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, Volume 22, Issue 1, pp 343–362 | Cite as

Modeling target volume flows in forest harvest scheduling subject to maximum area restrictions

  • Isabel Martins
  • Mujing Ye
  • Miguel Constantino
  • Maria da Conceição Fonseca
  • Jorge Cadima
Original Paper

Abstract

In forest harvest scheduling problems, one must decide which stands to harvest in each period during a planning horizon. A typical requirement in these problems is a steady flow of harvested timber, mainly to ensure that the industry is able to continue operating with similar levels of machine and labor utilizations. The integer programming approaches described use the so-called volume constraints to impose such a steady yield. These constraints do not directly impose a limit on the global deviation of the volume harvested over the planning horizon or use pre-defined target harvest levels. Addressing volume constraints generally increases the difficulty of solving the integer programming formulations, in particular those proposed for the area restriction model approach. In this paper, we present a new type of volume constraint as well as a multi-objective programming approach to achieve an even flow of timber. We compare the main basic approaches from a computational perspective. The new volume constraints seem to more explicitly control the global deviation of the harvested volume, while the multi-objective approach tends to provide the best profits for a given dispersion of the timber flow. Neither approach substantially changed the computational times involved.

Keywords

Forest harvest scheduling Area restriction model Volume constraint Integer programming Multi-objective programming 

Mathematics Subject Classification

90B50 90C10 

Notes

Acknowledgements

This research was partially supported by Centro de Investigação Operacional (through the project POCTI/ISGL/152) and Centro de Estatística e Aplicações from Universidade de Lisboa. We wish to thank Andres Weintraub and José G. Borges (through the project PTDC/AGR-CFL/64146/2006) for providing some real test forest data.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2012

Authors and Affiliations

  • Isabel Martins
    • 1
  • Mujing Ye
    • 2
  • Miguel Constantino
    • 3
  • Maria da Conceição Fonseca
    • 3
  • Jorge Cadima
    • 1
  1. 1.Departamento de Ciências e Engenharia de BiosistemasInstituto Superior de AgronomiaLisboaPortugal
  2. 2.Northwestern UniversityEvanstonUSA
  3. 3.Departamento de Estatística e Investigação Operacional, Faculdade de Ciências de LisboaCentro de Investigação OperacionalLisboaPortugal

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