A New Mixed-Integer Programming Model for Harvest Scheduling Subject to Maximum Area Restrictions

• Published in: Operations research Vol. 56; no. 3; pp. 542 - 551
• Main Authors: Constantino, Miguel, Martins, Isabel, Borges, Jose G
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.05.2008; Institute for Operations Research and the Management Sciences
• Subjects: Analysis; Applied sciences; Biological and medical sciences; Branch & bound algorithms; Exact sciences and technology; Forest ecosystems; Forest management; Forest management. Stand types and stand dynamics. Silvicultural treatments. Tending of stands. Natural regeneration; Forest stands; Forestry; Fundamental and applied biological sciences. Psychology; Harvest; harvest scheduling; Harvesting; Heuristics; Integer programming; Landscaping; Mathematical programming; Old growth forests; Operational research and scientific management; Operational research. Management science; Programming models; Scheduling; Scheduling algorithms; Scheduling, sequencing; spatial modeling; Studies; Timber; Timber production; Portugal; Forests; spatial modeling; Branch and bound method; Harvesting; Constraint satisfaction; Forest management; Mixed integer programming; Scheduling; Economic sciences; Modeling; Integer programming; Computation time; Ecosystem; Planning; Polygon; harvest scheduling
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1070.0472

Forest ecosystem management often requires spatially explicit planning because the spatial arrangement of harvests has become a critical economic and environmental concern. Recent research on exact methods has addressed both the design and the solution of forest management problems with constraints on the clearcut size, but where simultaneously harvesting two adjacent stands in the same period does not necessarily exceed the maximum opening size. Two main integer programming approaches have been proposed for this area restriction model. However, both encompass an exponential number of variables or constraints. In this work, we present a new integer programming model with a polynomial number of variables and constraints. Branch and bound is used to solve it. The model was tested with both real and hypothetical forests ranging from 45 to 1,363 polygons. Results show that the proposed model's solutions were within or slightly above 1% of the optimal solution and were obtained in a short computation time.