knowledge did not lead to a better solution. The knowledge added was incomplete. The problem appears to stem from the fact that the evaluation function has little knowledge when it first begins its scheduling. The heuristic appears to be a good end game heuristic only. All the years are initially defined as having large (or huge) deficits despite the fact that some of those years would have huge surpluses if the a priori best regimes were applied to each stand. Because all the years in the planning horizon are thus weighted equally, the Function essentially selects the regime that produces the largest volume in the period. This would not be appropriate if the stand could have produced volume in another year, and the year where the maximum volume is produced is a year where many stands could also produce volumes. It is not until several stands have been scheduled, and their volumes start to influence the relative weighting of years for future volume production, that the knowledge in the Function takes real effect. Because the Coolangubra plantation was so small, this effect came into play almost after the first stand was scheduled. However, Bombala’s much higher potential yield flow and number of stands meant that the effect was very much delayed. The scheduling of the first stands will  112  Discussion  have a major influence on whether the final strategy will be good because the StratSearch models do not allow backtracking. StratSearch-2 produced reasonable strategies for Bombala when the stands were ordered by increasing age. The later years in the planning period were scheduled operations first (e.g., first thinning of the 1988 age class would produce a volume no earlier than the year 2001).  These later years were not limiting for volume, and the Linear Evaluation Function would rank them as much less important for volume (i.e., not a huge deficit) when scheduling the remaining stands. The older stands would be scheduled for operations in the truly limiting periods (i.e., early in the planning period). StratSearch-3 produced a good strategy for Bombala using the Linear Evaluation Function to order stands as well as regimes. This may be caused by the younger stands again being scheduled first, thus giving a better indication of the truly limiting years. The young stands would be scheduled first because they tended to have larger areas, and hence larger volumes would be produced by operations on these stands. Thus, the only time that the Linear Evaluation Function was able to effectively schedule operations for Bombala was when additional knowledge enabled the determination of the truly deficit years before critical stands were scheduled. The Linear Evaluation Function should be able to rank the regimes using more information early in the problem. It may be necessary to expand the evaluation function to include a balance of potential and current factors. An initial unconstrained run could find where potential surpluses and deficits lay, and this information could control the early running of the model. As more stands are assigned, the current solution (i.e., a measure of how close the goals were currently being met), could be made increasingly important in controlling the search. Scoring heuristics in computer chess models are often best in the middle game. In the initial game, they usually draw on a compiled library of opening moves, while the end game is  113  Discussion  controlled by a different set of rules. Similarly, the StratSearch-2 model could be given a set of rules to relate to the different stages of the problem solution. The initial game could use a library of regimes related to the potential deficit and surplus of the various products. The middle and end games would be controlled by the heuristic already developed. Ideally, the evaluation function should also include some way of including non-wood values. Including thinning as an important component acts as a surrogate for a number of nonwood factors (e.g., health, scenic beauty as related to overstocking) and because of this, the health and beauty scores were often good. Note that StratSearch-3 had very high beauty scores because it was directed by the Linear Evaluation Function. However, values that are related to the spatial distribution of the stands are not incorporated very well in the Linear Evaluation Function. This is demonstrated by the water quality score. Water quality is mostly influenced by the spatial distribution of harvesting operations. The various strategies often had widely different water quality scores. While the Linear Evaluation Function helped to keep the timber flow, health and beauty scores relatively constant and high, the water quality essentially varied randomly. The problems with including spatial values into the Linear Evaluation Function are twofold: 1.  assumptions about the regimes of surrounding unscheduled stands must be made.  2.  the heuristic would be significantly influenced by the relative weighting of the spatial considerations against the other values. Therefore, a general evaluation function could not be determined.  114  Discussion  Figure 7.1 Potential linear evaluation function  Cost  Adj. Clearfall  N.P.W.  