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Cut sharing for multistage stochastic linear programs with interstage dependency

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Abstract

Multistage stochastic programs with interstage independent random parameters have recourse functions that do not depend on the state of the system. Decomposition-based algorithms can exploit this structure by sharing cuts (outer-linearizations of the recourse function) among different scenario subproblems at the same stage. The ability to share cuts is necessary in practical implementations of algorithms that incorporate Monte Carlo sampling within the decomposition scheme. In this paper, we provide methodology for sharing cuts in decomposition algorithms for stochastic programs that satisfy certain interstage dependency models. These techniques enable sampling-based algorithms to handle a richer class of multistage problems, and may also be used to accelerate the convergence of exact decomposition algorithms.

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Authors and Affiliations

  1. Department of Operations Research, Stanford University, 94305-4023, Stanford, CA, USA

    Gerd Infanger

  2. Department of Mechanical Engineering, The University of Texas at Austin, 78712, Austin, TX, USA

    David P. Morton

Authors
  1. Gerd Infanger
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  2. David P. Morton
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Corresponding author

Correspondence to Gerd Infanger.

Additional information

Research leading to this work was partially supported by the Department of Energy Contract DE-FG03-92ER25116-A002; the Office of Naval Research Contract N00014-89-J-1659; the National Science Foundation Grants ECS-8906260, DMS-8913089; and the Electric Power Research Institute Contract RP 8010-09, CSA-4O05335.

This author's work was supported in part by the National Research Council under a Research Associateship at the Naval Postgraduate School, Monterey, California.

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Infanger, G., Morton, D.P. Cut sharing for multistage stochastic linear programs with interstage dependency. Mathematical Programming 75, 241–256 (1996). https://doi.org/10.1007/BF02592154

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  • DOI: https://doi.org/10.1007/BF02592154

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