Combining a Decomposition Strategy with Dynamic Program. ming toSolve Spatially Constrained Forest Management Scheduling Problems Jos6 G. Borges, Howard M. Hoganson, and Dietmar W. Rose ABSTRACT. A decomposition approach to solve the forest management scheduling adjacency problem is developedfor applicationto large forests. Overlapping subproblemsamenable to exact dynamic programming solution are solved sequentially. A heuristic is used to define and link subproblems such that near-optimal solutions to the master problem are obtained. Both the contrasting size and the irregular shape of stands complicate the problem of formulating the dynamic programming network. Subproblem size and the sequencing of stands for each corresponding dynamic programming network are defined simultaneously, as model size is especially sensitive to stand sequencing.Emphasis is on efficient dynamicprogramming formulations to allow for large subprob- lems. Results from over 100 test computer runs are discussed for applicationsto 3 large problems. Results suggest that the strategy can consistently produce near-optimalsolutions at reasonable computationalcost. A procedureis developedto derive three slightlydifferent adjacencyproblems so that the optimal solutioncan be found. Results for applications to the modified problemsshow that the proposed heuristic's solutions were within 0.01, 0.04, and 0.01% of the optimal solution, respectively. The proposed solutionmethodconsistently outperformed two other heuristics that were applied. FOR. Scl. 45(1):201-212. Additional Key Words: Forest management, harvest scheduling, adjacency constraints, spatial analysis. ESEARCH ON QUANTITATIVE MODELING of forest man- agement has traditionally focused onthetemporal arrangement of harvests. The spatial arrangement of harvests has, however, become a critical environmental concern.Accordingly, spatial resolutionhas becomean important issuein forest management modeling. Stands are often aggregated into analysis areas, and spatial reso- lution is lost. Heuristic techniquesto addressharvest scheduling basedon the decomposition of a linear pro- gramming(LP) masterproblem suchas the onesdcv½l- oped by Hoganson and Rose (1984), Gunn and Rai (1987), and Lappi (1992) avoid that aggregation and have the ability to recognize considerable detail within a strategic planning framework. Nevertheless, in addition to theabil- ity to recognize individual stands in theoutput of a harvest scheduling model, managers musttake into account the interactions of management decisions between neighbor- ing stands. The spatial conditions generated by a model (e.g., amountand type of forest edge and interior space) become an additional forest output. Jos6G. Borges is Assistant Professor in the Departamento de Engenhada Rorestal, Instituto Superior de Agronomia, Tapadada Ajuda 1399 Lisboa Codex, Portugal--Phone: 351 13602086; Fax: 351 13645000; E-mail: joseborges@isa.utl.pt. Howard M. Hoganson is Associate Professor in the Department of Forest Resoumes, University of Minnesota, andis located at the North Central Experiment Station, 1861 Highway East, Grand Rapids, MN 55744 (hoganOO1•tc.umn,edu). DietmarW. Rose is Professor in the Department of ForestResoumes at the University of Minnesota,1530 North ClevelandAvenue, St. Paul, MN 55108 (drose•forestry.umn.edu). Acknowledgments: Partial support forthis research was provided by JuntaNacional de Investiga•;õo Cientifica e Tecno16gica (PBIC/AGR/2334/95), InstitutoNacional de Investiga•;fio Agrfiria (PAMAF 4043 and 8189) and Funda•;fio Luso-Amedcana para o Desenvolvimento. ManuscriptreceivedNovember26, 1997. Accepted November20, 1998. Copyright ¸ 1999 by the Society of Amedcan Foresters Forest Sctence 45(2) 1999 201