Adj.Thinnings Waterways Other  Another approach would be to treat the spatial factors as constraints. This is often done in linear programming approaches to yield scheduling, and also appears to be the approach used in many of the forestry random search models. For example, the area that can be cleared in one period is fixed, and then the best strategy that does not exceed this constraint is found. The StratSearch models could easily incorporate such constraints, but the problem would be the specification of the constraint level, and the fact that constraint setting is not optimization. The expert system improvements showed that often two or more scores could simultaneously be improved, but it is unlikely that these improvements would be realized if constraints were used to set levels. Setting these extra constraints may slow StratSearch-1 as more regimes may need to  115  Discussion be examined to find one that does not violate a spatial constraint. However, the constraints may actually improve the speed of StratSearch-2 as many regimes would be pruned early in the search and they would not need to be expanded and scored. If the Linear Evaluation Function is expanded, care must be taken to avoid making it appear too complex. Rather than having 20 coefficients in the function, the Function could be broken into three or four components, each of which may have three or four coefficients (e.g., Figure 7.1).  7.7 RiSK Managers tend to make decisions that minimize losses due to risk (Freudenburg 1988) or attempt to minimize the risk. For example, the Bombala MP notes the risk of significant loss through fire. Studies have shown that an appropriate response to the risk of fire would be to reduce the rotation length (Reed and Errico 1986). However, the Bombala managers do not reduce the rotation length in the presence of a significant risk of fire damage. They attempt to reduce the risk of fire (e.g., through prescribed burning), or reduce the risk of significant loss (e.g., by separating age class 7 areas ) . The managers appear unwilling to alter the general silvicultural practices or regimes, but will act operationally to deal with risk. The expert system risk experiment discussed in this dissertation is an attempt to help managers react to risk and uncertainties in growth. Certain stand / regime combinations (i.e., the game center-board) can be identified as important, and extra care could be devoted to those stands. As the foresters separate the age class areas so that one severe fire will not remove an entire age class and thus make operations scheduling very difficult, foresters can react 7  A fire is much less likely to destroy an entire age class when the plantings are spread over several spatially separate areas. Loss of an entire age class is very costly.  116  Discussion operationally to uncertainties in growth once the center-board is identified. Extra care could be devoted to these stands to ensure that the risk of damage or loss is reduced. The common_base strategy for Coolangubra identified those stand I regime combinations that were important in a good strategy under risky growth conditions. Ensuring that these combinations were scheduled lead to a strategy that was very robust. The variability in the R-50-60-50 expert system modified strategy (Table 6.14) was partially due to the longer interval between operations. The longer interval allowed larger deviations from the expected growth. The StratSearch models also provide a way of reacting to risk. Because multiple strategies are generated, sensitivity analysis is easy. A set of strategies can be selected and evaluated by scoring functions that represent the different possible future management objectives. Strategies that are disastrous under some potential futures would be excluded and the robust, good strategies determined.  117  8. CONCLUSIONS AND FUTURE RESEARCH Forest management planning problems exist at the stand and forest levels. Relevant knowledge about such problems also exists at these two levels. Stand level knowledge includes rules and heuristics about the timing and intensity of forest operations and can be used to generate good silvicultural management regimes for forest stands. This type of stand level knowledge was incorporated into the knowledge-based models developed during this research. The StratSearch-l model essentially used only this knowledge and a random ordering of stands to produce operations scheduling solutions that were close to, or better than, solutions produced by traditional operations scheduling techniques. For the small Coolangubra plantation forest, StratSearch-i found a solution that was higher scoring in timber flow, beauty and health than an integer programming solution, and better in at least two considerations than human expert PINEPLAN search solutions. For the larger Bombala plantation forest, StratSearch-i found a solution that was higher scoring in timber flow, beauty and water quality than an integer programming solution, but was not better than the human expert PINEPLAN solutions. Forest level knowledge was added to the stand level knowledge in StratSearch-2, StratSearch-3, ES-i and ES-2. This additional knowledge re-ordered the regimes developed by the stand level knowledge and to some extent was able to duplicate the approaches and successes of human operations scheduling experts. StratSearch-2 solutions dominated StratSearch-i solutions for the Coolangubra plantation forest and were also better scoring or within 5% of the human expert PIN EPLAN solutions for all aspects except stand health. StratSearch-3 applied the forest level knowledge in a different way to StratSearch-2, and produced solutions that dominated some human expert PIN EPLAN solutions and the integer programming solution for the Coolangubra plantation forest.  