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Old-growth forests for wilderness preservation and timber production in British Columbia: a goal programming… Wang, Sen 1994

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OLD-GROWTH FORESTS FOR WILDERNESS PRESERVATIONAND TIMBER PRODUCTION IN BRITISH COLUMBIA:A GOAL PROGRAMMING MODELbySEN WANGB.A., Beijing Foreign Studies University, 1982A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIES(Department of Forest Resource Management)We accept this thesis as conforminghyereds nTHE UNIVERSITY OF BRITISH COLUMBIANovember 1993© Sen Wang, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Forest Resources ManagenntThe University of British ColumbiaVancouver, CanadaDate Jan. 17, 1994DE-6 (2/88)ABSTRACTThe B.C. government’s Protected Areas Strategy (PAS), aimed at protecting12 per cent of the province’s land base, will affect the old-growth forestsconsiderably. Based on the Valhalla proposal, at least 0.65 million hectares of oldgrowth will need to be set aside as wilderness.Given the nature of multiple uses of the old growth, a Goal Programmingapproach is appropriate for the assessment of the preservation plan. For modelconstruction, six goal items have been identified: the net benefits from old-growthstands, wilderness expansion, direct forest employment, government stumpagerevenue, sustained yield, and current timber harvesting. Targets have beendetermined for each. On the basis of the results from a survey, goals are rankedin terms of priority, and their achievement is attempted in a sequential order toseek minimal deviations from the specified levels.The Goal Programming model indicates that old-growth preservation on thescale of the Valhalla proposal will cause reduction in the province’s level of directforest employment, and the magnitude of the adverse effects is variable,depending on the intensity of the goal constraints concerned. The goals of netbenefits and Crown revenue from stumpage charges do not appear to bevulnerable, but the conflicts between the preservation plan and the goals of longrun sustained yield and current timber harvest are serious.Table of ContentspageTITLE PAGEABSTRACT iiTABLE OF CONTENTS iiiLIST OF TABLES viLIST OF FIGURES viiiACKNOWLEDGEMENTS ix1 INTRODUCTION 11.1 Background 11 .2 Problem statement 41 .3 Objective of the study 71 .4 Methodology employed in the study 81 .4.1 Theoretical basis of the study 81 .4.2 Justification of the use of GP approach 92 THEORY AND METHODOLOGY 112.1 Goal Programming theory and literature review 122.1.1 Origin of Goal Programming 122.1.2 Evolution of Goal Programming techniques 132.2 Algebraic form of a Goal Programming model 17III2.3 Applications of Goal Programming 202.4 Some theoretical issues of Goal Programming 223 FORMULATION OF A GOAL PROGRAMMING MODEL FORWILDERNESS PRESERVATION IN B.C 263.1 Identification of goals 263.1.1 Identifying goal items 263.1.2 Ranking goals in priority sequence 283.1.3 Cardinal weighting of goals 313.2 The Goal Programming model 323.2.1 Steps in constructing the GP model 323.2.2 Identifying goal levels 333.2.3 Mathematical expressions of goal constraints 403.2.4 Identifying physical constraints 433.2.5 Identifying nonnegativity constraints 453.2.6 Formulating the objective function 453.2.7 The complete model 463.3 Assumptions in the model 484 DATA USED IN THE MODEL 514.1 Data sources 514.2 Data classification 534.2.1 Right-hand-side constants 534.2.2 Revenue/cost coefficients 56iv4.2.3 Technical coefficients 614.3 Other data 625 DISCUSSION OF THE RESULTS OF THE MODEL 635.1 Description of the computer software employed 635.2 Optimal goal levels and their achievements 645.3 Interpretation of the results 665.4 Implications of the results 695.5 Priority ranking tests 705.6 Different scenarios of harvesting levels 725.7 Trade-offs among various goals 736 SUMMARY AND CONCLUSIONS 826.1 Summary of model results 846.2 Recommendations 886.2.1 Recommendations for policy changes 886.2.2 Recommendations for future research 906.3 Conclusion 91BIBLIOGRAPHY 92APPENDICES 100vLIST OF TABLESnage1 Ranking of the goals 302 Goal items and their levels 403 Wilderness expansion in the Valhalla proposal by region 544 Level of employment supported by timber harvesting in B.C 555 Net operable mature stands and AAC levels in B.C 556 Average timber values of old growth by species 587 Timber vs. non-timber benefits of mature stands in B.C 598 Weights of recreation use and preservation values 609 Average levels of stumpage charges on MOF regulated land 6210 Goal targets and attainments at upper bound ofresource constraints 7511 Goal targets and attainments at lower bound ofresource constraints 7612 Resource use under various packages of goal items 7713 First test results in altering the goal ranking 7814 Second test results in altering the goal ranking 7915 Trade-off ratio between wilderness expansion and directforest employment reduction under different scenarios 80B.1 Land use in British Columbia 102B.2 B.C. Ministry of Forests’ regulated land 103viB.3 Quality of productive forest land in British Columbia 104B.4 Distribution and proportion of mature stands in B.C 105B.5 Inventory of mature stands by species and by region 106B.6 Species composition of log production in B.C 107B.7 Withdrawal of prime forest land into park areas in B.C 108B.8 Regional variations in withdrawal of prime forest landinto park areas 109viiLIST OF FIGURESDage1 Annual timber harvest scenarios in B.C.-- Differentgoal schemes compared 818.1 Land use in British Columbia 110B.2 Old growth preserved as wilderness- cumulative area in B.C 111VIIIACKNOWLEDGEMENTSI am deeply indebted to my supervisor, Dr. G. Cornelis van Kooten, for hisinitial suggestion of this study and continued guidance throughout. But mygratitude to him extends far beyond this thesis on account of his design of anexcellent program that has bridged the enormous gaps between my previousbackground and the current field of learning.I wish to thank Dr. Ilan Vertinsky, Director of Forest Economics and PolicyAnalysis Research Unit at the University of British Columbia, for his strong supportin terms of financial assistance.I am very grateful to Dr. John Nelson for his patience and criticism inreviewing my thesis. And I am also very grateful to Dr. David Haley for hisacademic enlightenment that sharpened my understanding of the forest sector inBritish Columbia.My sincere appreciation goes to my parents and daughter whose sentimentsaccompanied me during many sleepless nights. Above all, I would like to expressmy special thanks to my wife, Sulan Dai, for her wonderful love that has been aprincipal source of inspiration for my studies.ix1Chapter 1luction1.1 BackgroundBritish Columbia is territorially the third largest province in Canada. Covering94.78 million hectares, or 9.51 per cent of Canada’s total area, it represents20.72 per cent of the country’s timber-productive nonreserved forest land. As faras mature and overmature forests are concerned, the province accounts for 47.29per cent of the country’s gross standing volume1.British Columbia is one of thefew places where substantial areas of temperate old-growth forests still exist(Valhalla Society 1988). Of the provincial land base that measures 929,730square kilometres, around 65 per cent, or 60.57 million hectares, is classified asforest land. The timber-productive nonreserved forest land measures 49.05 millionhectares, but the area presently available and suitable for timber harvesting covers26.6 million hectares2.Forest resources are of vital importance to British Columbia in terms of theircontribution to the province’s economy and environmental quality. They representa source of timber supply for the forest industry that forms one pillar of the1 The information is from “Canada’s Forest Inventory 1991” which is carried, in part, byCompendium of Canadian Forestry Statistics 1992.2“Canada’s Forest Inventory 1991”; andB.C. Ministry of Forests Annual Report 1991-92.2provincial economy, and forest lands are an essential resource base in support ofrapidly growing tourism. What makes British Columbia attractive also generatesthe province’s principal wealth (B.C. Wilderness Advisory Committee 1986).In recent years the province has been faced with conflicting demands ofincreasing intensity over its forests, in particular with the old growth3.The longstanding forest industry relies on a continued supply of timber from the resourcebase. Meanwhile, rising environmental concerns call for the expansion ofwilderness area into the currently operable forest land. Viewed in an economicscontext, B.C.’s old-growth forests are a scarce resource that is nonrenewablewithin the lifetime of the present generation. The extraction of timber tends totake place at the expense of many non-timber products, whereas preserving forestland as wilderness is likely to cause economic losses in connection with thereduction in timber harvest.The issue of old-growth forests in British Columbia is one of land use. Thecompetitive nature of the old growth as a resource for satisfying diverse humanneeds compels planners to decide upon the choice of land uses with dueconsideration to the opportunity costs of each. Such a decision is often madewithin a given institutional framework. Having gone through a variety of studiesDefinitions of old-growth forests are varied. Some believe that old growth constitutesstands over 200 years in age. In this study, mature and overmature forests are referredto as old growth. The stand is considered mature when the age reaches 80 for lodgepolepine, white-bark pine and all deciduous species. Other stands of coniferous species areconsidered mature when their age is greater than 120 years (B.C. Ministry of Forests1991).3initiated in the past decade by separate government agencies, the old-growthissue finally found its way into the province’s Protected Areas Strategy (PAS) thatcame into being in 1992 (B.C. Ministry of Environment, Lands and Parks; Ministryof Forests 1992a).The Protected Areas Strategy commits the government to a doubling ofB.C.’s park and wilderness areas by the end of this century. Having identified 184study areas, ranging from less than 10 hectares to more than one million hectareseach, the strategy is designed to be an integrated process for coordinating all ofB.C.’s protected area programs. It represents a landmark in the transition on thepart of the provincial government from traditional piecemeal initiatives towardsplanning forest land uses in a more holistic fashion. However, a certain amountof productive forest land will necessarily be withdrawn into wilderness with theeffect of banning timber harvest activities altogether.PAS is the result of a lengthy and ongoing process with wide-ranging publicinvolvement and input. Hence, it serves as an established institutional frameworkthat sets both the stage and timetable for specific implementations (B.C. Ministryof Environment, Lands and Parks 1993). Seeking to protect representativeecosystems around the province, the strategy deals with the old-growth issue atits core. Given the proportion of forest lands in the province and the extent towhich British Columbians have been dependent on timber extraction for theireconomic well-being, assessment of the possible effects of the strategy becomesa matter of weighing the benefits and costs of wilderness expansion.4As a forerunner of PAS, the proposal put forward by the Valhalla Societyin 1988 mapped out specific geographic sites worthy of protection. Entitled BritishColumbia’s Endangered Wilderness:A Proposal for an Adequate System of TotallyProtected Lands, the proposal recommended that the amount of protected areasbe increased to 13.06 per cent of B.C.’s total area from the then 5.24 per cent.The implementation of the Valhalla proposal was expected to affect 650,459hectares of mature and overmature forests, involving 226.15 million cubic metresof commercial timber (Valhalla Society 1988; Simon Fraser University 1990).Originating from pin-points of grass-root opinions, the Valhalla proposal hasserved as an essential building block on which the unfolding Protected AreasStrategy stands. While PAS is expected to undergo a series of evaluations indetermining actual sites for protection, to begin with, the process is preferably acheck-and-acceptance verification of existing proposals to avoid duplication ofefforts (B.C. Ministry of Environment, Lands and Parks 1993). In view of theapparent similarities and connections between the Protected Areas Strategy andthe Valhalla proposal, the latter offers a sensible starting point in evaluating thePAS program for its overall viability and economic implications.1 .2 Problem StatementThe Protected Areas Strategy is aimed at bringing 12 per cent of BritishColumbia’s land area under protection by the turn of the century, namely,expanding the protected areas from the current 6.2 million ha to around 12 million5ha. In the hope of developing one of the most comprehensive and systematicplans for protected areas in North America, the provincial government isconfronted with a formidable challenge to strike a balance between protectingenvironment and securing socio-economic stability. B.C.’s high proportion offorest cover justifies the emphasis in PAS on forest land, especially mature andovermature stands. Further, because there are many uses of old growth, the PASprogram is, to begin with, a multi-objective undertaking. What is at issue is notwhether the PAS target is attainable, but rather, how it may be achieved and atwhat cost. The real question boils down to how much old growth, and in whichareas, is to be affected. An underlying assumption is that the impact of PAS onthe provincial economy is a function of the intensity of old-growth withdrawalfrom timber harvesting into wilderness with variations in respect of specificgeographical sites.In recognition of the multi-purposes of the old-growth forests, land useplanning for timber harvesting and wilderness preservation is an economic as wellas a political process that involves (1) the identification of the general shape ofrelevant production possibility curves in order to determine the trade-off functionsamong various activities, (2) the specification of the range and intensities ofconflicts and/or complementarities, and (3) the decision making on plans ofactions available and the consequences thereof (van Kooten 1993a). It is aprocess of specifying problems both qualitatively and quantitatively for theselection of alternatives.6In the context of the Protected Areas Strategy, reducing the area ofproductive operable forest area is expected to affect timber supply, employmentopportunities and Crown revenue in the short run, and has an impact, in the longrun, on many aspects of the province’s economy, such as industrial restructuringand the competitiveness of B.C’s wood products in the international market. Thedirection and intensity of the effects are determined by the magnitude of thewithdrawals and the time horizon over which the adopted program isimplemented. Although deletion of forest land in favour of wilderness preservationis not new to British Columbia in that 3,999 square kilometres of prime forest landwere turned into parks and conservation areas between 1965 and 1985, theProtected Areas Strategy has an aim that surpasses all previous endeavours interms of scale and time span (Environment Canada 1987). The distinctive featuresof PAS makes it all the more necessary to draw up appropriate plans formaximizing the benefits (both present and potential) of the program andminimizing the costs of implementation.The announcement of the Protected Areas Strategy by the provincialgovernment indicates the establishment of an institutional framework. With abroad objective of doubling protected areas in the province, the framework needsto be filled with contents that correspond to site-specific action plans. Theimplementation of the strategy is a process of attaining a series of sub-goals thatcontribute to the ultimate goal of enhancing British Columbians’ well-being. Theanticipated benefits of PAS will be associated with certain levels of costs that7vary from one type of action scheme to another. The adoption of a given plansuch as the Valhalla proposal should be based on an understanding of the plan interms of contents, specific targets or goals, the extent to which each of the goalsis achievable, and economic implications of attaining them. An analysis to thiseffect is needed for the implementation of B.C.’s Protected Areas Strategy, andit is the focus of this study.