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Stochastic optimization models in forest planning: a progressive hedging solution approach

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Abstract

We consider the important problem of medium term forest planning with an integrated approach considering both harvesting and road construction decisions in the presence of uncertainty modeled as a multi-stage problem. We give strengthening methods that enable the solution of problems with many more scenarios than previously reported in the literature. Furthermore, we demonstrate that a scenario-based decomposition method (Progressive Hedging) is competitive with direct solution of the extensive form, even on a serial computer. Computational results based on a real-world example are presented.

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References

  • Alonso-Ayuso, A., Escudero, L., & Ortuno, M. (2003). BFC, a branch-and-fix coordination algorithmic framework for solving some types of stochastic pure and mixed 0–1 programs. European Journal of Operational Research, 151(3), 503–519.

    Article  Google Scholar 

  • Andalaft, N., Andalaft, P., Guignard, M., Magendzo, A., Wainer, A., & Weintraub, A. (2003). A problem of forest harvesting and road building solved through model strengthening and Lagrangian relaxation. Operations Research, 51(4), 613–628.

    Article  Google Scholar 

  • Caroe, C. C., & Schultz, R. (1999). Dual decomposition in stochastic integer programming. Operations Research Letters, 24, 37–45.

    Article  Google Scholar 

  • Constantino, M., Martins, I., & Borges, J. G. (2008). A new mixed-integer programming model for harvest scheduling subject to maximum area restrictions. Operations Research, 56, 542–551.

    Article  Google Scholar 

  • Escudero, L. F., Garin, A., Merino, M., & Pérez, G. (2009). On BFC-MSMIP: An exact branch-and-fix coordination approach for solving multistage stochastic mixed 0–1 problems. TOP, 17, 96–122.

    Article  Google Scholar 

  • Frisk, M., Karlsson, J., & Rönnqvist, M. (2006). RoadOpt: A decision support system for road upgrading in forestry. Scandinavian Journal of Forest Research, 21(Suppl. 7), 5–15.

    Google Scholar 

  • Goycoolea, M., Murray, A. T., Barahona, F., Epstein, R., & Weintraub, A. (2005). Harvest scheduling subject to maximum area restrictions: Exploring exact approaches. Operations Research, 53(3), 490–500.

    Article  Google Scholar 

  • Goycoolea, M., Murray, A., Vielma, J. P., & Weintraub, A. (2009). Evaluating approaches for solving the area restriction model in harvest scheduling. Forest Science, 55(2), 149–165.

    Google Scholar 

  • Guglielmo, L., & Sen, S. (2004). A branch-and-price algorithm for multistage stochastic integer programming with application to stochastic batch-sizing problems. Management Science, 50(6), 786–796.

    Article  Google Scholar 

  • Guignard, M., Ryu, C., & Spielberg, K. (1994). Model tightening for integrated timber harvest and transportation planning. Proceedings International Symposium Systems Analysis Management Decisions Forestry, Valdivia, Chile, (pp. 364–369).

  • Hof, J., & Pickens, J. (1991). Chance-constrained and chance-maximizing mathematical programs in renewable resource management. Forest Science, 7(18), 308–325.

    Google Scholar 

  • Jones, J. G., Hyde, J. F. C., III, & Meacham, M. L. (1986). Four analytical approaches for integrating land management and transportation planning on forest lands (p. 33). Research Paper INT-361. Ogden, UT: U. S. Department of Agriculture, Forest Service, Intermountain Research Station.

  • Kirby, M. W., Hager, W., & Wong, P. (1986). Simultaneous planning of wildland transportation alternatives. TIMS Studies in the Management Sciences, 21, 371–387.

    Google Scholar 

  • Martell, D., Gunn, E., & Weintraub, A. (1998). Forest management challenges for operational researchers. European Journal of Operational Research, 104, 1–17.

    Article  Google Scholar 

  • Martell, D. (2007). Forest fire management: Current practices and new challenges for operational researchers. In A. Weintraub, C. R. Trond Bjorndal, R. Epstein, & J. Miranda (Eds.), Handbook of Operations Research in Natural Resources. New York, NY: Springer Science+Business Media.

    Google Scholar 

  • McNaughton, A. J., & Ryan, D. (2008). Adjacency branches used to optimize forest harvesting subject to area restrictions on clearfell. Forest Science, 4(13), 442–454.

    Google Scholar 

  • Murray, A. T., & Church, R. L. (1995). Heuristic solution approaches to operational forest planning problems. OR-Spektrum, 17, 193–203.

    Article  Google Scholar 

  • Quinteros, M., Alonso, A., Escudero, L., Guignard, M., & Weintraub, A. (2009). Forestry management under uncertainty. Annals of Operations Research, 190, 1572–9338.

  • Richards, W., & Gunn, A. (2000). A model and Tabu search method to optimize stand harvest and road construction schedules. Forest Science, 46, 188–203.

    Google Scholar 

  • Rockafellar, R. T., & Wets, R. J.-B. (1991). Scenario and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16, 119–147.

    Article  Google Scholar 

  • Römisch, A., & Schultz, R. (2001). Multistage stochastic integer programs: An Introduction. In M. Grötschel, S. Krumke, & J. Rambau (Eds.), Online Optimization of Large Scale Systems (pp. 581–600). Berlin: Springer.

    Chapter  Google Scholar 

  • Watson, J. P., & Woodruff, D. L. (2010). Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Computational Management Science, 8(4), 355–370.

    Article  Google Scholar 

  • Watson, J. P., Hart, W., & Woodruff, D. L. (2012). PySP: Modeling and solving stochastic programs in python. Mathematical Programming Computation, 4(2), 109–149.

    Article  Google Scholar 

  • Weintraub, A. & Wets, R.J.-B. Harvesting management: Generating wood-prices scenarios. Technical Report (2013). Santiago: Systemas Complejos en Ingeneria, Universidad de Chile.

  • Weintraub, A., & Navon, D. (1976). A forest management planning model integrating sylvicultural and transportation activities. Management Science, 22(12), 1299–1309.

    Article  Google Scholar 

  • Weintraub, A., & Vera, J. (1991). A cutting plane approach for chance constrained linear programs. Operations Research, 39(5), 776–785.

    Article  Google Scholar 

  • Weintraub, A., Jones, G. J., Magendzo, A., Meacham, M. L., & Kirby, M. W. (1994). A heuristic system to solve mixed integer forest planning models. Operations Research, 42, 1010–1024.

    Article  Google Scholar 

  • Weintraub, A., Jones, G. J., Magendzo, A., & Malchuk, D. (1995). Heuristic procedures for solving mixed-integer harvest scheduling-transportation planning models. Canadian Journal Forest Research, 25, 1618–1626.

  • Wets, R. (1975). On the relation between stochastic and deterministic optimization. In A. Bensoussan & J.L. Lions, (Eds.), Control theory, numerical methods and computer systems modelling, Lecture notes in economics and mathematical systems, vol. 107 (pp. 350–361). Berlin: Springer

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Acknowledgments

The comments of two anonymous referees greatly improved the exposition. This research was financed in part by the Complex Engineering Systems Institute (ICM:P-05-004-F, CONICYT: FBO16), and by Fondecyt under Grant 1120318.

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Correspondence to David L. Woodruff.

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Veliz, F.B., Watson, JP., Weintraub, A. et al. Stochastic optimization models in forest planning: a progressive hedging solution approach. Ann Oper Res 232, 259–274 (2015). https://doi.org/10.1007/s10479-014-1608-4

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