Computational Management Science

, Volume 8, Issue 4, pp 355–370 | Cite as

Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems

Open Access
Original Paper

Abstract

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.

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Discrete Math and Complex Systems DepartmentSandia National LaboratoriesAlbuquerqueUSA
  2. 2.Graduate School of ManagementUniversity of CaliforniaDavisUSA

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