‘1 .3 Objective of the StudyThe objectives of this study are threefold. The first is to identify existingproposals in regard to the use of old-growth forests for wilderness preservationand timber harvesting. Preliminary goals are defined on the basis of the Valhallaproposal, with the priority rankings of the goals sorted out in accordance withsolicited opinions of the general public. The second is to evaluate the goalsassociated with the given wilderness expansion proposal for their technicalviability. And the third is to indicate the possible trade-off functions among thevarious goals as implied in the plan under investigation.A goal programming model is constructed to serve as a methodological tool.Results from simulations of different scenarios, using data sets drawn frompublished sources, are presented. An economic analysis is attempted in the endto discuss the impacts of the proposed wilderness expansion plan on other relatedgoals. The study concludes with tentative recommendations for forest policychanges at the macro-level of the province.81 .4 Methodology EmDloved in the StudyGoal Programming (GP) is the mathematical modelling approach used in thisstudy. The need to employ a GP approach is dictated by the nature of the problembeing addressed and the objectives pursued. To date, Goal Programming has notbeen used to evaluate province-wide forest land use plans and estimate the tradeoffs between timber harvesting and wilderness preservation.1 .4.1 Theoretical Basis of the StudyThe theoretical basis of this study is multi-objective planning. In light of therecognition that old-growth forests are capable of multiple uses, the assumptionof positive non-timber values from forest resources is implied. Given BritishColumbia’s Protected Areas Strategy, it appears that deletion of old-growthforests from the net operable base is to be a political decision. However, this isan economic problem as well in that choices regarding the use of scarce resourcesare involved. According to Hartman (1976), a program such as PAS may beaccepted only when the values of the non-timber products exceed the timbervalues forgone. The proof that old-growth forests possess positive non-timbervalues is not sufficient to justify their withdrawal. The opportunity costs of oldgrowth preservation are, for the most part, the forgoing of immediate timberrevenue and resultant losses of employment related to timber harvesting. Despitethe many controversies that remain in measuring the non-timber values of the oldgrowth, in evaluating the feasibility of wilderness expansion plans and estimating9trade-offs, this study uses information available on the assumption that existingnon-market value estimates are reasonably reliable.1 .4.2 Justification of the Use of GP ApproachGoal Programming is a constrained optimization approach suitable for multi-objective planning. The adoption of the GP approach is justified on the followinggrounds. First, old-growth forests in British Columbia are capable of multiple uses.Unlike Linear Programming, which addresses one single objective at a time, GoalProgramming facilitates the planning of various old-growth uses simultaneously,making it possible to consider issues with different measurement units. Second,as decision makers do not know for sure the viability of their initial plans, theprocesses of evaluating feasibility and efficiency can be taken care of by GP,which deals with either overachievement or underachievement of preliminary goallevels to avoid the rigidity of the single directional operability characterized byLinear Programming. Third, results from GP may provide decision makers withinformation about the inherent relationships among the various goal componentsof a program in terms of economic values and about the rationality of goalstructures. The usefulness of Goal Programming as a technique lies in the wayproblems of a different nature and dimensions may be presented and handled.From the standpoint of British Columbia, the value dimensions of the old growthmake much sense in the aggregate (Vertinsky et a!. 1993). It is, therefore,deemed appropriate to adopt Goal Programming in assessing a province-wide10preservation program, with a regional breakdown to the levels of the Ministry ofForests regulated regions. Should the need arise to look at old-growth problemsfrom a local perspective, the information from this study may be decomposed toderive regional implications.11Chapter 2Theory and MethodologyForests are complex ecosystems capable of supporting multiple uses. Unlikeconventional forest practices whose emphasis was confined primarily to thecapture of commercial timber values through logging operations, modern forestryis evolving into a science that recognizes a wide range of services forests canprovide in meeting the diversified needs of the present generation and of those yetto come. As an important branch of this science, forest resource management isaimed at the development of a sustainable resource base in such a way thatsociety’s soclo-political, economic and environmental goals may be satisfied. It isa complex process of decision making before actual operations take place,involving, to a ‘arge degree, the identification of desired objectives and, in turn,the evaluation of various alternatives.As an aid to decision making, mathematical programming encompasses anarray of analytical techniques for optimizing some particular objective by placingspecific restraints on resources allocated to alternative activities (Bell 1977). Inforestry, Linear Programming (LP) is by far the most extensively used approachthat seeks optimal achievement of an objective within given economic, physicaland/or biophysical constraints. However, the management of forests for multiplepurposes such as timber values from logging activities and non-timber values from12wilderness preservation requires multi-objective programming. Goal Programmingis such an instrument.2.1 Goal Programming Theory and Literature Review2.1.1 Origin of Goal ProgrammingThe concept of goal programming was initiated by A. Charnes and W.Cooper in 1961 in a book entitled Management Models and IndustrialAppilcationsof Linear Programming (volume 1). They observed the limited capacity ofconventional linear programming in addressing only one objective function at atime, pointing out that managers often need to consider a decision packagecomprised of a variety of goals interrelated with one another.The solution proposed by Charnes and Cooper to multi-objective problemswas to transform the usual linear programming format by treating all goals as aseparate category of constraints along with the existing physical constraints, andturning the objective function into a process of minimizing deviations from thosespecific goals.The essence of Charnes and Cooper’s proposal lies in the alteration of thesubstance of the objective function. The object to be optimized becomes the sumof deviations from various goals. While preserving the form of linear programming,the new approach adopts an objective function that assembles a series ofdeviational terms associated with corresponding goals, and the optimizationprocess of the objective function is constrained by goal levels as well as by13resource availabilities. The technique is unique in that different goals can bestacked in conjunction with physical constraints, and the goal constraints arelinked with the objective function via deviational terms to be minimized. With theassumption that variables in a programming model have linear relationships, themethod offers a way of handling management problems with multiple goals ofdifferent categories.2.1 .2 Evolution of Goal Programming TechniquesOriginating from Linear Programming, Goal Programming is a constrainedoptimization approach. But unlike LP, which seeks the optimization of a singleobjective through adding up the commonly measurable contributions of all theactivities involved, Goal Programming aims at the fulfilment of an aggregateobjective by collectively achieving goals that may or may not be directlycompatible and commensurable with one another.The fundamental difference lies in the composition of the objective function.In form, GP resembles LP in that the objective function has one overall aim, sinceminimization of deviations from each of the goals contributes to the overallsuccess of the program. But in essence, minimization of the objective function isnot necessarily a single-step task. When the goals under consideration happen tobe compatible with common units of measurement, a GP problem boils down toan LP case. However, in the event that incompatible and unmeasurable goals haveto be dealt with in a decision problem, two things will need to be resolved. One14is to order goal items in terms of priority sequence, and the other is to determinethe magnitude of the relationships among the goals. Determining ordinal rankingand cardinal weights for goals are considered two essential issues in goalprogramming modelling.Y. ljiri (1965) made a significant contribution to the development of goalprogramming techniques. In his book Management Goals and Accounting forControl, Ijiri introduced “preemptive priority factors” for treating multiple goalsaccording to their respective importance, and he proposed the assignment ofweights to goals of the same priority level. It was ljiri who refined the concept ofgoal programming and turned it into a distinct mathematical programmingtechnique (Lee 1972).The first book entirely devoted to goal programming was Goal Programmingfor Decision Analysis written by S.M. Lee in 1972. Lee illustrated the variousapproaches for constructing GP models, and formalized the graphical and simplexmethods for solving GP problems. Lee’s chief contribution was his demonstrationof the wide applicability of Goal Programming as a tool for decision making inmany fields such as production, financial management, academic planning andgovernment services.The two decades following Lee’s works have witnessed debates as to howthe ordering and weighting ought to be done in formulating the objective function.A general agreement seems to have been achieved that preemptive orderingsuggests the notion of higher-level goals completely dominating lower-level goals15in the form of “> > >11. For instance, if there are goals that are ranked j’th inimportance, the preemptive priority factor P >>> nP+1 for all values of n,however large it may be (Field 1973). This means that the objective function hasto be dealt with in a sequential manner, namely, satisfying goals from the highestranking downwards.The determination of priority ordering is not without difficulties. It often isfilled with subjectivity that characterizes almost all decision making processes.Ranking priorities is to place goals in a hierarchical structure. In spite of real worldevidence demonstrating the advantages of this approach, a drawback is that itposes excessive difficulties for trade-off estimations.Cardinal weighting is viewed as an alternative approach that seeks toidentify the estimated weights as coefficients on each of the goals, allowingpossible estimation of trade-offs through the calculation of gains versus sacrificesamong different goals. However, one major problem is the difficulty in determiningthe weights in the first place. Goals, which differ from one another but aremeasurable with a common yardstick in their respective achievements, make iteasy for one to discover their weights when they are grouped into a decisionmaking package. After all, weights are but terms that indicate exchange factorsof activities for trade in values. What makes weights assignment difficult is caseswhere goals do not permit ready measurements of trade-offs due to, for instance,non-market values. Although the source of the non-market valuation problem liesdeep in economics, the trouble casts its shadow on Goal Programming, scaring16many people away from the use of the weight assigning approach.There has been a broad consensus on the combined use of ordering andweighting. One common suggestion is to use priority ranking for differentcategories of goals and, within each class of sub-goals, to employ a cardinalweighting scheme (Lee 1972). In an attempt to rearrange goals by type, thisintegrated approach helps reduce incompatibility and immeasurability amonggoals. Nevertheless, controversies over objectively specifying goal levels andweights have persisted, and the principal issue of assigning weights acrossdifferent priority levels remains unsettled (Dykstra 1984).J. Buongiorno and J.K. Gilless (1987) appear to favour the cardinalweighting approach. Asserting that few goats in the real world are absolute, theyquestion the usefulness of preemptive priority ranking. In their opinion, mostvalues are relative and goal programming with cardinal weights is more likely toreflect these values. They propose adoption of the relative weighting scheme. Inassigning weights, attention is supposed to be given to the relative importance ofdeviating by one percentage point from the respective goals. In other words, allweights are set equal to unity. In the case of goals expressed in large numbers,the derived weight coefficients can be very small, and serious round-off problemsmay occur in calculating a solution. To avoid this, all the coefficients may bemultiplied by an identical large number, which, of course, will not affect the finalsolution. The advantage of working with relative deviations from goals is toeliminate the different units of measurement. However, this scheme has to be17interpreted in terms of the relative value of the goals. Buongiorno and Gilless(1987) argue that the relative value of any items in a model can be determinedfrom the relationship as implied by the objective function. To be specific, theobjective function of a GP model is a summation of deviations from various goalitems. Suppose one singles out two of the items while treating the rest as given,then a specific relationship between the two items is established via the objectivefunction. Suppose, further, that the objective function is restricted to zero, anychanges in the two items will become relative to one another. Then, dividing thecoefficient of one deviational variable by the other will give a quotient that maybe seen as the trade-off ratio between the two goal items. In spite of the meritsof this approach, there are, at least, two problems. One is that it appears ratherrestrictive in establishing trade-off relations by choosing two items at a time,which is unrealistic for models with a considerable number of goal items. Theother problem is whether assigning unity as the universal weight to all items isjustifiable in the first place.2.2 Algebraic Form of a Goal Programming ModelThe general form of a goal programming problem is:mMinimize Z = Pk(’kdk + wkdk){d} k=1s.t. Ax + ld - ld = b (1)18Bx (2)x,d,d 0 (3)where d = positive deviational variable;negative deviational variable;w = weighted shares for positive deviational variables;w weighted shares for negative deviational variables;Pk = priority factor, with k 1 , .A = an m x n matrix, describing the technical relationships between goals;x = an n x 1 column vector of goal variables;I = an m x m identity matrix;b = an m x 1 column vector, representing the target levels;B = an r x n matrix of technical coefficients;h = a r x 1 column vector of physical constraints; andk = a subscript that denotes the goal, with k =Several observations are in place. First, the constraints are as follows: (1)goal constraints, (2) biophysical constraints, and (3) nonnegativity constraints.Another constraint may be added to the model, namely,• d = 0.19This means that at least one, if not both, of the deviational variables must bezero. As a matter of fact, it is the task of the objective function to drive thevalues of d and ci towards zero, and when d and ci are minimized to zero, goalswill be considered as having been achieved at an optimal value of the decisionvariables x.Second, the determination of the values of coefficients on deviationalvariables in the objective function can be the hardest part of any goalprogramming model formulation. The problem is twofold. On the one hand, thehierarchical structure of the various goals should be identified to indicate the orderof importance among the goals, and, on the other hand, the numerical significancefor deviations from the goals with identical priority factor should be determined.The ordinal values of Pk represent the subjective judgement by the plannersof goal rankings. Following a preemptive sequence, the ordering gives precedenceto higher ranking goals over lower ones. In other words, lower-level goals areconsidered only after higher-level goals are satisfied. Once the superior goals areachieved, they should not be violated, and they act as new constraints inredefining the feasible regions for subsequent lower-order priorities. Cohon (1978)calls this the “lexicographic” ordering approach, which resembles the way adictionary lists words. The sequential preemptive attempts at goal achievementsare expected to result in an accumulation of constraints.The numerical values of Wk must be nonnegative. If, for example, VVk =0, it means that only negative deviation needs to be minimized either because20positive deviation does not matter or overachievement of the goal would even bewelcome. These are known as one-sided goals (Cohon 1978) or one-way goals(Dykstra 1984). Of course, deviations of opposite directions can be minimized atthe same time. The effects of positive and negative deviations may not be thesame and, to reflect this, one may assign different weights to them.The weighting approach reflects the degrees to which managers permit theoccurrence of production activities. The cardinal is continuous while the ordinalis discrete. When the weighting says 100 per cent for one of the activities, thatactivity gets elevated to the fullest possible level of that priority order. Trade-offestimation may be obtained more easily with the cardinal approach.2.3 ApDlications of Goal ProgrammingGoal Programming was applied by Charnes (1968) to media planning, whileCharnes, Cooper and Nilhaus (1968) used GP techniques in manpowermanagement. During the late 1 960s and throughout the 1 970s, the approach wasapplied to many private sector problems. The apparent lack, in the early years, ofapplication to public problems was largely attributed to the difficulties inspecifying target levels of social goals (Cohon 1978). One reason for this is thatcorporate problems are primarily concerned with traded products, whereas publicproblems involve many nonmarket goods and services.Due to the nature of Goal Programming, the technique is most suitable formulti-objective planning. Natural resource management is an area where21conflicting goals often exist. While Bell (1976) used Goal Programming for landuse planning, Bottoms and Bartlett (1975) applied