Cutting Planes for Multistage Stochastic Integer Programs

Authors:
Yongpei Guan;Shabbir Ahmed;George L. Nemhauser
Affiliations:
School of Industrial Engineering, University of Oklahoma, Norman, Oklahoma 73019;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Venue:
Operations Research
Year:
2009

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Abstract

This paper addresses the problem of finding cutting planes for multistage stochastic integer programs. We give a general method for generating cutting planes for multistage stochastic integer programs based on combining inequalities that are valid for the individual scenarios. We apply the method to generate cuts for a stochastic version of a dynamic knapsack problem and for stochastic lot-sizing problems. We give computational results, which show that these new inequalities are very effective in a branch-and-cut algorithm.