• Annika Kangas
  • Mikko Kurttila
  • Teppo Hujala
  • Kyle Eyvindson
  • Jyrki Kangas
Part of the Managing Forest Ecosystems book series (MAFE, volume 30)


Linear programming is the most widely utilised optimisation method in forestry. Linear programming can be used to deal with many sustainability issues, such as the requirement of even flow of timber over time. It can also be used to deal with multiple goals, by using a constraint approach and Pareto front or by using a goal programming approach. Integer or mixed integer programming can also be used to deal with many spatial goals and constraints, like adjacency and green-up constraints or those of clustering timber harvests. In this chapter, we present different formulations of linear programming and their effect on the resulting harvest schedule with numerical examples. We also present different formulations of goal programming and the interpretation of the results in different cases. Furthermore, we present some more complicated planning cases involving hierarchical and spatial planning.


Harvest scheduling Production possibility frontier Even-flow constraints Shadow prices Goal constraints Weighted deviations from target Maximum deviation from target Adjacency constraints Top-down planning Bottom-up planning 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Annika Kangas
    • 1
  • Mikko Kurttila
    • 2
  • Teppo Hujala
    • 3
  • Kyle Eyvindson
    • 4
  • Jyrki Kangas
    • 5
  1. 1.Economics and SocietyNatural Resources Institute Finland (Luke)JoensuuFinland
  2. 2.Bio-based Business and IndustryNatural Resources Institute Finland (Luke)JoensuuFinland
  3. 3.Bio-based Business and IndustryNatural Resources Institute Finland (Luke)HelsinkiFinland
  4. 4.Department of Forest SciencesUniversity of HelsinkiHelsinkiFinland
  5. 5.School of Forest SciencesUniversity of Eastern FinlandJoensuuFinland

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