the method to rangemanagement, and Miller and Byers (1973) constructed a GP model for waterresources projects.The first application of goal programming to forestry was reported by Field(1973), who demonstrated the potential of goal programming in solving manyforest management problems. Important studies using GP models to solve forestproblems include the following:- management of small woodlands (Field 1973);- timber production (Rustagi 1976; Kao and Brodie 1979; Field eta!. 1980);- land use planning (Bell 1976; Dane eta!. 1977);- evaluation of alternative logging residue treatments (Bare and Anholt1976);- Christmas tree production (Hansen 1977);- evaluation of trade-offs between timber management, outdoor recreation,grazing and production of game animals for hunting (Schuler et a!. 1977);- range management (Bottoms and Bartlett 1975); and- outdoor recreation planning (Romesburg 1974).The above-mentioned applications all used linear goal programming.Porterfield (1976) employed a nonlinear goal programming model to evaluate treeimprovement programs, and Mitchell and Bare (1981) solved a forest inventorygoal programming problem with nonlinear constraints. Buongiorno and Gilless22(1987) highlight GP as one of the most widely used mathematical modellingtechniques.2.4 Some Theoretical Issues of Goal ProgrammingAside from the distinctive features of the goal programming approach,issues that have concerned GP scholars include sub-optimality or inferior solutionsand inadequate provision of trade-off information. Unlike Linear Programming forwhich the feasible region is defined by the constraints, the Goal Programmingapproach is capable of producing a solution in which constraints can be satisfiedas closely as possible, but need not all be met completely (Dykstra 1984). Thismeans that, even if some goals turn out to be unattainable within the limits ofavailable resources, with goal programming, we are driven towards the bestpossible levels of achievements insofar as the constraints and competing goalspermit.The guaranteed solvability of a problem does not ensure the attainment ofan efficient solution. As a matter of fact, the flip side of the flexibility of goalprogramming is the usual phenomenon of sub-optimality.Generally speaking, a non-inferior goal programming solution is associatedwith infeasible goal levels. In most cases where goals are all found to have beenachieved, it either suggests that the original goals are not high enough or solutionsare insensitive to the priority ordering. The manager needs to be suspicious thatlarge production potentials remain untapped, that is, the production possibility23curve probably lies far out in the northeasterly direction in an XY plane. Sensitivityanalysis may be necessary by means of altering the way priorities are placed andresetting the goal levels. Non-inferiority is guaranteed only when strictly positivedeviations are obtained (Cohon 1978). To avoid sub-optimality, it appears that weshould aim at the infeasible region. However, several problems arise. First, goalprogramming relies heavily on decision makers’ perception of the range offeasibility, but they do not necessarily have sufficient knowledge about the non-inferior region when setting goal levels. The consequences of initially aiming atlevels beyond the production possibility curve are that we are likely to end up withcorner solutions unless the shape of the production possibility curve indicatescomplementarity or supplementarity.According to the theory of production, complementarity andsupplementarity only occur within a certain range (van Kooten 1 993a). In the caseof British Columbia, as activities compete with one another for the use of limitedold-growth resources, the production possibility curve has to be negatively sloped.In the case of the old growth, which may be characterized by the two broadgroups of timber and non-timber products, the steeper is the production possibilitycurve, the more likely is the result of a corner solution, favouring the productionof one product group at the expense of another. In the event that one goal isinitially selected to exceed the production frontier to avoid inferior solutions, theachievement of this target will likely result in complete sacrifice of other goals.The sacrifices may not be justifiable unless the goal sought has sufficient24values to more than offset the losses. For instance, excessive timber harvestexpels tourists from logging sites proper and adjacent areas as well. The revenuelosses from recreation plus the sacrifices from other relevant non-timber uses mayconvince decision-makers to restrict timber extraction to reasonable levels. On theother hand, a complete ban of timber felling may be undesirable because theeconomic losses in terms of reductions in timber supply, forest employmentopportunities and community stability can be enormous. Therefore, the horizontalnature of goal level choices, coupled with the usual shape of negative slopes forproduction possibility curves, tends to rule out attainment of an optimal solutionin its pure sense and, consequently, an interior solution rather than one on theproduction possibility curve often is the case (Dyer eta!. 1979).Due to the sub-optimal nature of Goal Programming, while a solution isobtainable, it is often difficult to find the true level of production potential.Repeated parametric trials may help locate the production frontier, but identifyingtrade-offs between products is difficult as we may not be able to attain theoptimal spot on the production possibility curve.The extent of trade-offs depends largely on the shape of the transformationfunctions. The greater the competitiveness between two products, the more likelyit is for one of the products to be forced towards zero. In GP problems, there isa tendency for lower priorities to be precluded from consideration, especially whenconflicts among uses are tense and the higher-priority products are in greatdemand.25Therefore, ranking priorities and determining goal levels are instrumental forgenerating sound solutions. But it is, by and large, a subjective judgement andcould be unrealistic unless reliable evidence is ascertained in terms of productiontransformations and value exchanges. Inappropriate ranking of priorities will leadto a wrong sequence, unduly favouring some products at the expense of others.Given a priority ordering, incorrect setting of goal levels will cause non-productionof lower ranking products to give way to excessively high-level goals, and inferiorsolutions will likely occur if goals are lower than optimal levels. Trade-offsbetween products are meaningful only when priority ordering and weighting arerealistic.In summary, multiple objectives justify the use of goal programmingtechniques, and the usefulness of the GP approach is dictated by the shape of theproduction possibility curve. But the subjectivity problem inherent in GoalProgramming is serious. The method is merely a tool for aiding decision making.The effectiveness of the approach is as good as the dependability and soundnessof the judgements of the planners.26Chapter 3Formulation of a Goal Programming Model for Wilderness Preservation in B.C.The essential component of this study is a Goal Programming model. Theformulation of such a model depends on identifying (1) the relationships amongvarious goals, and (2) technical coefficients for the activities concerned. Withinthe general framework of allocating B.C.’s old-growth forests between the tworepresentative land uses of timber harvesting and wilderness preservation, theconstruction of the GP model follows a procedure of ranking goal items,specifying goal levels, defining physical resource constraints, and forming theobjective function.3.1 Identification of GoalsBefore the physical building of a GP model is contemplated, a system ofgoals needs to be defined, and the pre-requisite to specifying any goals is theidentification of issues to be dealt with by the model.3.1.1 Identifying Goal ItemsDespite the diversification of old-growth uses, this study is confined totimber harvesting and wilderness preservation, with an objective of investigatingthe viability of the Valhalla plan and assessing the implications of the proposed27wilderness expansions in terms of timber output reductions, employment losses,and alterations in government revenue. For the purpose of restricting the study toa manageable size and maintaining a realistic focus, the economic objectives ofmanaging old-growth forests as recommended by the Parksville Old-GrowthWorkshop held in 1989 serve as a basis of consideration (B.C. Ministry of Forests1989). Regrouping of the workshop findings results in the following goal itemsthat form the core of the GP model:- Wilderness preservation in terms of withdrawal of old-growth forests fromthe operable productive forest land;- Timber harvesting in terms of AAC;- Government revenue;- Direct forest employment;- Maximization of net benefits from all old-growth uses; and- Sustained timber yield.Reasons for adopting the above goal items are the following. Preserving old-growth forests for wilderness is the main argument of the study, so it has to bethere. Timber harvest at its current level is a status quo against which any newprogram will need to be evaluated since losses in commercial timber valuesindicate the most obvious opportunity costs of preservation (van Kooten 1 993b).As over 20 per cent of British Columbians depend, either directly or indirectly, onthe forest industry for employment, any negative effects on job opportunities haveto be taken into account when a new program is introduced (Environment Canada281987). Maintaining Crown revenue at an non-declining level is required in the hopeof sustaining social programs at a time of budget deficits. The inclusion of asustained timber yield goal reflects a philosophy about a stream of servicesexpected of forest resources -- sustainable development. Last, but not least,maximization of net benefits from all old-growth uses is an expression of thedesire for economic efficiency in the allocation of B.C.’s scarce resources.3.1.2 Ranking Goals in Priority SequenceDecision making is a process of determining the choice of solutions to welldefined problems on the basis of established value judgements. Since 95 per centof the inventoried timber-productive, nonreserved forest land in B.C. is owned bythe Crown, decisions regarding changes in the designated use of the forest mustcome from the general public or be made by appropriate authorities with thepublic’s endorsement (Canadian Council of Forest Ministers 1993). Due to theusual hierarchical nature of decision making and based on the assumption that thestakeholders in B.C. place different values and expectations over the old growth,a survey was conducted to solicit opinions on the ordering of those previouslyidentified goals. Entitled Identifying Priority Rankings on Old-Growth Uses inBritish Columbia, a total of 57 questionnaires were distributed among participantsin a socio-economic impacts workshop of the Commission on Resources andEnvironment (CORE) held in June 1993. The CORE process, which was firstintroduced in early 1992, is expected to provide guidance for resolving conflicts29in the use of publicly-owned land resources (B.C. Ministry of Environment, Landsand Parks 1993). The individuals who completed the questionnaires wererepresentatives of B.C.’s forest industries, academe, environmental groups andgovernment agencies. The response rate was about 25 per cent. Thequestionnaire is found in Appendix A.Of the six goals proposed to respondents, maximization of net benefits fromall old-growth uses received the first priority status4. The second ranking wentto wilderness expansion. Employment occupied the third place. The goal ofmaintaining government revenue came next, followed by the sustained yield goal.Keeping the current level of timber harvesting was considered the least priority.The wording of the survey was such that additional information wasexpected from respondents regarding the scope of old-growth withdrawal infavour of wilderness preservation. The range turned out to vary considerably fromthe government proposed 12 per cent. Extreme answers were received, on oneend, asking for no withdrawal at all and, on the other, demanding that all old-growth forests be preserved as wilderness.For setting up the priority sequence of the goals, the importance of eachitem was determined by the number of votes cast by the respondents, with 6points being awarded to the highest item and 1 point to the lowest. The item thatearned the highest scores became the first rank. Both the ordering and scoring areRespondents did not provide information about, or a ranking for, the last or “other”category. Hence, six rather than seven goals are used.30summarised in Table 1 to show, in a descending manner, the ordinal importanceof the various goal items.Table 1: Ranking of the GoalsItem Rank ScoresMaximize net benefits from all old-growth uses 1 71Permanently withdraw % of the old growth 2 63scheduled for future timber harvestSecure regional stability by maintaining the current level 3 59of employment in forest industriesMaintain Crown revenue from forest harvesting 4 56Maintain maximum sustained yield in timber harvest 5 51Maintain current level of timber harvest in B.C. 6 36Given the small sample size, the priority ranking may be arguablyrepresentative of the perceptions and attitudes of B.C.’s general public.Nevertheless, the results are found consistent with those of the national surveyof Canadian public opinion on forestry issues (Environics 1989). Besides, answersto the same questions in a mini survey of 11 individuals conducted on the campusof the University of British Columbia revealed an identical ordering5.Therefore,this ranking is adopted for the model, although sensitivity analysis is used at alater stage of model validation.This survey was conducted by the author between June 28 and July 3, 1993.313.1.3 Cardinal Weighting of GoalsIf the ordinal ranking of goats is viewed as a step in establishing thehierarchy of various items, it is merely a qualitative expression of the relationshipsamong the goals. The importance of a goal is meaningless when it stands inisolation. Goals make more sense when they are compared in relative terms withone another, and goals as well as physical constraints jointly form the decisionenvironment in a GP problem.In many instances, the knowledge that one goal is considered moreimportant than another is not adequate. It is desirable to move one step furtherin discovering the extent to which that goal prevails over the other. The purposefor so doing is to identify the exchange rate, in terms of economic values,between two activities that compete for the same scarce resources. It is impliedin production theory that a trade-off relationship exists between two activities aslong as they both are sub-elements of a joint production function (Doll and Orazem1985). This is true of B.C.’s old-growth forests that produce two broad types ofproducts, namely, timber and non-timber products. What makes it hard to revealthe trade-off functions of the old growth is the difficulty in obtaining the valuesof many non-timber products that are not readily available in the market place.Nevertheless, efforts at quantifying the importance of goals relative to one anotherare helpful in the efficient allocation of resources, and some insights may begained by means of determining the cardinal weights of goals that belong to anidentical problem package.32Cardinal weights may also refer to decision makers’ subjective considerationof the degree of importance one goal possesses over another if the two goalshappen to be on the same priority ordering. For instance, the achievement of therevenue plan of the whole province may be considered twice as important asachieving the revenue plan for one specific government agency. Even for anindividual goal alone, over-fulfilment of the target, say, by 10 per cent, may carrymuch more weight than underachievement by the same percentage, and if policymakers should decide that the former be four times as important as the latter, thisdecision would form a basis in assigning cardinal weights.The usefulness of weight assignment is matched by a complexity thatinvolves considerable subjective judgement. Given the scope and objectives of thisstudy, weighting of goals is ignored for the sake of simplicity.3.2 The Goal Programming ModelA Goal Programming model comprises an objective function and constraintsthat break down to goal constraints, physical constraints, and non-negativityconstraints.3.2.1 SteDs in Constructing the GP ModelAs a first step in formulating the model, choice variables are determined.In this model, the choice variables are defined as x and q, where x is the area ofold-growth forests for commercial timber harvesting and q is the area to be33withdrawn into wilderness status.The second step is to specify constraints. Both goal constraints andphysical constraints need to be identified. It is a process of defining the right-hand-side constants that are supposed to indicate goal levels and/or resourcelimitations.The objective function is developed as the third step. This is the stagewhen the ordinal rankings of the goals can be allocated as priority factors on thedeviational variables.3.2.2 Identifying Goal Levels(1) Wilderness goalThe Protected Areas Strategy attempts to incorporate all major initiatives,including Parks and Wilderness for the 90s and the Old Growth Strategy that havebeen launched by various government agencies. Similar to PAS which is aimed atplacing 12 per cent of B.C.’s representative land base under protection, theValhalla proposal indicates the need