Multicut Benders decomposition algorithm for process supply chain planning under uncertainty
In this paper, we present a multicut version of the Benders decomposition method for solving two-stage stochastic linear programming problems, including stochastic mixed-integer programs with only continuous recourse (two-stage) variables. The main idea is to add one cut per realization of uncertainty to the master problem in each iteration, that is, as many Benders cuts as the number of scenarios added to the master problem in each iteration. Two examples are presented to illustrate the application of the proposed algorithm. One involves production-transportation planning under demand uncertainty, and the other one involves multiperiod planning of global, multiproduct chemical supply chains under demand and freight rate uncertainty. Computational studies show that while both the standard and the multicut versions of the Benders decomposition method can solve large-scale stochastic programming problems with reasonable computational effort, significant savings in CPU time can be achieved by using the proposed multicut algorithm.
KeywordsBenders decomposition Stochastic programming Planning Supply chain
Unable to display preview. Download preview PDF.
- Archibald, T. W., Buchanan, C. S., McKinnon, K. I. M., & Thomas, L. C. (1999). Nested Benders decomposition and dynamic programming for reservoir optimisation. The Journal of the Operational Research Society, 50, 468–479. Google Scholar
- Bahn, O., Dumerle, O., Goffin, J. L., & Vial, J. P. (1995). A cutting plane method from analytic centers for stochastic-programming. Mathematical Programming, 69, 45–73. Google Scholar
- Birge, J. R., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer. Google Scholar
- Contreras, I., Cordeau, J. F., & Laporte, G. (2010). Benders decomposition for large-scale uncapacitated hub location. Operations Research, in press. Google Scholar
- Infanger, G. (1994). Planning under uncertainty: solving large-scale stochastic linear programs. Danvers: Boyd and Fraser. Google Scholar
- Rosenthal, R. E. (2010). GAMS—a user’s manual. Washington: GAMS Development Corp. Google Scholar
- Ruszczyński, A. (1997). Decomposition methods in stochastic programming. Mathematical Programming, 79, 333–353. Google Scholar
- Shapiro, A. (2000). Stochastic programming by Monte Carlo simulation methods. Stochastic Programming E-Prints Series, 03. Google Scholar
- Shapiro, A., & Homem-de-Mello, T. (1998). A simulation-based approach to two-stage stochastic programming with recourse. Mathematical Programming, 81, 301–325. Google Scholar