A Strengthening Procedure for the Path Formulation of the Area-Based Adjacency Problem in Harvest Scheduling Models
キーワード:
Spatially-explicit harvest scheduling、 area-based adjacency、 integer programming要旨
Spatially-explicit harvest scheduling models optimize the spatiotemporal layout of forest management actions to best meet management objectives such as profit maximization, even flow of products, or wildlife habitat preservation while satisfying a variety of constraints. This investigation focuses on modeling maximum harvest opening size restrictions whose role is to limit the size of contiguous clear cuts on a forested landscape. These restrictions, a.k.a. green-up constraints, allow adjacent forest stands to be cut within a pre-specified timeframe, called green-up period, only if their combined area does not exceed a limit. We present a strengthening procedure for one of the existing integer programming formulations of this so-called Area Restriction Model and test the computational performance of the new model on sixty hypothetical and seven real forest planning applications. The results suggest that the strengthened model can often outperform the other three existing formulations. We also find that the original Path Model is still competitive in terms of solution times.
参考文献
Barrett, T. M., J. K. Gilles, and L. S. Davis. 1998. Economic and fragmentation effects of clearcut restrictions. For. Sci. 44: 569-577.
Borges, J. G., and H. M. Hoganson. 2000. Structuring a landscape by forestland classification and harvest scheduling spatial constraints. For. Ecol. Manage. 130: 269-275.
Boston, K., and P. Bettinger. 2002. Combining tabu search and genetic algorithm heuristic techniques to solve spatial harvest scheduling problems. For. Sci. 48(1): 35-46.
Caro, F., M. Constantino, I. Martins, and A. Weintraub. 2003. A 2-opt tabu search procedure for the multiperiod forest harvesting problem with adjacency, greenup, old growth, and even flow constraints. For. Sci. 49(5): 738-751.
Carter, D. R., M. Vogiatzis, C. B. Moss, and L. G. Arvanitis. 1997. Ecosystem management or infeasible guidelines? Implications of adjacency restrictions for wildlife habitat and timber production. Can. J. For. Res. 27: 1302-1310.
Constantino, M., I. Martins, and J.G. Borges. 2008. A New Mixed-Integer Programming Model for Harvest Scheduling Subject to Maximum Area Restrictions. Oper. Res. 56(3): 542-551.
Crowe, K., J. Nelson, and M. Boyland. 2003. Solving the area-restricted harvest-scheduling model using the branch and bound algorithm. Can. J. For. Res. 33: 1804-1814.
Floyd, Robert W. (June 1962). Algorithm 97: Shortest Path. Communications of the ACM 5 (6): 345.
Franklin, J. F., and R. T. Forman. 1987. Creating landscape patterns by forest cutting: Ecological consequences and principles. Land. Ecol. 1: 5-18.
Goycoolea, M., A.T. Murray, J.P. Vielma, and A. Weintraub. 2009. Evaluating Approaches for Solving the Area Restriction Model in Harvest Scheduling. For. Sci. 55(2): 149-165.
Goycoolea, M., A. T. Murray, F. Barahona, R. Epstein, and A. Weintraub. 2005. Harvest scheduling subject to maximum area restrictions: exploring exact approaches. Oper. Res. 53(3): 490-500.
Gunn, E. A., and E. W. Richards. 2005. Solving the adjacency problem with stand-centered constraints. Can. J. For. Res. 35: 832-842.
Harris, L. D. 1984. The fragmented forest: Island biogeography theory and the preservation of biotic diversity. The University of Chicago Press. Chicago, IL. 211 p.
IBM ILOG Inc. 2009. CPLEX 12.1 Reference Manual. IBM ILOG Documentation.
Jones, J. G., B. J. Meneghin, and M. W. Kirby. 1991. Formulating adjacency constraints in linear optimization models for scheduling projects in tactical planning. For. Sci. 37(5): 1283-1297.
Lockwood, C., and T. Moore. 1993. Harvest scheduling with spatial constraints: a simulated annealing approach. Can. J. For. Res. 23: 468-478.
McDill, M.E., and J. Braze. 2000. Comparing adjacency constraint formulations for randomly generated forest planning problems with four age-class distributions. For. Sci. 46(3): 423-436.
McDill, M. E., S. Rebain, and J. Braze. 2002. Harvest scheduling with area-based adjacency constraints. For. Sci. 48(4): 631-642.
Meneghin, B. J., M. W. Kirby, and J. G. Jones. 1988. An algorithm for writing adjacency constraints efficiently in linear programming models. The 1988 Symposium on Systems Analysis in Forest Resources, USDA Forest Service.
Martins, I., F. Alvelos, and M. Constantino. 2011. A branch-and-price approach for harvest scheduling subject to maximum area restrictions. Comput. Optim. Appl. DOI: 10.1007/s10589-010-9347-1.
Murray, A. T. 1999. Spatial restrictions in harvest scheduling. For. Sci. 45(1): 45-52.
Murray, A. T., and R. L. Church. 1996b. Constructing and selecting adjacency constraints. INFOR 34(3): 232-248.
Murray, A. T., and R. L. Church. 1996a. Analyzing cliques for imposing adjacency restrictions in forest models. For. Sci. 42(2): 166-175.
Rebain, S., and M. E. McDill. 2003a. Can mature patch constraints mitigate the fragmenting effect of harvest opening size restrictions? Int. Trans. Oper. Res. 10(5): 499-513.
Rebain, S., and M. E. McDill. 2003b. A mixed-integer formulation of the minimum patch size problem. For. Sci. 49(4): 608-618.
Richards, E. W., and E. A. Gunn. 2003. Tabu search design for difficult forest management optimization problems. Can. J. For. Res. 33: 1126-1133.
Roy, B. 1959. Transitivité et connexité. C.R. Acad. Sci. Paris 249: 216-218.
Snyder, S., and C. ReVelle. 1996a. Temporal and spatial harvesting of irregular systems of parcels. Can. J. For. Res. 26: 1079-1088.
Snyder, S., and C. ReVelle. 1996b. The grid packing problem: Selecting a harvest pattern in an area with forbidden regions. For. Sci. 42(1): 27-34.
Snyder, S., and C. ReVelle. 1997a. Multiobjective grid packing model: an application in forest management. Loc. Sci. 5(3): 165-180.
Snyder, S., and C. ReVelle. 1997b. Dynamic selection of harvests with adjacency restrictions: The SHARe Model. For. Sci. 43(2): 213-222.
Sustainable Forest Initiative, 2010. Requirements for the Sustainable Forest Initiative 2010-2014 Program: Standards, Rules for Label Use, Procedures and Guidance. January 2010. URL: http://www.sfiprogram.org/files/pdf/s_requirements_2010-2014.pdf (last accessed: 11/28/2011).
Thompson, E. F., B. G. Halterman, T. J. Lyon, and R. L. Miller. 1973. Integrating timber and wildlife management planning. The Forestry Chronicle: 247-250.
Thompson, W., M. Halme, S. Brown, I. Vertinsky, and H. Schreier. 1994. Timber harvest scheduling subject to wildlife and adjacency constraints. Symposium on Systems Analysis in Forest Resources - Management Systems for a Global Economy with Global Resource Concerns, Pacific Grove, CA, Society of American Foresters.
Warshall, S. 1962. A theorem on Boolean matrices. Journal of the ACM 9(1): 11-12.
Wolsey, L. A. 1998. Integer programming. J. Wiley. New York. xviii, 264 p.
ダウンロード
発行日
巻号
セクション
ライセンス
Authors who publish with this journal agree to the following terms:- Authors grant the journal right of first publication, with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) following the publication by the journal, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