to protect 13.06 per cent of the province,involving 650,459 hectares of old-growth forests (Simon Fraser University 1990).The most recent information reveals that the mature and overmature stands onprovincial Ministry of Forests’ regulated productive land are estimated at 26.6million ha, which is 58 per cent of the total productive forest land of the TimberSupply Areas (TSAs) and Tree Farm Licences (TFL5) in the province (B.C. Ministryof Forests 1992).34The practice of allocating Crown forest land for wilderness preservationdates back several decades. Between 1965 and 1985 alone, 399,900 hectaresof prime forest land were designated for parks and recreation purposes(Environment Canada 1987). Since the mid 1980s, deletion of forest land infavour of wilderness preservation picked up in scale, and it peaked in 1990 by147,010 hectares. By 1991, the amount of forest land primarily used for parksand recreation purposes was believed to have reached two million hectares6.During the period from 1983 to 1991, for parks and recreation purposes,deletion of land from provincial forests amounted to nearly one quarter of a millionhectares, and almost two thirds of the land use changes occurred on the Coastwith much of the rest in the Northern Interior (B.C. Ministry of Forests 1983-91).Review of land use alterations during this period reveals a pattern of response tothe call for wilderness preservation and, at the same time, provides informationfor policy makers in deciding on how much more forest land the inhabitants couldafford to set aside and where. Little information is available about the maturityclass of the forest land deleted. It is assumed that at least half of the forest landwithdrawn consisted of mature stands on account of the special designated usefor parks and recreation. If valid, this assumption is of importance for it may havesignificant bearing on the allocation of targets among different regions as far asthe old-growth withdrawal goal is concerned.6 Prior to 1965, 186 parks, both National and provincial, were in existence on 2,864hectares. It is assumed that half of it was on prime forest land.35Based on the assumption that half of the previous wilderness expansionsinvolved old growth, the Coast seems less capable of handling additionalwithdrawals of large areas than the Interior in view of resource constraints andopportunity costs of timber values. This belief has found expression in the Valhallaproposal, which spells out the need to assign some 175,000 hectares of thewithdrawal task to the Coast and about 475,000 hectares to the Interior over theplanning horizon to the end of this century (M’Gonigle et aI 1992).On the provincial level, the withdrawals suggested in the Valhalla proposalindicate a reduction of the Ministry of Forests’ regulated mature stands by 4.7 percent. Effects are expected to vary from one area to another, especially betweenthe generally highly productive Coast area and many less productive areas in theInterior (Binkley eta!. 1993). The adoption of the Valhalla plan as a basis for thewilderness goal of this study is attributed to its typical comprehensiveness inrespect of altering old-growth uses across British Columbia.(2) Timber goalIt is required by law that sustained timber yield has to be maintained inBritish Columbia. The allowable annual cut (AAC), which refers to the volume oftimber that may be harvested each year, is a proxy for sustained timber yield.During the past decade, B.C.’s levels of timber harvest fluctuated considerably.In the peak year of 1987, the level rose above 90 million cubic metres (ForestryCanada 1992). But the AAC for the province’s Timber Supply Areas (TSA5) andTree Farm Licences (TFLs) fell to around 73 million cubic metres in 1991 (Binkley36eta!. 1993).Due to the predominance of coniferous species in British Columbia, outputsof hardwoods are ignored in this study, and privately owned forest land, whichis merely 4 per cent of the province’s total forest area, is excluded fromconsideration. Given a variable allowable annual cut from one period to another,the average AAC level of 73.33 million cubic metres is used as the timber goal inthe model.M’Gonigle eta!. (1992) pointed out that implementation of the Valhalla planwould result in an exclusion of 226.15 million cubic metres of commercial timberfrom the net operable base, which means a reduction of B.C.’s AAC by about 2.6million cubic metres.(3) EmDlovment goalDuring the decade between 1982 and 1991, B.C.’s forest sector witnessedfluctuations in the levels of employment. The total number of employees in forestindustries was 75,138 in 1982, and was pegged to remain around this level in theensuing few years. Forest sector employment rose above eighty thousand in themid 1980s and reached 81,375 in 1989. However, the following two years sawa considerable decline.Consisting of those employed in logging, wood industries and paper andallied industries, the above figures only reflect the levels of direct employment inthe forest sector. The indirect and induced employment, or the multiplier effect,is believed to almost double the direct employment level. The provincial Ministry37of Forests is convinced that, through economic linkages, each job in the forestindustry is associated with two jobs elsewhere in the economy (Council of ForestIndustries of British Columbia 1990). In spite of reports that tourism hassurpassed the forest industry and become the province’s largest employer, it isassumed that any job losses resulting from timber land withdrawal can hardly beoffset by employment growth in wilderness tourism due to lack of labour mobilityand a lengthy period required for economic restructuring7.Therefore, maintainingregional stability by keeping the level of employment in the forest sector isexpressed as one of the goals that PAS should be concerned with. To modifyeffects of annual fluctuations, a ten-year average of 77,600 is viewed as arepresentation of the level of employment goal for the model.(4) Revenue goalStriving for a non-declining revenue for the provincial government has beenidentified as an important economic objective in the old growth strategyformulation process (B.C. Ministry of Forests 1989). As this study focuses on theuse of forest land for timber harvesting versus wilderness preservation, thereappears a need to differentiate the Crown revenue from forestry in such a waythat only the relevant items are considered. For the sake of simplicity andpertinence, stumpage charges are singled out for analysis. This is assumedappropriate because stumpage is a particular source of revenue to which theCrown has legitimate entitlement. From the standpoint of the provincialThe definition of tourism is so broad-based that it includes travel for business purposes.38government, the principal opportunity costs of withdrawing old-growth forestsinto wilderness are the forgoing of stumpage fees that would otherwise beavailable for collection.It must be made very clear that taking stumpage receipts as a goal is purelyfor the purpose of measuring government revenue so as to assess givenwilderness expansion programs. The reason for caution is that variations instumpage levels during the past 10 years have been substantial. For instance, inOctober 1987, significant changes were introduced in B.C.’s stumpage system.In lieu of the 15 per cent tax on softwood lumber exports to the United States,forest industries were confronted with sharp increases in stumpage charges (PriceWaterhouse 1988). The rise in stumpage levels coincided with acceleratedwithdrawal of old-growth forests for parks and recreation. The increase in forestland deletion was possible partly because a 5-percent reduction in the AACaccompanied the policy change in the stumpage system (Price Waterhouse 1988).Nevertheless, it is inadequate for one to draw an inference that shrinking AACinduced price rises and, in turn, resulted in higher stumpage values for the Crown.In the model, the level of average stumpage charges for the recent few years isused as the government revenue goal.(5) Goal of maximizing net benefits from all old-growth usesOne assumption of the model is that old-growth stands possess, on the onehand, timber values that may be captured through extraction and, on the otherhand, non-timber values that exist through recreational uses and persist when the39stands are left in the state of wilderness. Although market prices are available formost timber products, non-timber values embodied in wilderness preservation arenot easily measurable and obtainable. The levels of non-timber values of B.C.’s oldgrowth in the forms of recreation values and preservation values adopted in thisstudy are adapted from van Kooten (1993b). As timber values comprise asignificant portion of the total values of the old-growth forests, it is decided thatthe contributions of forest industries to the provincial gross domestic product(GDP) at factor costs are taken as the level of net benefits goal. It serves as ayardstick against which PAS may be evaluated in terms of overall economicprofitability despite apparent non-commensurability problems between GDP andnon-timber values (van Kooten 1993b).(6) Sustained yield goalForest industries have been a driving force for British Columbia’s economythanks to the province’s natural endowments of productive forests. Maintainingthe share of the forest sector’s contribution to the provincial economy depends,to a large extent, on sustaining timber yield over a long period of time. The longrun sustainable yield (LRSY) is a representation of this goal to which the AAC issupposed to converge. However, declaring old-growth stands as wilderness statuswill exert downward pressure on the allowable annual cut. It is believed that theValhalla plan is likely to remove some 3.52 per cent of the AAC on a provincialscale (Simon Fraser University 1990). New AAC calculations, with relevanteffects being netted out, are adopted to serve as physical constraints against40which the sustained yield goal may be evaluated. A summary of the goals andtheir levels is presented in Table 2.Table 2: Goal Items and Their LevelsGoal Unit Level PriorityrankingMaximization of total net 1,244.4 million 1benefits from all usesOld-growth withdrawal ha 650,459 2Employment security job 77,600 3Non-declining government $ 408.73 million 4stumpage revenueSustained timber yield m3 58.94 million 5Maintain current timber m3 73.33 million 6harvest3.2.3 Mathematical Exrressions of Goal Constraints(1) Wilderness expansion goal6Z q + d - d = 650,459 ha (GC1)j=1where q is the number of hectares of old growth affected by wildernessexpansion in regionj, with) 1,...,6 to denote the six B.C. Ministry of Forests’regulated regions of Cariboo, Kamloops, Nelson, Prince George, Prince Rupert, andVancouver; ci is negative deviation from goal level, and d for positive deviation.41The provincial authorities have placed study areas for withdrawal evaluationinto four categories. The first two categories are areas to be designated by theend of 1993, the third by 1995, and the last by 2000 (B.C. Ministry ofEnvironment 1992). Obviously, this is necessary because of the enormous amountof work involved, and besides, an even allocation of tasks is conducive tominimizing negative effects of the program.(2) Timber harvesting goal6xj • V + d - d = 73.33 million m3 (GC2)j=1where xj is the number of hectares of timber harvest in regionj, withj 1 ,2,...,6;and is the weighted average of timber stock volume, measured in m3/ha, inregionj, taking into account species compositions and site qualities. The allowableannual cut reflects B.C.’s legislative requirement that sustained timber yield shouldbe achieved on a provincial scale. This goal is synonymous with the objective ofan even flow of timber supply.(3) Employment goal6• x + d - d = 77,600 (GC3)j=1where , is the level of direct forest employment in region j in terms of jobsprovided by one hectare of timber harvesting. To calculate this coefficient, one42needs to convert the usually used job generation level per thousand cubic metresof timber cut into a basis of job/ha. Since the withdrawal of old growth fromtimber production will likely cause job losses in the forest industry, theemployment goal may be unattainable. However, one wants to get as close to thegoal as possible in order to minimize any adverse effects of old-growthwithdrawals on employment in the forest sector.(4) Revenue goal6Z c • x • V + d - d = $ 408.73 million (GC4)j=1where c is the rate of stumpage charges, measured in dollars, per cubic metre oftimber in region j. The coefficient c is calculated from the provincial Ministry ofForests’ annual reports of the past few years. The level of this goal represents anannual average of stumpage charges by the provincial government from 1988onwards. Revenues from wilderness expansions are deliberately ignored in themodel on the assumption that the government will be unable to immediately derivenet revenues from expanded wilderness areas due to considerable costsassociated with the PAS program in the beginning years.(5) Total net benefits goal6(x3 • V • PT + • PW) + d - d = $1,244.4 million (GC5)j=143where P7 are the net timber benefits per cubic metre, in dollars, in regionj; andPl4ç are the non-timber values on a hectare in regionj. The right-hand side denotesthe contribution of forestry to the province’s GDP at factor costs. In this equation,the intention is to maximize the values of combined benefits from timberharvesting and wilderness expansion. The average level of GDP at factor costsover the past 10 years is used as a target.(6) Sustained yield goal6x1 • V. + d- d = 58.94 million m3 (GC6)j=1The right-hand side reflects the long-run sustainable yield (LRSY) for all TSAs andmost TFLs in British Columbia (Binkley eta!. 1993) . This level is both a target anda constraint in the long run.3.2.4 Identifying Physical ConstraintsThe mature and overmature stands constitute a resource base that may beused either for timber production or for non-timber purposes, or for both. At theprovincial level, the availability of old-growth forests is a physical constraint onthe designation of various uses (Ludwig and Conrad 1991). Specifically, the totalarea of old-growth forests amounts to 28.77 million ha.Wilderness preservation is viewed, in this model, as a proxy for all nontimber uses. Basically, two resource constraints are identified for the model.44(1) The constraint of net operable productive mature stands:6(x + q)j=126.6 million ha (PCi)(2) AAC constraint:6x • V + q • U 73.33 million m3 (PC2)j=:lwhere U, is the amount of AAC to be affected by old-growth withdrawal perhectare in regionj.The first physical constraint is redundant because, in any given year, theallowable annual cut is not supposed to be exceeded, and the AAC may betranslated into harvestable area based on established volume tables. The breakdown of the AAC constraints by B.C. Ministry of Forests’ regulated regions is asfollows:(1) Cariboo x1 • V1 + q1 • U1 8.56 million m3(2) Kamloops x2 • V2 + q2 • U2 8.14 million m3(3) Nelson x3 • V3 + q3 • U3 6.1 million m3(4) Prince George x4 • V4 + q4 • U4 17.77 million m3(5) Prince Rupert x5 • V5 + q5 • U5 9.44 million m3(6) Vancouver x6 • V6 + q6 • U6 23.32 million m345Sources and explanations about the AAC are found in the chapter on data.3.2.5 Identifying Nonneaativitv ConstraintsBy definition, all choice variables and deviational variables are nonnegative.3.2.6 Formulating the Objective FunctionMinimize Z=p1 (d1) +P2 (d;) +p3 (d3) +p4 (di) +p5 (d + d5) +p6 (d6 + d61where Z is the value of the objective function to denote the sum of deviations; Pkis the priority factor associated with goal item k, with k =In accordance with the priority rankings that have already been established,maximization of net benefits from both timber harvesting and wildernesspreservation on mature stands is the first priority. Hence, we assign p1 to thisitem. For p1, it is a minimum target to achieve. By assumption, the plannersshould not be concerned with overachievement, so d1 is omitted from theobjective function. Only negative deviations are minimized.Withdrawal of old-growth forests from timber harvesting is the secondhighest priority, which is denoted by p2. Similarly, the planners are assumed to beconcerned only with underachievement of the goal. Therefore, d24 is omitted.46The employment goal has been identified as the third priority. Forp3,over-achievement is actually welcome, so it can be safely ignored. We only minimizeunderachievement in order to get as close to the specified goal level as possible.The fourth priority goes to the Crown revenue goal. For p4, the averagestumpage level of recent years is taken as the basis from which anyunderachievement is to be minimized.Sustained yield is the fifth priority. For p5, the planners are assumed toutilize available capacity of timber harvesting to the full, while avoiding thetendency to hasten the liquidation of old-growth resources. Therefore, bothpositive and negative deviations from the goal level are minimized.The timber production goal happens to be the last priority. For p6. exactachievement of the goal level is preferred and, therefore, neither positive nornegative deviations are encouraged.3.2.7 The ComDlete ModelMinimize: Z = p1(d) + p2(dj) + p3(d) + p4(d) +p5(d + d51 + p6(d + d6jSubject to:(A) Goal constraints:6(x • V • PT + q • PW) + d - d = $1,244.4 million (GC1)j=1j=16qj=147+ d - d = 650,459 ha (GC2)6• x + d - d = 77,600 (GC3)6cJ • x V + d - d = $408.73 million (GC4)j=16x • V + d- d = 58.94 million m3 (GC5)j=16I x • V + d - d 73.33 million m3 (GC6)j=1(B) Physical constraints:6I x • V1 + q1 • U1 73.33 million m3 (PC)j=1x1 V1 + q1 • U1 8.56 million m3 (PCi)x2 • V2 + q2 • U2 8.14 million m3 (PC2)x3 • V3 + q3 • U3 6.1 million m3 (PC3)x4 . V4 + q4 . U4 17.77 million m3 (PC4)48x5 • V5 + q5 • U5 9.44 million m3 (PC5)x6 • V6 + q6 • U6 23.32 million m3 (PC6)(C) Nonnegativity constraints:d1, d2, d3, d4, d5, d5+, d6, d6+ 0x, q, dk, dk 0 forj = 1,...,6; and k =dk d1( = 0 fork = 1,...,6.3.3 Assumptions in the ModelThe basis of the Goal Programming model is a Linear Programming modelthat seeks the optimal values of x and q* for timber and non-timber products,respectively. Once the optimal levels of annual timber harvesting and old-growthwithdrawal are established, they become rules to abide by in planning processes.Given the market timber prices and estimates of non-market values for wildernesspreservation, when the single goal of net benefits maximization is consideredsubject to some specific constraints, an LP problem may be formulated as follows:Max Z= xPT + q•PWs.t. x+qblx b2q b3x, q O49where x = level of timber harvesting (ha);q = level of old growth preservation as wilderness (ha);b1 = net operable productive mature stands available (ha);b2 operable mature stands for timber harvesting (ha);b3 = proposed area for withdrawal (ha);PT = net benefits from timber harvesting ($/ha); andPW = non-timber values ($/ha).The LP problem can also be set up to minimize the opportunity costs of agiven withdrawal plan. The latter approach better fits the needs in calculating theoptimal levels of timber harvesting and wilderness expansion in the conviction thatcomparison of opportunity costs clearly reveals the advantages and/ordisadvantages of specific management programs concerning old growth.Nevertheless, the two approaches are inherently related because they are theprimal and the dual of essentially the same problem.In Linear Programming, finding an optimum is to locate the intersectionpoint of all the production functions concerned in conjunction with the ratios ofproduct values, which is indeed the slope of the objective function. In the case ofthe old-growth problem under analysis, what is needed is information regarding(1) resource availability and goals, (2) input requirements in producing certainproducts, and (3) unit value terms. Some data are readily available whereas othershave to be generated based on assumptions. For instance, timber production is50known in terms of technical rates and product values. But the picture for non-timber products is not so clear due to difficulty in quantifying the many servicesthey provide and in measuring their dollar values. As the two types of productsoriginate from the same resource base, knowledge of their relationship in termsof exchange rates for economic valuation and resource equivalence is importantin providing a basis on which sensible decisions rest. It appears that the allowableannual cut can serve as a yardstick for measuring both biophysical resources andeconomic values. Although wilderness preservation on mature stands is not easilyquantifiable in terms of benefits and costs, the effects of a given withdrawal planmay be traced by looking at the resulting changes in the AAC, which can, in turn,be translated into dollars on the basis of prevailing market prices of timberproducts. Of course, the strength of the linkage is open to debate, and it tends tomake more sense along with improved accuracy in measuring the values of non-market goods.In this study, the optimal values for the levels of timber harvesting andwilderness expansion are derived from timber harvest adjustments, taking intoaccount the proposed old-growth withdrawal plan. Based on the assumption thatan increase in protected areas is competitive with existing timber harvestoperations, reduction in the AAC is unavoidable, and this effect can be convertedinto an area measure. In short, an essential assumption is that wildernessexpansion and protection of old-growth forests has to take place at the expenseof reduced timber supply from the net operable forest land in British Columbia.51Chapter 4Data Used in the ModelData are fabrics, weaving decision variables into a model according topredetermined relationships. In this study, data of essentially two types have beengathered. One category are figures that help identify the right-hand-side (RHS)constants for fixing various goal targets and resource availabilities, and the othercategory are those that specify the technical coefficients indicative of resourcerequirements in the transformation from inputs to outputs. However, given thenature of the problem under analysis, the existing data are inadequate. Forinstance, non-timber values of the old growth for wilderness preservation areneither available at the provincial level nor at regional levels. Therefore, necessarydata are generated on the basis of existing data (perhaps for other regions) andassumptions.4.1 Data SourcesThe data used in the model are drawn from various publications. The majorsources include the following:(1) Selected Forestry Statistics Canada 1991 (Forestry Canada);(2) Economic Forestry Statistics 1992 (Forestry Canada);(3) Canada’s Timber Supply: Current Status and Outlook (Runyon 1991);52(4) Compendium of Canadian Forestry Statistics 1992 (Canadian Council ofForest Ministers);(5) British Columbia Land Statistics (B.C. Ministry of Lands, Parks and Housing1985 & 1989);(6) British Columbia Forest Industry Fact Book 1990-1992 (Council of ForestIndustries of British Columbia);(7) B. C. Ministry of Forests Annual Reports 1982-1992;(8) Parks and Conservation Areas on Prime Forest Land in B. C., 1965-1985(Environment Canada 1987);(9) Canadian Forestry Statistics (Statistics Canada 25-202);(10) The Forest Industry in Canada (Price Waterhouse);(11) British Columbia Economic & Statistical Review 1991-1992 (B.C. Ministryof Finance and Corporate Relations);(12) Opportunity Cost of Preservation of Old Growth and the Present Value ofSilviculture (Ludwig and Conrad 1991);(13) British Columbia’s Endangered Wilderness: A Proposal for an AdequateSystem of Totally Protected Lands (The Valhalla Society 1988);(14) Wilderness and Forestry: Assessing the Cost of Comprehensive WildernessProtection in British Columbia (Simon Fraser University 1990);(15) Economics ofProtecting Wilderness Areas and Old-Growth Timber in BritishColumbia (van Kooten 1993b); and(16) The Economic Impact of a Reduction in Harvest Levels in British Columbia:53A Policy Perspective (Binkley et al. 1993).4.2 Data ClassificationThe data extracted from the above sources are classified into two broadgroups, namely, the right-hand-side constants and technical coefficients. Theycentre around the six goal items that have been identified as the elements of themodel. Some of the data are shown in the form of tables and figures whereverthey appear fit, and others are presented at the end of this chapter.4.2.1 Right-hand-side ConstantsIn Goal Programming modelling, the right-hand-side constants fall into twocategories, namely, the levels of goals and availability of resources.Constants for Goal Levelsa) The annual contribution of forestry and logging to B.C.’s real GDP at factorcosts is $1,244.4 million at 1986 constant prices for an average level of a ten-year period from 1982 to 1991 (B.C. Ministry of Finance and Corporate Relations1992).b) The levels of the old-growth withdrawal goal are based on the Valhalla proposaland the Simon Fraser University study report on B.C.’s wilderness protection.Details are presented in Table 3.c) Information on the levels of employment by B.C.’s forest industry sector isshown in Table 4. The data for the years 1982-89 are from Selected ForestryStatistics Canada (Forestry Canada 1991), and figures for 1990 and 1991 arederived from Statistics Canada 1990 and British Columbia Forest Industry Fact54Book 1992, respectively. The annual average of 77,611 is rounded off to 77,600which is adopted for the model.d) Crown stumpage revenue data are drawn from B.C. Ministry of Forests annualreports. The level of $408.73 million is an average of the four years of 1988-1991, reflecting a considerable increase in stumpage charges as a result ofgovernment policy changes introduced in 1987 (Price Waterhouse 1988).e) The level of maximum sustained yield is represented by the long run sustainableyield (LRSY) for all of the TSAs and most TFLs in British Columbia. The mostrecent LRSY estimates for the whole province are 58.94 million cubic metres(Binkley eta!. 1993).f) The AAC level of 73.33 million cubic metres is taken both as a target and aconstraint for timber harvesting in the province. Break-downs by region arepresented in Table 5.Table 3: Wilderness Expansion in the Valhalla Proposal by RegionRegion Area Volume m3/ Reduction Effect on AAC(ha) affected ha in AAC AAC in effect(000 m3) (000 m3) the region (m3/ha)(%)Cariboo 109866 27960 254 448 -5.2 4.08Kamloops 47965 13587 283 173 -2.1 3.61Nelson 49249 17214 350 253 -4.1 5.14Prince George 155217 35801 231 337 -1.9 2.17Prince Rupert 142852 43679 306 394 -4.2 2.76Vancouver 145310 87908 605 972 -4.2 6.69Province 650459 226149 348 2578 -3.52 3.96Source: SFU-NRM Report No.6 “Wilderness and Forestry,” 199055Table 4: Level of Employment Supported by Timber Harvesting in B.C.Region m3/ha Job/haCariboo 243 0.25Kamloops 256 0.26Nelson 297 0.30Prince George 273 0.28Prince Rupert 342 0.35Vancouver 737 0.75Province 341 0.35Source: B.C. Ministry of Forests Annual Report 1991-92; andForestry Canada. “Selected Forestry Statistics.”Note: Price Waterhouse and COFI indicate an employment coefficientof 1 .2 per thousand cubic metres of timber harvesting. ButB.C. Ministry of Forests figures show a ten-year average of1 .02 per thousand cubic metres.Table 5: Net Operable Mature Stands and AAC Levels in B.C.Region Area (ha) Stock m3/ha AAC level(000 m3) (000 m3)Cariboo 2235849 544084 243 8560Kamloops 1829048 469002 256 8139Nelson 934582 277972 297 6099Prince George 5081986 1388844 273 17768Prince Rupert 1950078 667734 342 9435Vancouver 1911276 1409433 737 23324Province 13942819 4757069 341 73325Source: SFU-NRM Report No.6. “Wilderness and Forestry,” 1990.56Resource AvailabilityAs mentioned above, the AAC by region is identified as a resourceconstraint in the model. As a matter of fact, two AAC levels are involved. In theequations which do not take old-growth withdrawal plans as given, the provincialtotal AAC is used; but when the wilderness expansion program enters intoconsideration, a new level of AAC that nets out the relevant effects are adopted.4.2.2 Revenue/Cost CoefficientsThe values of old-growth forests lie in the services they are capable ofproviding. The quality of these services may be indicated by means of valuationin dollar terms. Basically, two types of products are involved in the study, namely,timber and non-timber products. Determination of their values is necessary for tworeasons. One is for understanding the opportunity costs of a program like PASthrough product values comparison because, given the AAC constraint,withdrawing old growth into wilderness will lead to reductions in timber harvestand the timber benefits forgone constitute the opportunity costs of the old-growthprotection scheme. The other reason is an extension of the first. The values oftimber and non-timber products are needed in calculating benefit ratios that serveto measure the slope of iso-profit lines in a linear programming model concerningproduction functions with joint products such as timber and non-timber goods andservices. Knowledge of the slopes is crucial in finding optimal solutions that aresupposed to occur at points where iso-profit lines touch the frontiers of feasible57regions (Dowling 1980).In this study, timber benefits are represented by average net returns fromharvesting mature and overmature stands (Ludwig and Conrad 1991). The netreturns are expressed algebraically as follows:NB = (PTCH)*VCRwhere NB is net benefits ($/m3);PTis market price of timber ($/m3);CH is harvesting cost ($/m3);V is the volume per hectare (m3/ha); andCR is the restocking cost ($Iha).As site quality in British Columbia varies considerably from one region toanother, it is desirable that site classes be taken into account when calculatingtimber volumes. Species type is another important factor affecting the values oftimber products. Table 6 is a summary of weighted average net timber benefitsby region. The non-timber values of B.C.’s old growth for recreation use andpreservation are presented in Table 7, which covers all six regions regulated bythe Ministry of Forests. The calculations are based on van Kooten (1993b). Thesecond table of van Kooten’s paper provides the basis for calculating the weightsfor recreation use values and preservation values for old growth. Under the58assumption that recreation values account for 25 per cent and preservation valuesfor the remaining 75 per cent of the total non-timber values, a combined weightfor both recreation and preservation values can be worked out. Van Kooten(1993b) estimates that the non-timber benefits on a provincial scale are around$1,000 per hectare at the pre-1992 levels of old-growth protection. The combinedweights of non-timber values of old-growth protection by region may be used incomputing sub-total non-timber values for each of the six regions. The results ofcalculations are presented in Table 8.Table 6: Average Timber Values of Old Growth by Species($/ha)Species Coast Southern NorthernInterior InteriorDouglas fir 16470 5842 7689Cedar/Hemlock 28978 23635 31512Pines 11991 2057 2395Balsam 12886 7906 9675Spruce 22104 10647 8026Source: Ludwig and Conrad 1991. Opportunity cost ofpreservation ofold growth and present value of silviculture.Timber values refer to the net return defined as:market price - harvest cost - restocking cost59Table 7: Timber vs Non-timber Benefits of Mature Stands in B.C.($/ha)Region Timber Non-timberCariboo 5002 312Kamloops 6905 915Nelson 8106 1641Prince George 5778 247Prince Rupert 14080 429Vancouver 22803 4304Source: Based on van Kooten 1 993b.”Preservation Benefits - Table 2”,and SFU-NRM Report No.6 “Wilderness and Forestry,” 1990,the calculation of the non-timber values is done by thefollowing formula:net mature area x 1000 x weights + area of each region;The figure 1000 is the approximate level of non-timber benefitsper hectare estimated by van Kooten (1993b).60Table 8: Weights of Recreation Use and Preservation ValuesRegion Weights for Weights for Combinedrecreation preservation weights forvalue value both valuesCariboo 0.13 0.02 0.05Kamloops 0.25 0.08 0.12Nelson 0.21 0.07 0.11Prince George 0.17 0.06 0.09Prince Rupert 0.13 0.03 0.06Vancouver 0.11 0.75 0.59Source: Adapted from van Kooten (1993b) “Preservation benefits -Table 2”.For combined weights, it is assumed that recreation valuesaccount for 25% and preservation values for 75% of entirenon-timber values. This weighting seems to make more sensefor old growth which tends to have higher preservation values.On stands with less stock, recreation values tend to be high.Another way is to assign half weights to both.614.2.3 Technical CoefficientsAnother important category of data involves the input requirementcoefficients. Again, all the coefficients are related with the identified goal items,and the unit area stock volume serves as a common linkage among differentcoefficients.(1) The timber values and non-timber values are used as coefficients for the netbenefits goal.(2) Withdrawal of old growth into wilderness is bound to reduce the AAC in theforest region concerned. The coefficients that indicate the reduction in AAC interms of cubic metre per hectare are included in Table 3.(3) B.C. Ministry of Forests data on timber harvesting and employment suggestthat, on the provincial scale, 1 .02 is the average level of employment providedfrom harvesting 1,000 cubic metres of timber over the past decade. In the model,however, different coefficients are used, as shown in Table 4, to reflect regionalvariations in terms of stock volumes and species compositions.(4) The levels of stumpage charges, by region, are derived from B.C. Ministry ofForests annual reports and presented in Table 9.