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

Universidade de Lisboa, Faculdade de Ciências, DEIO/Centro de Investigação Operacional, Bloco C6, piso 4, Cidade Universitária,1749-016 Lisboa, Portugal
Universidade Técnica de Lisboa, Instituto Superior de Agronomia/Centro de Investigação Operacional, Tapada da Ajuda, 1349-017 Lisboa, Portugal
Universidade Técnica de Lisboa, Instituto Superior de Agronomia/Centro de Estudos Florestais, Tapada da Ajuda, 1349-017 Lisboa, Portugal
miguel.constantino{at}fc.ul.pt
isabelinha{at}isa.utl.pt
joseborges{at}isa.utl.pt

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.

Subject classifications: forest management; harvest scheduling; spatial modeling; integer programming.
History: Received February 2006; revision received May 2007; accepted May 2007.