Abstract
Optimization models have been used to support decision making in the forest industry for a long time. However, several of those models are deterministic and do not address the variability that is present in some of the data. Robust Optimization is a methodology which can deal with the uncertainty or variability in optimization problems by computing a solution which is feasible for all possible scenarios of the data within a given uncertainty set. This paper presents the application of the Robust Optimization Methodology to a Sawmill Planning Problem. In the particular case of this problem, variability is assumed in the yield coefficients associated to the cutting patterns used. The main results show that the loss in the function objective value (the “Price of Robustness”), due to computing robust solutions, is not excessive. Moreover, the computed solutions remain feasible for a large proportion of randomly generated scenarios, and tend to preserve the structure of the nominal solution. We believe that these results provide an application area for Robust Optimization in which several source of uncertainty are present.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bai, D., Carpenter, T., & Mulvey, J. (1997). Making a case for robust optimization models. Management Science, 43, 895–907.
Ben Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of Operations Research, 23(4), 769–805.
Ben Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations Research Letters, 25, 1–13.
Ben Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 88(3), 411–424.
Ben Tal, A., & Nemirovski, A. (2002). Robust optimization- methodology and applications. Mathematical Programming, 92(3), 453–480.
Ben Tal, A., Margalit, T., & Nemirovski, A. (2000). Robust modeling of multi-stage portfolio problems. In H. Frenk, K. Roos, T. Terlaky, & S. Zhang (Eds.), High performance optimization (pp. 303–328). Dordrecht: Kluwer Academic.
Ben Tal, A., Goryashko, A., Guslitzer, E., & Nemirovski, A. (2004). Adjustable robust solutions of uncertain linear programs. Mathematical Programming, 99(2), 351–376.
Ben Tal, A., Golany, B., Nemirovski, A., & Vial, J. P. (2005). Retailer-supplier flexible commitments contracts: a robust optimization approach. Manufacturing & Service Operations Management, 7(3), 248–271.
Bertsimas, D., & Sim, M. (2003). Robust discrete optimization and network flows. Mathematical Programming, 98(1–3), 49–71.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53.
Birge, J. R., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer.
Bohle, C., Maturana, S., & Vera, J. (2010). A robust optimization approach to wine grape harvesting scheduling. European Journal of Operational Research, 200(1), 245–252.
Carino, H. F., & Willis, D. B. (2001a). Enhancing the profitability of a vertically integrated wood products production system: Part 1. A multistage modelling approach. Forest Products Journal, 51(4), 37–44.
Carino, H. F., & Willis, D. B. (2001b). Enhancing the profitability of a vertically integrated wood products production system: Part 2. A case Study. Forest Products Journal, 51(4), 45–53.
Chen, X., & Zhang, Y. (2009). Uncertain linear programs: extended affinely adjustable robust counterparts. Operations Research, 57(6), 1469–1482.
Dantzig, G. (1955). Linear programming under uncertainty. Management Science, 1, 197–206.
El-Ghaoui, L., Oustry, F., & Lebrel, H. (1998). Robust Solutions to uncertain semidefinite programs. SIAM Journal on Optimization, 9, 33–52.
Epstein, R., Morales, R., Serón, J., & Weintraub, A. (1999). Use of OR systems in the Chilean forest industries. Interfaces, 29(1), 7–29.
Epstein, R., Karlsson, J., Rönnqvist, M., & Weintraub, A. (2007). Harvest operational models in forestry. In A. Weintraub, C. Romero, T. Bjornald, & R. Epstein (Eds.), Handbook of operations research in natural resources (pp. 365–377). Berlin: Springer.
Hillier, F., & Liberman, G. (2001). Introduction to operations research. New York: McGraw-Hill.
Jensen, H., & Maturana, S. (2002). A possibilistic decision support system for imprecise mathematical programming problems. International Journal of Production Economics, 77(2), 145–158.
Kazemi Zanjani, M., Ait-Kadi, D., & Nourelfath, M. (2010a). Robust production planning in a manufacturing environment with random yield: a case in sawmill production planning. European Journal of Operational Research, 201(3), 882–891.
Kazemi Zanjani, M., Nourelfath, M., & Ait-Kadi, D. (2010b). A multi-stage stochastic programming approach for production planning with uncertainty in the quality of raw materials and demand. International Journal of Production Research, 48(16), 4701–4723.
Kouvelis, P. (1997). Robust discrete optimization and its applications (p. 356). Dordrecht: Kluwer Academic.
Leung, S., Wu, Y., & Lai, K. (2002). A robust optimization model for a cross-border logistics problem with fleet composition in an uncertain environment. Mathematical and Computer Modelling, 36, 1221–1234.
Martell, D., Gunn, E., & Weintraub, A. (1998). Forest management challenges for operational researchers. European Journal of Operational Research, 104, 1–17.
Maturana, S., & Contesse, L. (1998). A mixed integer programming model of the logistics of sulfuric acid in Chile. International Transactions in Operational Research, 5(5), 405–412.
Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large scale systems. Operations Research, 43(2), 264–281.
Palma, C., & Nelson, J. (2009). A robust optimization approach protected harvest scheduling decisions against uncertainty. Canadian Journal of Forest Research, 39, 342–355.
Singer, M., & Donoso, P. (2007). Internal supply chain management in the Chilean sawmill industry. International Journal of Operations & Production Management, 27, 524–541.
Soyster, A. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21, 1154–1157.
Takriti, S., & Ahmed, S. (2004). On robust optimization of two-stage systems. Mathematical Programming, 99(1), 109–126.
Vladimirou, H., & Zenios, S. (1997). Stochastic programming and robust optimization. In T. Gal & H. J. Greenberg (Eds.), Advances in sensitivity analysis and parametric programming. Dordrecht: Kluwer Academic. Chap. 12.
Weintraub, A., & Abramovich, A. (1995). Analysis of uncertainty of future timber yields in forest management. Forest Science, 41(2), 217–234.
Weintraub, A., & Bare, B. (1996). New issues in forest land management from an operations research perspective. Interfaces, 26(5), 9–25.
Weintraub, A., & Epstein, R. (2002). The supply chain in the forest industry: models and linkages. In J. Geunes, P. M. Pardalos, & H. E. Romeijn (Eds.), Applied optimization, supply chain management models, applications, and research directions (pp. 343–362). Dordrecht: Kluwer Academic.
Weintraub, A., & Romero, C. (2006). Operations research models and the management of agricultural and forestry resources: a review and comparison. Interfaces, 36(5), 446–457.
Weintraub, A., & Vera, J. (1991). A cutting plane approach for chance constrained linear programs. Operations Research, 39, 776–785.
Yang, D., & Zenios, S. (1997). A scalable parallel interior point algorithm for stochastic linear programming and robust optimization. Computational Optimization and Applications, 7, 143–158.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alvarez, P.P., Vera, J.R. Application of Robust Optimization to the Sawmill Planning Problem. Ann Oper Res 219, 457–475 (2014). https://doi.org/10.1007/s10479-011-1002-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-011-1002-4