(5) The per hectare stock volume figures are shown in Table 5.62Table 9: Average Levels of StumDage Charges on MOF Regulated LandsRegion $/m3 $IhaCariboo 4.93 1 198Kamloops 6.13 1569Nelson 4.91 1458Prince George 8.54 2331Prince Rupert 5.11 1748Vancouver 9.49 6994Province 7.23 2465Source: B.C. Ministry of Forests Annual Reports 1989-19924.3 Other DataIn order to better illustrate the model, additional information of relevanceis provided in Appendix B in the form of tables and graphs.63Chapter 5Discussion of the Results of the ModelThe results of the Goal Programming model for planning old-growth usesfor wilderness preservation and timber production in British Columbia are providedin this chapter. Upon brief explanation of the computer software adopted for themodel, the levels of goal achievements are presented. Although the objectivefunction of the model is to minimize deviations from various established goals, theultimate purpose of assessing the deviations is to determine what implications thewilderness expansion proposal at hand may have. In order for the model toprovide relevant information, sensitivity analysis is carried out in such a way thatpriority rankings are rearranged in the hope of revealing changes in terms of goalattainments. Trade-offs between different goals are discussed at the end of thechapter.5.1 Descrijytion of the Computer Software EmDloyedThe computer software used in the study is called General AlgebraicModelling System (GAMS). Developed at the World Bank in the 1980s, GAMS isa mathematical programming software package (Brooke, Kendrick, and Meeraus1988). Designed to handle a wide range of modelling problems, the software hasbeen successfully employed in research projects of diverse disciplines (Jefferson64and Boisvert 1989). One distinctive feature of the software is its accommodationof linear, nonlinear, and mixed integer optimization problems.The adoption of GAMS as the computer software for this study is attributedto its design characterized by a programming language in making standardalgebraic statements. This straightforward feature of model construction,complemented by the way data are supposed to be organized and solutionsreported, offers considerable credit to the software for, after all, a goodmathematical programming software is expected to facilitate the description of aproblem and to provide effective means of solving it.The several GAMS manuals available have no mention as to how goalprogramming may be handled. Nevertheless, GAMS is adopted in the belief thatthe software is capable of handling the GP model in such a way that goalconstraints are isolated to allow sequential treatment of goal items according totheir respective ordering. This piecemeal approach requires separate computerruns in generating solutions, which are subsequently put together forinterpretation. The full GAMS command file is provided in Appendix C.5.2 ODtimal Goal Levels and Their AchievementsThe main computer simulation results are summarised in Table 10. Recallthat decision variables x and q stand for the levels of timber harvesting andwilderness expansion, respectively. The variables are denoted by subscripts from1 to 6, referring to the six B.C. Ministry of Forests regions, namely, Cariboo,65Kamloops, Nelson, Prince George, Prince Rupert and Vancouver. Negativedeviations from corresponding goals are represented by D1,.. .,D6 and the fifthand sixth goals are the only ones that are permitted to acquire positive deviations,denoted by D5 and D5.The solution of the goal programming model provides the following results.First, a pattern of goal item grouping is discernable. Second, given the specificconstraints in the model, negative deviations occur for the employment goal andthe goal of maintaining current timber harvest, while a positive deviation resultsfor the sustained timber yield goal. Third, the rankings of the goal items have beensuch that goal constraints tend to build up progressively.As is revealed in Table 10, the six goal items may be classified into fourgroups. (1) The goals of net benefits and stumpage revenues form one groupsince they both are expressed in dollar terms. (However, the two goals are notcommensurable in an economic sense since the first measures economicefficiency, while the second is an income transfer). (2) The employment goalstands on its own and is judged by the number of jobs. (3) The sustained timberyield and current timber harvesting goals share an identical measurement of cubicmetres. (4) Viewed as an institutional constraint, the wilderness expansion goalis a distinctive category measured in hectares. In the optimal solution, for itemsof the first group, one observes over-fulfilment of goal targets. In the case of theemployment goal, negative deviations occur the moment it is introduced. The twotimber related goals are found to be binding constraints on direct forest66employment in the province.5.3 Interpretation of the ResultsAs Table 10 indicates, the first and fourth goal items do not register anyundesirable negative deviations. As far as the total-net-benefits goal is concerned,the target represents an average annual level of contribution by the forestry andlogging sector towards the GDP of the province. According to Table 10, if theAAC is fully exploited and maximization of timber benefits is the onlyconsideration, the total net benefits from timber harvesting can reach $2,050million, or $810 million higher than the target. But this result should not beinterpreted as saying that the original target was set too low, because in thismodel that item happens to have been ranked as the first priority. Settingexcessively high targets is likely to result in corner solutions, often leading tocomplete sacrifice of lower ranking goal items. Likewise, the stumpage revenuegoal poses no difficulty for accomplishment because, as Table 10 shows, that themaximum stumpage revenue can be up to $525 million which is $116 millionhigher than the target. These results lend support to a wilderness expansion planof a scale similar to that of the Valhalla proposal on the argument that total netbenefits tend to be positive and government stumpage revenues are non-declining.The computer work file has been constructed in such a way that thewilderness expansion component is submitted for two separate solutions. On oneoccasion, the scheme is not site specific, and on the other it is made to conform67with the given plan precisely. When wilderness expansion is evaluated in termsof provincial acreage only, that is, without reference to particular sites,preservation takes place in the Cariboo Forest Region. The reason is that the perhectare stock volume in Cariboo is the lowest in the six regions (see Table 5). But,as has been explained earlier, the Valhalla proposal enters into the model as aninstitutional goal constraint and, therefore, wilderness expansion targets have tobe allocated to identified areas in each of the six B.C. Ministry of Forests’ regions.Direct forest employment is negatively affected by wilderness expansion onold growth. Table 10 reveals that it is impossible to achieve the goal becauseattainment falls short by 5,384 jobs the moment the goal is introduced. Inaccordance with goal programming rules, once deviations from a certain goal havebeen brought to a minimal level, they would be treated as a fresh constraint andshould not be violated thereafter. Therefore, when it comes to pursue thesustained timber yield goal, retaining the minimal deviation levels from theemployment goal turns out not to be possible without breaking the sustained yieldceiling by 2.58 million cubic metres each year. In spite of this rigid feature,information is generated from computer runs about the changes in the levels oftimber harvesting in each of the regions.Finally, maintaining the current timber harvesting level is not feasiblebecause to insist on achieving that goal will necessarily disturb the immediatelyhigher-ranking item, namely, the sustained timber yield goal. However, by now,the even higher wilderness expansion goal rules out such a possibility by having68reduced the AAC already through wilderness designation of certain old-growthstands. This means that negative deviations from the sixth goal are unavoidable.Table 10 shows the results of evaluating goals at the upper bound ofresource constraints, and this approach tells about the obtainability of variousgoals. For comparison, Table 11 indicates the results when the lower bound ofresource availabilities are adopted in goal evaluation.The additional information provided by Table 11 is the following.(1) Achieving the minimum level of the first goal does not have to involvetimber cut in the Cariboo forest region at all, and logging only needs to occur inthe Vancouver forest region on a small scale. Since the concern now is to reachthe specified goal level with minimal use of resources, it is economical not toinclude Cariboo because it is at the bottom among all six regions in terms oftimber values per hectare and its unit area stock volume is the lowest as well. Themoderate level of timber harvest in the Vancouver forest region is attributable tothe region’s high stock volume on a hectare basis. The computer algorism is suchthat one wants to save as much resource as possible in meeting given goals.(2) Wilderness expansion in the order of 0.65 million hectares can takeplace entirely in Prince George. The reason is that the region’s forest landidentified by the Valhalla plan for preservation is of the lowest quality (see Table3). Besides, achieving the two specific goals makes it unnecessary for logging tooccur either in Cariboo or in the Vancouver forest region on account of resourcesaving principles.69(3) The employment goal is particularly vulnerable to constraint build-up inthat negative deviations are hardly avoidable, and it can be tripled should the goalof sustained timber yield be pursued.(4) The consideration of the sustained yield goal is likely to diminish timberharvesting in the Southern Interior because, as Table 11 shows, logging may fallto zero for Nelson and it can drop to 7,845 hectares from the usual level of31,117 hectares per year.5.4 lmDlications of the ResultsThe above results indicate that the real conflicts between timber harvestingand wilderness preservation rest with the level of employment being directlyprovided by the forest industry in the province. Given the fact that old-growthforests are input factors common to both timber harvesting activities andwilderness preservation, review of changes in the levels of resource use maythrow some light on various listings of goal items.As indicated by Table 12, given the current timber prices and non-timbervalues used in the model, the total-net-benefits goal may be accomplished withoutever reaching the upper limit of B.C.’s old-growth resources. The last column ofthe table suggests that a considerable amount of resources can be left untouchedin the Ministry of Forests’ Cariboo and Vancouver regions. A wilderness expansionprogram of the scale such as the Valhalla plan, but not site specific, is unlikely tohinder attainment of the first goal. The situation would probably be such that70available mature stands are subjected to fuller use in the Southern Interior andPrince George, where the wilderness expansion scheme could concentrate.However, in view of the Valhalla plan which is identified with specificgeographical sites, the old-growth resources become a real constraint everywherein the province in conjunction with employment considerations. As shown inTables 10 and 11, even if all the AAC is utilized, there is still a shortfall of 5,384jobs. The adoption of the sustained yield goal favours relieving pressure on old-growth resources in the Southern Interior, but the cost in terms of job losses inforest-dependent communities would rise to a high level because negativedeviations from the average annual employment level would widen by 17,339instead of 5,384.In order to validate the model, various tests are necessary in the hope ofrevealing as much information as possible about the impacts of wildernessexpansion on other goal items concerned. A sensible thing to do is to alter priorityrankings.5.5 Priority Ranking TestsAs the employment and sustained timber yield goals have stood out as theones that witness large deviations, they are singled out for priority rankingalteration tests.Test 171During this test, the employment goal is upgraded to the first prioritystatus, while the remaining items maintain their positions relative to one another.The purpose of doing this is to isolate the effects of the proposed wildernessexpansion plan on direct forest employment. Table 13 provides information aboutthe level of forest employment losses associated with various goal item packages.It shows that the current timber harvesting level is unable to support the averagelevel of 77,600 jobs and the shortfall amounts to 2,747. This is important forevaluating the Valhalla proposal because the negative effects of the wildernessexpansion plan on forest employment is actually not as high as suggested in Table10. Another interesting thing about this table is the revelation that, without sitespecifications, all of the wilderness expansion task would go to Prince Georgewhere the average opportunity costs are lower than other regions for old-growthpreservation.Test 2When the sustained yield goal is allowed to assume the first ranking,significant changes would occur with regard to the allocation of old-growthresources among different regions to satisfy the new ordering of various goalitems. As can be seen from Table 14, if the sustained yield goal is the firstpriority, as many as 2.15 million hectares of old growth may be protected aswilderness, occurring entirely in the Vancouver forest region. In the event that awilderness expansion plan of the Valhalla scale is implemented without site72specifications, Vancouver would still be the region for concentrated wildernesspreservation. The reason is that non-timber values are much higher in this regionthan elsewhere, although it is true of timber values as well.5.6 Different Scenarios of Harvesting LevelsThe results of the priority sequence tests indicate that the levels of annualtimber harvesting can vary from one ranking scheme to another. For instance,given the original ranking of the GP model, annual timber cut is likely to start offwith 149,300 hectares each year to achieve the net benefits goal, and it slidesto 137,191 hectares to accommodate the need of preserving 650,000 hectaresof forests that are not geographically specific. But, in the framework of theValhalla plan which serves as an institutional constraint, timber harvesting needsto be maintained at around 204,800 hectares, and retreating from this level onaccount of long-run sustainable yield will have to cause decline in direct forestemployment. This result is shown by Figure 1, which also indicates two otherscenarios, one having the employment goal as the first priority and the otheradopting sustained yield as the first ranking. These two scenarios start off withhigher amounts of timber cut, but both level off as goal constraints pile up. Inspite of the differences, the three scenarios show a common feature of conflictsbetween employment and timber harvesting goals.735.7 Trade-offs among various goalsGoal Programming is known to be deficient in generating trade-offinformation (Field, Dress and Fortson 1980). This is particularly the case whenonly the preemptive approach is used in ordering goal items. Nevertheless, theranking alteration tests as shown in Table 13 and Table 14 provide information onthe trade-offs between the proposed wilderness expansion plan and the reductionin employment for B.C.’s forest industry. Expressed in terms of trade-off ratios assummarized in Table 15, the indications are that additional goal constraintsproduce adverse effects on the level of direct forest employment given theValhalla proposal. It appears that adding goal items in the decision package isassociated with additional job losses. In other words, the accumulation of goalelements tends to reduce the exchange rate between wilderness expanded areaand the lowering of forest related employment.For instance, when the decision package consists of a plan to expandwilderness by about 650,000 million hectares without specific requirements aboutsite conditions, the number of jobs lost would be (4194 - 2747) = 1447, and theratio of expanded wilderness area versus job losses would work out to be -450,meaning that losing one forest job is the price for protecting 450 hectares of oldgrowth. However, when site specification is required in accordance with theValhalla proposal, the absolute value of the ratio would drop to 247, indicatingthat the disappearance of one forest job is now worth 247 hectares. By the sametoken, by the time the sustained yield constraint is included in the decision74package, loss of one forest job could exchange for merely 45 hectares ofwilderness. Therefore, inclusion of goal considerations in decision makingprocesses will likely shrink the resource base of mature stands for timberharvesting, and the most obvious price that British Columbians have to pay, andat an increasing rate, is in terms of forest related employment.Given the ranking and target levels of the goals, the results of the modeldemonstrate a serious conflict between timber harvesting and wildernesspreservation. Strictly speaking, the conflict originates because the forest base isnot unlimited. Wilderness protection (e.g., the Valhalla proposal) merelyexacerbates the resource scarcity problem since, even without the proposedprotection program, the current AAC is inadequate in supporting the currentaverage level of employment, as shown by Table 13. Yet implementing theValhalla proposal will incur a greater degree of job losses. The magnitude of thelosses can vary considerably, depending on site specification and intensity ofconstraints. Whether or not to accept the losses is ultimately a political decision.75Table 10: Goal Targets and Attainments at Unøer Bound of Resource ConstraintsGoal Item Target Achievement Deviation Wilderness Annual cutexpansion (ha)” (ha)***- 1st 1.24x109 2.05x109 D1=0 Total 0 xl 35226x2 31797x3 20539x4 65092x5 27602x6 31642Total 211898- 1st 1.24x109 2.2x10° D1=0 ql 650459 xl 243052nd* 6.5x10 6.5x10 D2=O Total 650459 x2 31797x3 20539x4 65092xS 27602x6 31642Total 200977- 1st 1.24x109 1.97x10 D1=0 qi 109866 xl 33383-2nd” 6.5x10 6.5x10 D2=0 q2 47965 x2 31117-3rd 77600 72216 3=5384 q3 49249 x3 19682q4 155217 x4 63849q5 142852 x5 26436q6 145310 x6 30327Total 650459 Total 204794- 1st 1.24x109 1.97x10 D1=0 same as above same as above- 2nd” 6.5x10 6.5x10 D2=0-3rd 77600 72216 D=5384-4th 4.09x10° 5.25x108 D4=0- 1st 1.24x109 1.97x10 D1=0 same as above same as above-2nd” 6.5x10 6.5x10 D2=0-3rd 77600 72216 3=5384-4th 4.09x10° 5.25x108- 5th 5.89x107 5.89x10? D5=0=1.18x107- 1st 1.24x109 1.97x10 D1=0 same as above same as above-2nd” 6.5x10 6.5x10 D2=0-3rd 77600 72216 3=5384-4th 4.09x108 5.25x108- 5th 5.89x1& 7.07x10• 6th 7.33x10 7.33x105 D5=1.l8x107D6 = 2.58x1 06D6 =0not area specific; “ regions: 1 -- Cariboo; 4-- Prince George;* * area specific 2 — Kamloops; 5 -- Prince Rupert;3 -- Nelson; 6 -- Vancouver76Table 11: Goal Targets and Attainments at Lower Bound of Resource ConstraintsGoal Item Target Achievement Deviation Wilderness Annual cutexpansion (ha)*** (ha)***- 1st 1.24x109 1.24x109 D1=0 Total 0 xl 0x2 31979x3 