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Computational Management Science

, Volume 8, Issue 4, pp 355–370

First Online: 29 July 2010Received: 20 August 2009Accepted: 13 July 2010


Numerous planning problems can be formulated as multi-stage stochastic programs and many possess key discrete integer decision variables in one or more of the stages. Progressive hedging PH is a scenario-based decomposition technique that can be leveraged to solve such problems. Originally devised for problems possessing only continuous variables, PH has been successfully applied as a heuristic to solve multi-stage stochastic programs with integer variables. However, a variety of critical issues arise in practice when implementing PH for the discrete case, especially in the context of very difficult or large-scale mixed-integer problems. Failure to address these issues properly results in either non-convergence of the heuristic or unacceptably long run-times. We investigate these issues and describe algorithmic innovations in the context of a broad class of scenario-based resource allocation problem in which decision variables represent resources available at a cost and constraints enforce the need for sufficient combinations of resources. The necessity and efficacy of our techniques is empirically assessed on a two-stage stochastic network flow problem with integer variables in both stages.

Sandia is a multipurpose laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.

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Autor: Jean-Paul Watson - David L. Woodruff


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