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Summary: Cutting planes for multi-stage stochastic integer programs
Yongpei Guan
, Shabbir Ahmed
and George L. Nemhauser
School of Industrial Engineering, University of Oklahoma, Norman, OK 73019
School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332
September 15, 2006
Abstract
This paper addresses the problem of finding cutting planes for multi-stage stochastic integer programs.
We give a general method for generating cutting planes for multi-stage 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 to stochastic lot sizing problems. We
give computational results which show that these new inequalities are very effective in a branch-and-cut
algorithm.
1 Introduction
This paper deals with polyhedral aspects of multi-stage stochastic integer programs. Our basic idea is to ex-
tend known results concerning cutting planes for a deterministic model of the problem to a stochastic model.
In other words, suppose we know valid inequalities that make it possible to solve efficiently the deterministic
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