20539x4 65092x5 27602x6 4088Total 149300- 1st 1.24x109 1.24x109 D1=0 q4 650459 xl 02nd* 6.5xlOS 6.5x10 D2=0 Total 650459 x2 31797x3 20539x4 59921x5 24934x6 0Total 137191- 1st 1.24x109 1.97x10° D1=0 qi 109866 xl 33383-2nd” 6.5x10 6.5x10 D2=O q2 47965 x2 31117-3rd 77600 72216 D=5384 q3 49249 x3 19682q4 155217 x4 63849q5 142852 x5 26436q6 145310 x6 30327Total 650459 Total 204794- 1st 1.24x10° 1.97x10 D1=0 same as above same as above• 2nd** 6.5x10 6.5x10 D20-3rd 77600 72216 D=5384- 4th 4.09x108 5.25x108- 1st 1.24x10° 1.63x109 D0 same as above xl 333832nd** 6.5x10 6.5x10 D2=0 x2 7845-3rd 77600 60249 3=17339 x3 0- 4th 4.09x108 4.39x10° D4=0 x4 63849- 5th 5.89x107 5.89x107 D5=0 x5 26436x6 30327Total 161840- 1st 1.24x109 1.97x10 D1=O same as above xl 333832nd** 6.5x10 6.5x10 D2=0 x2 31117-3rd 77600 72216 Da=5384 x3 19682- 4th 4.09x108 5.25x108 D4=0 x4 63849- 5th 5.89x107 7.O8xlOS D5=0 x5 26436- 6th 7.33x101 7.08x105 =2.58x10° x6 30327D=1.18x107 Total 204794* not area specific; * regions: 1 -- Cariboo; 4 -- Prince George;* area specific 2 -- Kamloops; 5 -- Prince Rupert;3-- Nelson; 6 -- Vancouver77Table 12: Resource Use under Various Packages of Goal ItemsGoal package Region Resource use Upper limit Potential leftlevel (million m3) (million m3) (million m3)-1st Cariboo 0 8.56 8.56Kamloops 8.14 8.14 0Nelson 6.10 6.10 0P.George 17.77 17.77 0P.Rupert 9.44 9.44 0Vancouver 3.01 23.32 20.31Total 44.46 73.33 28.87-1st Cariboo 0 8.56 8.562nd* Kamloops 8.14 8.14 0Nelson 6.10 6.10 0P.George 17.77 17.77 0P.Rupert 8.53 9.44 0.91Vancouver 0 23.32 23.32Total 40.54 73.33 32.79-1st Cariboo 8.11 8.11 02nd** Kamloops 7.97 7.97 0-3rd Nelson 5.85 5.85 0P.George 17.43 17.43 0P.Rupert 9.04 9.04 0Vancouver 22.35 22.35 0Total 70.75 70.75 0-1st Cariboo 8.11 8.11 02nd** Kamloops 7.97 7.97 0-3rd Nelson 5.85 5.85 0-4th P.George 17.43 17.43 0P.Rupert 9.04 9.04 0Vancouver 22.35 22.36 0Total 70.75 70.75 0-1st Cariboo 8.11 8.11 0-2nd” Kamloops 2.01 7.97 5.96-3rd Nelson 0 5.85 5.85-4th P.George 17.43 17.43 0-5th P.Rupert 9.04 9.04 0Vancouver 22.35 22.35 0Total 58.94 70.75 11.80-1st Cariboo 8.11 8.11 0-2nd” Kamloops 7.97 7.97 0-3rd Nelson 5.85 5.85 0-4th P.George 17.43 17.43 0-5th P.Rupert 9.04 9.04 0-6th Vancouver 22.36 22.35 0Total 70.75 70.75 0* not area specific;** area specific.Table 13: First Test Results in Altering Goal RankingGoal Item Target Achievement Deviation Area cut (ha) Wildernessexpansion (ha)- Employment 77600 74853 2747 xl 35226 0x2 31797x3 20539x4 65092x5 27602xB 31642Total 211898- Employment 77600 73406 4194 xl 35226 q4=650459Wilderness x2 31797x3 20539x4 59921x5 27602x6 31642Total 206727-Employment 77600 72216 5384 xl 33383 qi 109866Wilderness* x2 31117 q2 47965x3 19682 q3 49249x4 63849 q4 155217x5 26436 q5 142852x6 30327 q6 145310Total 204794- Employment 77600 72216 5384 same as above same as above- Wilderness- Net benefits- Stumpago- Employment 77600 60261 17339 xl 33383 same as above- Wilderness x2 7845- Net benefits x3 0- Stumpage x4 63849- Sustained yield x5 26436x6 30327Total 16184078* not site specific;** site specific.Table 14: Second Test Results in Altering Goal RankingGoal Item Region Wilderness expansion Annual cut (ha)(million ha)- Sustained yield Cariboo 35226Kamloops 31797Nelson 20539Prince George 65092Prince Rupert 27602Vancouver 2.15 12121Total 2.15 192377- Sustained yield Cariboo 0Wilderness Kamloops 26033Nelson 20539Prince George 65092Prince Rupert 27602Vancouver 0.65 25737Total 0.65 165003- Sustained yield Cariboo same as Valhalla plan 33383• Wilderness Kamloops 7845- Employment Nelson 0Prince George 63849Prince Rupert 26436Vancouver 30327Total 161840- Sustained yield Cariboo same as above 33383- Wilderness Kamloops 7845- Employment Nelson 0- Net benefits Prince George 63849Prince Rupert 26436Vancouver 30327Total 161840- Sustained yield Cariboo same as above 33383- Wilderness Kamloops 7845- Employment Nelson 0- Net benefits Prince George 63849- Stumpage Prince Rupert 26436Vancouver 30327Total 161840- Sustained yield Cariboo same as above 33383- Wilderness Kamloops 311 17- Employment Nelson 19682- Net benefits Prince George 63849- Stumpage Prince Rupert 26436- Harvesting Vancouver 30327Total 20479479* not Site specific;* * site specific80Table 15:Trade-off Ratio between Wilderness Expansion and Forest-relatedEmployment Reduction under Different ScenariosGoal items Wilderness Direct forest Wilderness gainedexpansion employment per job lost(thousand ha)- Employment 0 74853 0- Employment 650 73406- 450- Wilderness (notsite specific)- Employment 650 72216 - 247- Wilderness(site_specific)- Employment 650 72216- 247- Wilderness- Net benefits- Stumpage- Employment 650 60261- 45- Wilderness- Net benefits- Stumpage- Sustained yieldFigure 1:81Annual Timber Harvest Scenarios in B.C. - Different Goal Schemes ComDared21000019-Jw-J1?15ANNUAL TIMBER HARVEST IN B.C.DIFFERENT GOAL SCHEMES COMPARED21-19IT15U1 2 3 4 5 6GOAL ITEMS-- ORIGINAL RANKING -A• EMPLOYMENT FIRST +• SIJSVED YIELD FIRST82Chapter 6Summary and ConclusionsBritish Columbia is endowed with large areas of old-growth forests thatafford its residents ample opportunities to pursue diverse goals. However,intensification of activities related to the old growth over the last few decades hasrun parallel with a growing awareness of limits to the resource base. Conflictsarise primarily from rival human needs for both timber and non-timber productsthat may be translated into jobs on the part of local communities, profits on thepart of forest industries, and revenues on the part of the provincial government.From the standpoint of the province at large, the old growth has an essential roleto play in the well-being of the average British Columbian.Managing the old-growth forests for multiple uses is a decision-makingprocess that involves diverse goals. Identification of goal items provides aframework in which a problem may be addressed, and specification of goal targetsputs the problem into perspective, which, along with the consideration of resourceavailabilities, delineates the required decision environment.For a multiple-use decision problem, instead of any single item, theobjective is necessarily to seek the achievement of all goals concerned to thelargest extent possible. What underlies the optimal solution is a most preferredstatus characterized by a well-placed system of goals related to one another via83an exchange rate or trade-off function that may or may not be directly expressiblein value terms. The result is the choice, among all alternatives available, of theone most satisfactory to the stakeholders.The identification of goals serves the purpose of focusing decision makers’attention on fewer selected aspects of an issue. The specification of goal levelscreates concrete criteria by which judgement may be formed. And ranking goalsin an ordinal fashion establishes a rule of procedure that guides a sequentialtreatment of the goats. All this leads to the ultimate objective of maximizing thecontribution of the old growth to the well-being of British Columbians.Alternatively, the objective can be expressed as minimizing deviations fromestablished targets, which is precisely what this study is concerned with.The aim of this study is to evaluate a specific plan concerning the use ofold-growth forests for timber harvesting and wilderness preservation at theprovincial level in British Columbia. In the context of B.C.’s Protected AreasStrategy, the old growth is placed under two polarized land use considerations,namely, commercial harvesting for the realization of timber values and designationas wilderness status for the provision of non-timber benefits. Of the six goals thathave been identified, the wilderness expansion plan is represented by the Valhallaproposal on account of its similarity to PAS in terms of philosophy and scale. Asa matter of fact, it is an essential item whose impacts on other goals are subjectmatters for assessment.846.1 Summary of model resultsThe goal programming model has generated the following results.(1) In view of the priority rankings of the goals, implementations canproceed from the first goal through the fourth. Of the goals that are included, thewilderness plan serves as an institutional framework in which action plans arepursued and evaluated. Under the Valhalla scheme, the chosen levels for the goalsof total net benefits from the old growth and government stumpage revenues areunlikely to suffer from any underachievement. However, under the samecircumstances, direct forest employment is expected to fall from the recent ten-year average by 5,384 jobs.(2) It is not possible to consider the fifth and sixth goals in the decisionpackage without jeopardizing the accomplishments of higher-ranking goals. In thecase of the sustained timber yield goal, its inclusion is likely to worsen forest-related employment shortfalls from 5,384 to 17,339. This problem might bepartially rectified by insisting on the current timber harvesting goal; but the costof minimising employment losses back to 5,384 is the breaking of the sustainedyield ceiling by 2.58 million cubic metres in terms of AAC.(3) The six goal items tend to fall into the following four categories:a) wilderness expansion plan;b) employment goal;C) total net benefits and government stumpage revenues; andd) sustained timber yield and current level of timber harvesting.85Conflicts are evident between the employment goal, on the one hand, and thesustained timber yield goal on the other. The impacts of the wilderness expansionplan as a constraint on timber harvesting operations are clearly visible. The twogoals of net benefits and stumpage revenues are not binding on the rest.(4) As far as resource use is concerned, the results of the model seem toindicate that resource allocation has a tendency of gravitating towards its efficientuse on the basis of unit area stock volume and prevailing value terms. Forinstance, the specified target of the net benefits goal may be attained at least costin terms of old-growth resource use by not involving Cariboo due to its low levelof stock volume and timber values per hectare and by incurring limited loggingactivities in the Vancouver forest region. As far as wilderness expansion isconcerned, should there be no geographical requirements, a program on the scaleof the Valhalla proposal is least costly to occur in Cariboo judging by site indexalone, and the task is likely going to Prince George if minimizing negative effectson AAC is the sole consideration.In the model, when the site specific wilderness plan is introduced inconjunction with the employment goal, excess resource reserves immediately dropto zero. The pressure on resource uses can be mitigated, mainly in the SouthernInterior, when the sustained yield goal is brought into consideration, but theassociated cost is enormous in terms of the reduction in the level of direct forestemployment.(5) Altering the priority ordering of goals has been undertaken for the86purposes of sensitivity analysis. Unlike in Linear Programming problems, thealteration of goal rankings is merely to change the sequences by which the sameproblem is approached. The test has proved helpful in generating supplementaryinformation.Suppose that the system of goals is altered in such a way that employment isupgraded to the first priority. Given the current AAC constraints, the maximumlevel of timber harvest is then 211 ,898 hectares, allowing no wildernessexpansion. This so-called optimal level could only support 74,853 jobs. In otherwords, given the current technology, the annual employment level of 77,600 isactually higher than what can be supported by the forest industry in the provinceand, therefore, the negative deviation of 2,747 from the average level is theminimum required due to the AAC constraints. It then follows that any schemesthat erode the AAC will have adverse impacts on forest employment. A wildernessexpansion program such as the Valhalla plan, but without specific requirementson geographic sites, is likely to result in a total shortage of 4,194 jobs. That is,the net impact is to sacrifice 1 ,447 jobs, but the wilderness designated forprotection is 0.65 million hectares of mature stands in the Prince George forest.Implementation of a full-fledged Valhalla proposal is likely to cause a net loss of2,637 jobs across the province. The negative effects are almost double those ofa similar plan that is non-site specific. Adding a sustained timber yield goal overand above the Valhalla plan would cause forest employment to shrink to 60,261,which is 17,339 below the average level of the past decade, or 14,592 below the87current level. To say the very least, the negative impacts of this additionalconstraint more than doubles the total effects of the Valhalla proposal alone ondirect forest employment.A similar test has been done in altering the priority ranking of the sustainedyield goal. The most important information is that the pursuit of a sustained timberyield goal favours wilderness preservation in the Vancouver region. Such ascheme tends to drive wilderness expansion activities entirely to the Vancouverforest region.The implications of these results of the model are the following. First, theold-growth forests are resources that should be managed for multiple uses. Therecognition that wilderness is a land use category as well has secured a place forit to be included in any decision package concerning the old-growth issue. Hence,it is legitimate and justifiable for PAS to be pursued, and in the case of this study,for the Valhalla plan to be considered. Second, the lack of information on non-timber values makes it difficult to evaluate a wilderness expansion program bymeans of benefit/cost analysis. Instead, consequences of the given program maybe analyzed by looking at common linkages such as the AAC in the case of thisstudy. Third, British Columbia is currently operating at its upper limit of theavailable old-growth resources, and reliance on old growth for employmentopportunities is so strong that a slight reduction in the availability of resources forharvesting is likely to bring about immediate negative effects. As the modelignores job increases associated with wilderness expansion, there is a possibility88that employment losses to the whole province may not be as high as what theforest industry would be confronted with.6.2 RecommendationsThe recommendations fall into two parts. The first part is targeted towardspolicy makers at the provincial level, and the second part is concerned with futureresearch.6.2.1 Recommendations for Policy ChangesThe Protected Areas Strategy has emerged in response to calls forpreserving a sound environment in the interests of the inhabitants in BritishColumbia. It is an undertaking that involves planning and implementation, andclearly, planning is of much more concern to policy makers. During the planningprocess, three essential things need to be considered -- state of technology,resource allocation effects, and human aspirations. The first point is to knowabout the status quo of natural endowments and inherent relationships in termsof transformation from inputs to outputs. This knowledge leads to understandingproduction functions that hold promises as well as constraints for humanactivities. The second point is about what the resource situation is to be like asthe result of a specific action plan. Its concern with resource allocation is virtuallythe same as the first point, although different time horizons are involved. The thirdpoint is an interface that connects the first two, and is about human preferences89and their desire to be satisfied. The pursuit of welfare is constrained by the limitedavailability of resources.Although, in the long run, advances in technology can alter the rate oftransformation between inputs and outputs to allow a greater degree of humansatisfaction, the reality of resource scarcity has to be faced in the short run. Thesolution to such a problem lies in equating human valuation of products to the rateof production transformations, taking sustainability into due account.In view of the foregoing observation, recommendations for decision makerson the issue of old growth for wilderness expansion in British Columbia are thefollowing.(1) Although there exist a large amount of data about the inventory aspectsof the mature stands in the province, information is lacking on many bio-physicalaspects of old grovvth. What accounts for this is the historical predominance oftimber extraction. Acquisition of adequate information on the non-timber uses ishelpful for understanding production functions of timber and non-timber products,and new knowledge of this kind may generate a more convincing case in supportof an old-grovvth preservation plans such as the Valhalla proposal.(2) There is an imperative need to carry out studies on the non-timbervalues of old growth. Current information falls short of providing a sound basis forestimating the benefits from implementing the ambitious PAS program.(3) Talking about PAS specifically, withdrawal of old-growth forests intowilderness, for instance, at the scale of the Valhalla proposal, is acceptable90provided that the overall gain from the standpoint of the province outweighs thecombined losses of the regions concerned. This will ensure that the program canbe paid for on its own account.(4) The necessary administrative costs associated with PAS can be huge,and hence should not be neglected. Generally known as transactions costs,expenditures are required both at the planning stage and in various implementationphases. It is indeed a dilemma that a well conceived and carefully prepared PASprogram should improve the efficiency of the program, but the enormousexpenses for doing this may be so costly as to make the program uneconomic.