118  Conclusions and Future Research However, contrary to the basic tenet mentioned in Section 3.1, the addition of more knowledge to the knowledge-based models did not always lead to a better solution. The StratSearch-2 model contained more knowledge than the StratSearch-1 model, but was unable to find solutions that were as good as the StratSearch-1 model solutions for the Bombala plantation forest. The StratSearch-3 model was unable to find any solution for Coolangubra or Bombala that did not have a significant deviation in the timber flow score. This finding demonstrates the truth of the old saying “a little knowledge is a dangerous thing”. The forest level knowledge was related to the structure of the example forests, and this relationship should have been included in the heuristics (i.e., the fact that the knowledge was based on small forests or situations near the  end of the scheduling problem should have been included to constrain the heuristic). Thus, for any improvement in a knowledge-based model, the additional knowledge must be a complete whole, explicitly including any assumptions used in the extraction of the knowledge. The expert systems ES-i and ES-2 used additional forest level knowledge a hierarchy -  of forest management goals. This additional knowledge, and interaction with the user, allowed these systems to find solutions that dominated the previous best solutions. With only a fairly simple additional knowledge-base, the expert systems were able to complete the routine work of yield scheduling to find these good solutions. However, interaction with the user was required to make those intuitive leaps that computers find so difficult, to ensure that the best strategy found was a feasible optimal. Expert systems can deal with a large number of goals, constraints and stands and seem to be the tool requested by O’Hara (1987). The knowledge-based search and expert systems developed during this research are new tools for the forester involved in operations scheduling. The systems can exploit the intuition of the forester while removing the burden of routine decision making. They also provide a new way of dealing with uncertainty in operations scheduling by allowing robust solutions to be  119  Conclusions and Future Research developed. Combinations of stands and regimes that are important to any good solution can be identified using the search models. The expert system then incorporates these combinations into a strategy that is more robust than traditionally developed solutions. Using this approach, the important stand I regime combinations and other factors in a problem can be identified. Management can be directed to operational procedures that minimize the uncertainty for these factors or the effects of uncertainty, and hence produce an even more robust solution. Knowledge-based models essentially are not limited in the size of the problem that they can solve. However, some heuristics may have a problem of scale if they are developed from examples drawn exclusively from smaller plantations. The speed of the solution may also be influenced by the size of the problem, but because the models developed will run on any inexpensive IBM compatible microcomputer, this is not seen as a serious limitation. An estimate of the potential success of the search models can be made in as little as five repetitions using the Cooke (1979) algorithm. The Golden and Alt (1979) algorithm will more accurately estimate the confidence limits for the scores, but it requires more than 50 repetitions before it is of practical use. This dissertation demonstrates that knowledge-based models can provide good decision support systems for forest operations scheduling problems. The knowledge-based approach can incorporate spatial and non-quantitative problem aspects to produce strategies that are realistic and at least as good as conventional operations scheduling tools. Knowledge-based systems are simple to use and understand. The user has a great deal of control and can readily direct the search along preferred lines. Thus, even the simple search and expert systems used in this dissertation can act as consultants. The models can also incorporate risk through an implicit sensitivity analysis or through identifying the most important factors in the operations scheduling problem.  120  Conclusions and Future Research The search models and expert systems will improve as more (complete) knowledge is incorporated. The search models, in particular, need an improved starting game heuristic or library of regimes. Heuristics are also needed which will allow current and potential spatial conditions to be accurately incorporated into the decision making process. This will probably require a geographic information system for data storage and spatial modelling. A knowledge-based approach to operations scheduling support systems has the potential to provide a system that acts as a perfectly informed consultant. 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