Finding the Efficient Frontier of a Bi-Criteria, Spatially Explicit, Harvest Scheduling Problem

This article evaluates the performance of five traditional methods and one new method of generating the efficient frontier for a bi-criteria, spatially explicit harvest scheduling problem. The problem is to find all possible efficient solutions, thus defining the trade-offs between two objectives: (1) maximizing the net present value of the forest and (2) maximizing the minimum area over the planning horizon in large, mature forest patches. The methods for generating the efficient frontier were tested using a hypothetical forest consisting of 50 stands. The methods were compared based on the number of efficient solutions each method can identify and on how quickly the solutions were identified. The potential to generalize these algorithms to 3- or n-criteria cases is also assessed. Three of the traditional approaches, the - constraining; the triangles method, the decomposition algorithm based on the Tchebycheff metric; and the new, proposed method are capable of generating all or most of the efficient solutions. However, the triangles and the new method far outperformed the other approaches in terms of solution time. The new method, called alpha-delta, appears to be the simplest to generalize to the tri-criteria case. FOR .S CI. 52(1):93-107.

[1]  Alan T. Murray Spatial restrictions in harvest scheduling , 1999 .

[2]  H. Moskowitz,et al.  Algorithms for nonlinear integer bicriterion problems , 1989 .

[3]  P. Arp,et al.  Planning with Goal Programming: A Case Study for Multiple-Use of Forested Land , 1982 .

[4]  C. Revelle,et al.  Dynamic Selection of Harvests with Adjacency Restrictions: The SHARe Model , 1997 .

[5]  Sowmyanarayanan Sadagopan,et al.  Interactive solution of bi‐criteria mathematical programs , 1982 .

[6]  A. M. Geoffrion Proper efficiency and the theory of vector maximization , 1968 .

[7]  V. Bowman On the Relationship of the Tchebycheff Norm and the Efficient Frontier of Multiple-Criteria Objectives , 1976 .

[8]  E. Gunn,et al.  A model and Tabu search method to optimize stand harvest and road construction schedules , 2000 .

[9]  Alan T. Murray,et al.  Analyzing Cliques for Imposing Adjacency Restrictions in Forest Models , 1996, Forest Science.

[10]  J. P. Roise,et al.  Red-Cockaded Woodpecker Habitat and Timber Management Production Possibilities , 1990 .

[11]  G. Mendoza Goal programming formulations and extensions: an overview and analysis , 1987 .

[12]  Marc E. McDill,et al.  Using the branch and bound algorithm to solve forest planning problems with adjacency constraints , 2001 .

[13]  L. Lasdon,et al.  On a bicriterion formation of the problems of integrated system identification and system optimization , 1971 .

[14]  Richard L. Church,et al.  Understanding the tradeoffs between site quality and species presence in reserve site selection. , 2000 .

[15]  Harold E. Burkhart,et al.  A Linear Programming Model for Multiple-use Planning , 1975 .

[16]  Justin C. Williams,et al.  Delineating protected wildlife corridors with multi‐objective programming , 1998 .

[17]  B. Bruce Bare,et al.  Resolving multiple goal conflicts with interactive goal programming , 1987 .

[18]  Jerry F. Franklin,et al.  Creating landscape patterns by forest cutting: Ecological consequences and principles , 1987, Landscape Ecology.

[19]  L. Joyce,et al.  A mixed integer linear programming approach for spatially optimizing wildlife and timber in managed forest ecosystems , 1993 .

[20]  G. Nemhauser,et al.  Integer Programming , 2020 .

[21]  Richard C. Field,et al.  Complementary linear and goal programming procedures for timber harvest scheduling. , 1980 .

[22]  Richard E. Wendell,et al.  Efficiency in multiple objective optimization problems , 1977, Math. Program..

[23]  T. Pukkala Multi-objective Forest Planning , 2002, Managing Forest Ecosystems.

[24]  Dietmar W. Rose,et al.  A methodology for estimating production possibility frontiers for wildlife habitat and timber value at the landscape level , 1996 .

[25]  Charles ReVelle,et al.  The grid packing problem : selecting a harvesting pattern in an area with forbidden regions , 1996 .

[26]  Jean-Charles Billaut,et al.  Multicriteria scheduling , 2005, Eur. J. Oper. Res..

[27]  L. S. Davis,et al.  Integrated forest planning across multiple ownerships and decision makers , 1991 .

[28]  Charles B. Moss,et al.  Reply: Ecosystem management or infeasible guidelines? Implications of adjacency restrictions for wildlife habitat and timber production , 1997 .

[29]  Eric S. Cox,et al.  Harvest scheduling with spatial wildlife constraints: An empirical examination of tradeoffs , 1995 .

[30]  Ralph E. Steuer Multiple criteria optimization , 1986 .

[31]  John Sessions,et al.  Using Tabu search to schedule timber harvests subject to spatial wildlife goals for big game , 1997 .

[32]  Charles ReVelle,et al.  Multiobjective grid packing model: An application in forest management , 1997 .

[33]  Charles ReVelle,et al.  Temporal and spatial harvesting of irregular systems of parcels , 1996 .

[34]  Richard L. Church,et al.  Reserve selection as a maximal covering location problem , 1996 .

[35]  Bernard G. Halterman,et al.  Integrating timber and wildlife management planning , 1973 .

[36]  C. Revelle Facility siting and integer-friendly programming , 1993 .

[37]  Marc E. McDill,et al.  Can mature patch constraints mitigate the fragmenting effects of harvest opening size restrictions , 2003 .

[38]  James E. Hotvedt,et al.  Application of Linear Goal Programming to Forest Harvest Scheduling , 1983, Journal of Agricultural and Applied Economics.

[39]  J. Keith Gilless,et al.  Economic trade-offs of managing forests for timber production and vegetative diversity , 1994 .

[40]  Marc E. McDill,et al.  A mixed-integer formulation of the minimum patch size problem , 2003 .

[41]  Alan T. Murray Ecosystem management or infeasible guidelines? Implications of adjacency restrictions for wildlife habitat and timber production , 1998 .

[42]  J. Cohon,et al.  Generating multiobjective trade-offs: an algorithm for bicriterion problems , 1979 .

[43]  S. Deming Multiple-criteria optimization , 1991 .

[44]  Carolyn Harrison,et al.  The Archipelago Approach to Conservation: Inspiring but Unproven@@@The Fragmented Forest: Island Biogeography Theory and the Preservation of Biotic Diversity. , 1984 .

[45]  Marc E. McDill,et al.  Harvest Scheduling with Area-Based Adjacency Constraints , 2002, Forest Science.

[46]  D. J. Elzinga,et al.  An algorithm for the bi-criterion integer programming problem , 1986 .

[47]  J. G. Jones,et al.  Formulating adjacency constraints in linear optimization models for scheduling projects in tactical planning , 1991 .

[48]  Alan T. Murray,et al.  Constructing And Selecting Adjacency Constraints , 1996 .

[49]  C. Kao,et al.  Goal programming for reconciling economic, even-flow, and regulation objectives in forest harvest scheduling , 1979 .