(5) Lastly, a temptation should be avoided in turning PAS into a gigantic all-in-one project. Beyond a certain point, the plan would be too clumsy to moveahead. Should decision makers choose a large size for the program, meticulousplanning and coordination are necessary, and realistic targets along with clearlydefined time-tables will facilitate implementation.6.2.2 Recommendations for future researchFuture research is required to deal with the following concerns.(1) The employment generation capacities associated with wildernesstourism need to be studied.(2) The relationships among the various goal items of the model need to bestudied in terms of assigning cardinal weights to various goals so that trade-offfunctions can be accurately determined.91(3) The dynamic aspect of the issue of old-growth preservation deservesattention.6.3 ConclusionThe issue of old growth is of concern to virtually every inhabitant in BritishColumbia for the simple reason that it concerns the economy and theenvironment. 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EPAT/MUCIA Working Paper No. 6 November1992, USAID-funded Environmental and Natural Resources Policy andTraining ProjectMcKillop, W. 1978. “Economic costs of withdrawing timber and timberland fromcommercial production,” Journal of Forestry 7:414-417.M’Gonigle, M., Thomas Gunton, Chris Fletcher, Murdoch McAllister, and DougMacKnight. 1992. “Comprehensive wilderness protection in BritishColumbia: An economic impact assessment,” The Forestry Chronicle68(3):357-364.Miller, W.L., and D.M. Byers. 1973. “Development and display of multiple-objective project impacts,” Water Resources Research 9(1 ):1 1-20.Mitchell, B.R., and B.B. Bare. 1981. “A separable goal programming approach tooptimizing multivariate sampling designs for forest inventory,” ForestScience 27(1):147-162.Nelson, J.D., and J.S. Hackett. 1993. An EconomicAnalysisof Timber HarvestingRegulations for Coastal British Columbia. Forest Economics and PolicyAnalysis Research Unit Working Paper 177. UBC. Vancouver.Pearse, P.H. 1969. “Toward a theory of multiple use: the case of recreationversus agriculture,” Natural Resources Journal 9(1 0):561 -575.Percy, M.B. 1986. Forest Management and Economic Growth in British Columbia.Supply and Services Canada, Ottawa.Porterfield, R.L. 1976. “A goal programming model to guide and evaluate treeimprovement programs,” Forest Science 22(4):41 7-430.98Price Waterhouse. Forest Products Industry Survey 1988/89/90.Price Waterhouse. 1991. The Forest Industry in Canada.Romesberg, H.C. 1974. Scheduling models for wilderness recreation,” Journalof En vironmen tat Management 2(2): 159-177.Runyon, K.L. 1991. Canada’s Timber Supply: Current Status and Outlook.Information Report E-X-45, Forestry Canada, Ottawa.Schrage, L. 1986. Linear, Integer and Quadratic Programming with LINDO. ThirdEdition. The Scientific Press. Palo Alto, California.Schuler, A., and J.C. Meadows. 1975. “Planning resource use on national foreststo achieve multiple objectives,” Journal of Environmental Management3:351-366.Schuler, A.T., H.H. Webster, and J.C. Meadows. 1977. “Goal programming inforest management,” Journal of Forestry 75(6): 320-324.Schuster, E.G., L.A. Leefers, and J.E. Thompson. 1993. A Guide to Computer-based Analytical Tools for Implementing National Forest Plans. U.S. ForestService General Technical Report INT-296. February 1993.Simon Fraser University. 1990. Wilderness and Forestry: Assessing the Cost ofComprehensive Wilderness Protection in British Columbia. SFU-NRM ReportNo. 6. January 1990. Burnaby, B.C.Sinden, J.A., and A.C. Worrell. 1979. Unpriced Values: Decisions without MarketPrices. John Wiley & Sons, New York.Statistics Canada. 1990. Canadian Forestry Statistics. Statistics Canada 25-202.Steuer, R.E. 1986. Multiple criteria optimization: Theory, computation, andapplication. John Wiley & Sons, New York.Thompson, R.P. 1993. “Compensated takings and negotiated solutions: new hopefor a balanced policy,” Journal of Forestry. 91(4):14-18.University of Oregon. 1982. Old Growth Forests: A Balanced Perspective.Proceedings of Valley River Inn Conference February 12-14, 1982.Published by University of Oregon’s Bureau of Governmental Research andService.99Valhalla Society, The. 1988. British Columbia’s Endangered Wilderness: AProposal for an Adequate System of Totally Protected Lands. The ValhallaSociety. New Denver, B.C.van Kooten, G.C. 1993(a). Land Resource Economics and SustainableDevelopment. UBC Press, Vancouver.van Kooten, G.C. 1993(b). Economics of Protecting Wilderness Areas and Old-growth Timber in British Columbia. Forest Economics and Policy AnalysisResearch Unit Working Paper 189. UBC. Vancouver.Vertinsky, I., S. Brown, H. Schreier, W.A. Thompson, and G.C. van Kooten.1993. An Hierarchical-GIS Based Decision Model for Forest Management:the Systems Approach. Forest Economics and Policy Analysis Research UnitWorking Paper 187. April 1993. UBC. Vancouver.Walter, G.R. 1977. “Economics of multiple-use forestry,” Journal ofEnvironmental Management 5:345-356.Yo uds, J . K. 1989. Protection of Old-growth Forests in British Columbia: AComparison of Statutes, Mandates, and Objectives, prepared for theIntegrated Resources Branch of B.C. Ministry of Forests.100Appendix AQUESTIONNAIREIdentifying Priority Rankings on Old-Growth Uses in British ColumbiaBritish Columbia is one of the few places where substantial areas oftemperate old-growth forests and wilderness still exist. It has been proposed thatsome of the old growth should be protected or preserved along with other areasof wilderness. Government policy is to increase the amount of wilderness areafrom the current 6 percent of the province’s land base to about 12% by the year2000; somewhere between 4% and 10% of the wilderness area to be protectedis actually old-growth forest.At the Forest Economics and Policy Analysis Research Unit at UBC, we areinvestigating both the larger issue of wilderness (old-growth) protection andresolution of forestland use conflicts at the local level -- the Tangier watershedbetween Revelstoke and Glacier National Parks in eastern B.C.In order to help us in these research projects, we would appreciate yourcooperation in completing the following questionnaire. We are attempting simplyto get some idea concerning the importance of various issues that can provideguidance for a mathematical model an M.Sc. student is developing to studyprovince-wide wilderness protection. Your answers will be anonymous and,101hence, confidential.Please rank the following policy items from 1 (most important) to 7 (leastimportant). If you feel two items should be given the same rank, please assignthe same number to them. The rankings will be used to help construct a goalprogramming model for wilderness protection.Item RankMaintain the current level of timber harvest in B.C.Permanently withdraw % (please fill in) of theold growth scheduled for future timber harvestMaintain the maximum sustainable yield in timberharvestSecure regional stability by maintaining the currentlevel of employment in forest industriesMaintain the level of provincial government revenuefrom forest harvestingMaximize the net revenue from all forestland uses,even if that means less timber harvestOther (please specify)102Appendix BSurnlementary DataTable B.1: Land Use in British ColumbiaCategory Area (ha) PercentageForest 43264603 45.6Grazing 8490602 9.0Agriculture 2369226 2.5Recreation 5848628 6.2Settlement 549000 0.6Other 229776 0.2Uncategorized 32221 165 34.0Total land area 92973000 98.1Total water area 1807000 1.9B.C. total area 94780000 100.0Source: British Columbia Land Statistics.B.C. Ministry of Crown Lands. Victoria. 1989.103Table B.2: B.C. Ministry of Forests’ Regulated Land(ha)Region Land area Productive Matureforests standsCariboo 7531982 5949000 3634000Kamloops 5887756 4438000 2446000Nelson 6456748 3448000 1320000Prince George 29571666 17421000 9552000Prince Rupert 23033169 9395000 6396000Vancouver 10564875 4945000 3293000MOF total 83046196 45596000 26641000B.C. total 92973000 49054000 28774200Source: Compendium of Canadian Forestry Statistics 1992;B.C. Ministry of Forests Annual Report 1991-92; andSFU-NRM Report NO.6 Wilderness and Forestry (SFU 1990).104Table 8.3: Quality of Productive Forest Land in British Columbia(ha)Site class Immature Mature Total PercentageTFLGood 180363 253309 433672 10.9Medium 817188 1103545 1920733 48.4Poor 280523 1003608 1284131 32.4Low 53733 275077 328810 8.3Sub-total 1331807 2635539 3967346 100.0TSAGood 968435 1918350 2886785 7.3Medium 5038709 8693931 13732640 35.0Poor 7690895 00990318 19681213 50.1Low 1374213 1609960 2984173 7.6Sub-total 15072252 24212559 39284811 100.0TFL and TSAGood 1148798 2171659 3320457 7.7Medium 5855897 9797476 15653373 36.2Poor 7971418 12993926 20965344 48.5Low 1427946 1885037 3312983 7.6Total 16404059 26848098 43252157 100.0Source: British Columbia Land Statistics. B.C. Ministry ofCrown Lands. Victoria. 1989.105Table B.4: Distribution and Pronortion of Mature Stands in B.C.(ha)Region Mature stands Total productive PercentageCariboo 3634000 5949000 0.61Kamloops 2446000 4438000 0.55Nelson 1320000 3448000 0.38Prince George 9552000 17421000 0.55Prince Rupert 6396000 9395000 0.68Vancouver 3293000 4945000 0.67B.C. total 26641000 45596000 0.58Source: B.C. Ministry of Forests Annual Report 1991-92.106Table B.5: Inventory of Mature Stands by Species and by Region(million m3)Species Coast % Interior % Total %Douglas fir 275.7 9.0 260.0 4.7 535.7 6.2Red cedar 703.0 23.0 172.5 3.1 875.5 10.2Hemlock 1234.6 40.3 583.7 10.6 1818.3 21.2Balsam 497.3 16.2 1130.8 20.4 1628.1 19.0Spruce 146.4 4.8 1625.0 29.4 1771.4 20.6Lodgepole pine 23.3 0.8 1385.6 25.1 1408.9 16.4Other conifers 164.7 5.4 60.3 1.1 225.0 2.6Deciduous 15.9 0.5 309.5 5.6 325.4 3.8Total 3061.1 100.0 5527.4 100.0 8588.5 100.0Source: 1992 British Columbia Economic & Statistical Review.B.C. Ministry of Finance and Corporate Relations. 1993.107Table B.6: Species Composition of Log Production in B.C. - 1991(in percentage)Region Doug. fir Ced/Hem Pines Balsam Spruce OthersCariboo 12.8 1.6 59.8 5.0 19.9 0.9Kamloops 17.3 8.4 41.1 10.2 21.2 1.8Nelson 14.4 18.0 40.6 6.5 15.6 4.9Prince George 2.4 0.4 36.8 10.4 44.6 5.4Prince Rupert 0 30.3 24.6 25.4 18.5 1.2Vancouver 13.4 60.2 0.3 18.0 3.6 4.5Province 9.9 26.8 26.6 13.8 19.3 3.6Source: British Columbia Forest Industry Fact Book 1992. COFI.108Table B.7: Withdrawal of Prime Forest Land into Park Areas in B.C.Year Annual level (ha) Cumulative (ha)1965-85 399900 3999001986 11620 4115201987 74390 4859101988 183 4860931989 2550 4886431990 147010 6356531991 3703 639356Source: Parks and Conservation Areas on Prime Forest Land in B. C.,1965-1985. Environment Canada 1987;B.C. Ministry of Forests Annual Reports 1986-1992.109Table B.8: Regional Variations in Withdrawal of Prime Forest Land into Park Areas(ha)Year Coast Southern Northern TotalInterior Interior1983 0 662 5 6671984 0 14 608 6221985 1 1 3573 35751986 0 11620 0 116201987 0 357 74033 743901988 162 21 0 1831989 1976 529 45 25501990 146680 330 0 1470101991 3662 0 41 3703Source: BC. Ministry of Forests Annual Reports 1983-1992.110Figure 8.1Land Use in British ColumbiaLand Use In British ColumbiaIn HectaresUncategorizedOtherSettlementRecreation______IAgricultureGrazing__Forest( ( ( I I I I0 5 10 15 20 25 30 35 40 45(Millions)Source: British Columbia Land Statistics. B.C. Ministry of Crown Lands.Victoria. 1989.111Figure B.2:Old Growth Preserved as Wilderness - Cumulative Area in B.C.Old Growth Preserved As WildernessCumulative Area in B.C.650600......-.__.--.....(6(6-------.450--_... ...400.I I I I I I1985 1986 1987 1988 1989 1990 1991PeriodSource: Environment Canada 1987. “Parks and Conservation Areas onPrime Forest Land in B.C., 1965-1985’ andB.C. Ministry of Forests Annual Reports 1986-1 992.112Appendix CThe GAMS Command File for the Goal Programming ModelThis command file is compiled for the GP model concerning the multiple uses ofthe old-growth forests in British Columbia. The objective is to minimize deviationsfrom specified goal targets subject to predetermined constraints. In the work file,every equation stands on its own to allow sequential treatment. The goal itemsfollow the original ordering based on the results of a survey.SETSJ Harvesting/X1 CaribooX2 KamloopsX3 NelsonX4 Prince GeorgeX5 Prince RupertX6 Vancouver!K Withdrawal/Q1 CaribooQ2 KamloopsQ3 NelsonQ4 Prince GeorgeQ5 Prince RupertQ6 Vancouver!L Deviation!D1 NEGDEV1D2 NEGDEV2D3 NEGDEV3D4 NEGDEV4D5 NEGDEV5D6 NEGDEV6D7 POSDEV1D8 POSDEV2D9 POSDEV3D1O POSDEV4Dli POSDEV5D12 POSDEV6II Inputs all goals/INP1 benefitsINP2 wildernessINP3 employment113INP4 stumpageINP5 newAACINP6 oIdAAC/Ii first input /INP1/12 second input /INP2/13 third input /INP3/14 fourth input /INP4/15 fifth input /INP5/16 sixth input /INP6/H Resource by region/RES1 CaribooRES2 KamloopsRES3 NelsonRES4 Prince GeorgeRES5 Prince RupertRES6 Vancouver!Parameter P(L) Objective function coefficients/D11D21D31D41D51D61D70D80D90D1O 0DillD12 1!;Parameter B(I) Requirements of inputs!INP1 1244000000INP2 650459INP3 77600INP4 408730000INP5 58943000INP6 73330000/;Parameter B1(I1) Requirements of first input/INP1 1244000000/;Parameter B2(12) Requirements of second input/INP2 650459/;Parameter B3(13) Requirements of third input/INP3 77600!;Parameter B4(14) Requirements of fourth input!INP4 408730000/;114Parameter B5(15) Requirements of fifth input/INP5 58943000/;Parameter B6(16) Requirements of sixth inputIINP6 73330000/;Table A(l,J) Rate of inputs per harvesting activityX1X2X3X4 X5 X6INP1 5002 6905 8106 5778 14080 22803INP2INP3 0.25 0.26 0.30 0.28 0.35 0.75INP4 1198 1569 1458 2331 1748 6994INP5 243 256 297 273 342 737INP6 243 256 297 273 342 737;Table A1(l1,J) Rate of first input per activityX1X2X3X4 X5 X6INP1 5002 6905 8106 5778 14080 22803;Table A2(12,J) Rate of first two inputs per activityX1X2X3X4 X5 X6INP2Table A3(13,J) Rate of first three inputs per activityX1X2X3X4 X5 X6INP3 0.25 0.26 0.30 0.28 0.35 0.75;Table A4(14,J) Rate of first four inputs per activityX1X2X3X4 X5 X6INP4 1198 1569 1458 2331 1748 6994;Table A5(15,J) Rate of first five inputs per activityX1X2X3X4 X5 X6INP5 243 256 297 273 342 737;Table A6(16,J) Rate of all six inputs per activityX1X2X3X4 X5 X6INP6 243 256 297 273 342 737;Table C(I,K) Rate of inputs per wilderness activity01 02 03 04 05 06INP1 312 915 1641 247 429 4304INP2 1 1 1 1 1 1INP3INP4INP5INP6Table C1(l1,K) Rate of first input per activity01 02 03 04 05 06INP1 312 915 1641 247 429 4304;Table C2(12,K) Rate of first two inputs per activity01 02 03 04 05 06INP2 1 1 1 1 1 1;115Table C3(l3,K) Rate of first three inputs per activity01 02 03 04 05 06INP3Table C4(14,K) Rate of first four inputs per activity01 Q2 03 04 05 06INP4Table C5(15,K) Rate of first five inputs per activity01 02 03 04 Q5 06INP5Table C6(l6,K) Rate of all six inputs per activity01 02 03 04 05 06INP6Table E(l,L) DeviationDl D2 D3 D4 D5 D6 D7 D8 D9 DlO Dli D12INP1 1INP2 1INP3 1INP4 1INP5 1 -1INP6 1 -1;Table Ei(ll,L)Dl D2 D3 D4 D5 D6 D7 D8 D9 D1O Dli D12INP1 1Table E2(l2,L)Dl D2 D3 D4 D5 D6 D7 D8 D9 D1O Dli D12INP2 1Table E3(l3,L)Dl D2 D3 D4 D5 D6 D7 D8 D9 D1O Dli D12INP3 1Table E4(l4,L)Dl D2 D3 D4 D5 D6 D7 D8 D9 D1O Dli D12INP4 1Table E5(15,L)Dl D2 D3 D4 D5 D6 D7 D8 D9 DlO Dli D12INP5 1 -1;Table E6(l6,L)Dl D2 D3 D4 D5 D6 D7 D8 D9 DiO Dii D12INP6 1 -1;Parameter N(H) Physical constraints/RES1 8560000RES2 8140000RES3 6100000RES4 17770000RES5 9440000116RES6 23320000/;Parameter NP(H) New physical constraints/RES1 8112077RES2 7966026RES3 5845689RES4 17430697RES5 9040954RES6 22351014/Table F(H,J) Technical coefficients of constraints per activityX1X2X3X4 X5 X6RES1 243RES2 256RES3 297RES4 273RES5 342RES6 737;Table G(H,K) Technical coefficients of constraints per activityQi Q2 Q3 Q4 Q5 Q6RES1 4.08RES2 3.61RES3 5.14RES4 2.17RES5 2.76RES6 6.69;VariablesZ Total deviationsX(J) Harvesting levelsQ(K) Wilderness levelsD(L) DeviationsPositive variables X, Q, DEquationsTOD objective functionGOAL1(l1) first goalGOAL11(l1) altered first goalGOAL2(l2) second goalGOAL21 (12) altered second goalGOAL3(13) third goalGOAL4(l4) fourth goalGOAL5(15) fifth goalGOAL6(16) sixth goalCONS1 (H) physical constraints with variable Q valuesCONS2(H) physical constraints with fixed Q values;TOD.. SUM(L,D(L)*P(L)) =E= Z;GOAL1 (Ii ).. SUM(J,X(J)*A1 (Ii ,J)) + SUM(K,Q(K)*C1 (Ii ,K))117+SUM(L,D(L)*E1 (Ii ,L)) =G = Bi (Ii)GOAL1 1(11).. SUM(J,X(J)*A1 (Ii ,J)) +SUM(K,Q.L(K)*C1 (Ii ,K))+SUM(L,D(L)*E1(I1,L)) =G= B1(I1)GOAL2(l2).. SUM(J,X(J)*A2(12,J)) + SUM(K,Q(K)*C2(12,K))+SUM(L,D(L)*E2(12,L)) =E= B2(12)GOAL21 (12).. SUM(J,X(J)*A2(12,J)) + SUM(K,Q.L(K)*C2(12,K))+SUM(L,D(L)*E2(12,L)) =E= B2(12)GOAL3(13).. SUM(J,X(J) *A3(l3,J)) + SUM(K,Q.L(K) *C3(13,K))+SUM(L,D(L)*E3(13,L)) =G= B3(13)GOAL4(14).. SUM(J,X(J)*A4(l4,J)) + SUM(K,Q.L(K)*C4(14,K))+ SUM(L,D(L)*E4(l4,L))= G = B4(14);GOAL5(15).. SUM(J,X(J)*A5(l5,J)) + SUM(K,Q.L(K)*C5(15,K))+SUM(L,D(L)*E5(l5,L)) =E= B5(15)GOAL6(16).. SUM(J,X(J)*A6(16,J)) + SUM(K,Q.L(K)*C6(16,K))+SUM(L,D(L)*E6(16,L)) =E= B6(16)CONS1 (H).. SUM(J,X(J)*F(H,J)) + SUM(K,Q(K)*G(H,K)) = E = N(H);CONS2(H).. SUM(J,X(J)*F(H,J)) =E= NP(H);QL(”Q1”) = 109866;Q L(”Q2”)— 47965;Q L(”Q3”) — 49249;Q L(”04”) — 155217;Q L(”Q5”) = 142852;Q.L(”Q6”) = 145310;Model GP1 lstgoal /TOD, GOAL1, CONS1/Solve GP1 using LP minimizing ZModel GP2 2ndgoal /TOD, GOAL2, GOAL1, CONS1/;Solve GP2 using LP minimizing ZModel GP3 3rdgoal /TOD, GOAL3, GOAL21, GOAL11, CONS2/;Solve GP3 using LP minimizing ZModel GP4 4thgoal /TOD,GOAL4,GOAL3,GOAL21 ,GOAL1 1 ,CONS2I;Solve GP4 using LP minimizing ZModel GP5 5thgoal /TOD,GOAL5,GOAL4,GOAL3,GOAL21 ,GOAL1 1 ,CONS2I;Solve GP5 using LP minimizing ZModel GP6 6thgoal/TOD,GOAL6,GOAL5,GOAL4,GOAL3,GOAL21,GOAL 11 ,CONS2/Solve GP6 using LP minimizing Z


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