A fractional stochastic integer programming problem for reliability-to-stability ratio in forest harvesting
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We propose a new fractional stochastic integer programming model for forestry revenue management. The model takes into account the main sources of uncertainties—wood prices and tree growth—and maximizes a reliability-to-stability revenue ratio that reflects two major goals pursued by forest owners. The model includes a joint chance constraint with multirow random technology matrix to account for reliability and a joint integrated chance constraint to account for stability. We propose a reformulation framework to obtain an equivalent mixed-integer linear programming formulation amenable to a numerical solution. We use a Boolean modeling framework to reformulate the chance constraint and a series of linearization techniques to handle the nonlinearities due to the joint integrated chance constraint, the fractional objective function, and the bilinear terms. The computational study attests that the reformulation of the model can handle large number of scenarios and can be solved efficiently for sizable forest harvesting problems.
KeywordsStochastic programming Joint probabilistic constraint Integrated chance constraint Forestry management Fractional programming
We are grateful to Mikko Kurttila and the Finnish Forest Research Institute for providing the data used in this paper and for providing insightful suggestions about the models and the analysis of their results. M. Lejeune was partially supported by the Office of Naval Research, Grant #N000141712420.
- Boros E, Hammer PL, Ibaraki T, Kogan A (1997) Logical analysis of numerical data. Math Program 79(1–3):163–190Google Scholar
- Bullard SH (2001) How to evaluate the financial maturity of timber. For Landowner 60(3):36–38Google Scholar
- Eyvindson KJ, Petty AD, Kangas AS (2017) Determining the appropriate timing of the next forest inventory: incorporating forest owner risk preferences and the uncertainty of forest data quality. Ann For Sci 74(2):1–10Google Scholar
- Favada IM, Karppinen H, Kuuluvainen J, Mikkola J, Stavness C (2009) Effects of timber prices, ownership objectives, and owner characteristics on timber supply. For Sci 55(6):512–523Google Scholar
- Food and Agriculture Organization of the United Nations (2014) Trends and status of forest products and services. http://www.fao.org/docrep/w4345e/w4345e05.htm. Accessed 26 Sept (2017)
- Innofor (2017) Everything starts from a forest plan (translated from Finnish). http://www.ostammepuuta.fi/metsanhoidon-palvelut/metsasuunnittelu/. Accessed 26 Sept 2017
- Jacobson M (2008) To cut or not to cut: tree value and deciding when to harvest timber. Technical report, http://extension.psu.edu/natural-resources/forests/finance/forest-tax-info/publications/forest-finance-8-to-cut-or-not-cut-tree-value-and-deciding-when-to-harvest-timber. Accessed 26 Sept 2017
- Marques AS, Audy JF, D’Amours S, Rönnqvist M (2014) Tactical and operational harvest planning. In: Borges JG, Dias-Balteiro L, McDill ME, Rodriguez LCE (eds) Theoretical foundations and applications. Springer, New York, pp 239–267Google Scholar
- Pasalodos-Tato M, Mäkinen A, Garcia-Gonzalo J, Borges JG, Lämås T, Eriksson LO (2013) Assessing uncertainty and risk in forest planning and decision support systems: review of classical methods and introduction of innovative approaches. For Syst 22(2):282–303Google Scholar
- Weintraub A, Abramovich A (1995) Analysis of uncertainty of future timber yields in forest management. For Sci 41(2):217–234Google Scholar
- Weintraub A, Wets RJ-B (2014) Harvesting management: generating wood-prices scenarios. Available from www.math.ucdavis.edu/~rjbw/mypage/Stochastic Optimization files/WntW13.pdf