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A note on the regularity of a new metric for measuring even-flow in forest planning

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  • González-González, José M.
  • Vázquez-Méndez, Miguel E.
  • Diéguez-Aranda, Ulises

Abstract

In this work we deal with the mathematical analysis of a new metric for measuring even-flow in even-aged forest management planning. We begin writing the most used way of measuring even-flow, and showing the main disadvantages of this classical procedure. Next, we introduce the new metric and study the regularity of the corresponding function, which results to be continuous and to have continuous derivatives in almost all points. We give an explicit expression for these derivatives and analyze its usefulness by comparing a gradient-type method with a derivative-free algorithm (widely used in forestry) to maximize even-flow in a forest of 51 Eucalyptus globulus Labill. stands in Galicia (NW Spain). We observe that gradient-type methods work well with the new even-flow metric, which enables this type of methods for solving the multi-objective problems that can be formulated in forest planning.

Suggested Citation

  • González-González, José M. & Vázquez-Méndez, Miguel E. & Diéguez-Aranda, Ulises, 2020. "A note on the regularity of a new metric for measuring even-flow in forest planning," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1101-1106.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:3:p:1101-1106
    DOI: 10.1016/j.ejor.2019.10.029
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    References listed on IDEAS

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    1. Brumelle, Shelby & Granot, Daniel & Halme, Merja & Vertinsky, Ilan, 1998. "A tabu search algorithm for finding good forest harvest schedules satisfying green-up constraints," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 408-424, April.
    2. Álvarez-Miranda, Eduardo & Garcia-Gonzalo, Jordi & Ulloa-Fierro, Felipe & Weintraub, Andrés & Barreiro, Susana, 2018. "A multicriteria optimization model for sustainable forest management under climate change uncertainty: An application in Portugal," European Journal of Operational Research, Elsevier, vol. 269(1), pages 79-98.
    3. Constantino, Miguel & Martins, Isabel, 2018. "Branch-and-cut for the forest harvest scheduling subject to clearcut and core area constraints," European Journal of Operational Research, Elsevier, vol. 265(2), pages 723-734.
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