Two-stage integer programs with stochastic right-hand sides

Nan Kong; Andrew J. Schaefer; Brady Hunsaker

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SPEPS Preprint

Author(s):	Nan Kong, University of Pittsburgh Andrew J. Schaefer, University of Pittsburgh Brady Hunsaker, University of Pittsburgh
Title:	Two-stage integer programs with stochastic right-hand sides – A superadditive dual approach
Date of Acceptance:	02.10.2004
Submission Date:	26.07.2004
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10059669)
Keywords (eng):	Stochastic Programming, Integer Programming, Superadditive Duality, Level Sets
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Abstract (eng):

We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms for finding the value functions. To solve the reformulation after obtaining the value functions, we develop a global branch-and-bound approach and a level-set approach to find an optimal tender. We show that our method can solve randomly generated instances that are several orders of magnitude larger than those found in the literature.

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