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Stochastic Decomposition for Two-Stage Stochastic Linear Programs with Random Cost Coefficients

Author

Listed:
  • Harsha Gangammanavar

    (Southern Methodist University, Dallas, Texas 75275)

  • Yifan Liu

    (84.51°, Cincinnati, Ohio 45202;)

  • Suvrajeet Sen

    (University of Southern California, Los Angeles, California 90089)

Abstract

Stochastic decomposition (SD) has been a computationally effective approach to solve large-scale stochastic programming (SP) problems arising in practical applications. By using incremental sampling, this approach is designed to discover an appropriate sample size for a given SP instance, thus precluding the need for either scenario reduction or arbitrary sample sizes to create sample average approximations (SAA). When compared with the solutions obtained using the SAA procedure, SD provides solutions of similar quality in far less computational time using ordinarily available computational resources. However, previous versions of SD were not applicable to problems with randomness in second-stage cost coefficients. In this paper, we extend its capabilities by relaxing this assumption on cost coefficients in the second stage. In addition to the algorithmic enhancements necessary to achieve this, we also present the details of implementing these extensions, which preserve the computational edge of SD. Finally, we illustrate the computational results obtained from the latest implementation of SD on a variety of test instances generated for problems from the literature. We compare these results with those obtained from the regularized L-shaped method applied to the SAA function of these problems with different sample sizes.

Suggested Citation

  • Harsha Gangammanavar & Yifan Liu & Suvrajeet Sen, 2021. "Stochastic Decomposition for Two-Stage Stochastic Linear Programs with Random Cost Coefficients," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 51-71, January.
    • Handle: RePEc:inm:orijoc:v:33:y:2021:i:1:p:51-71
    DOI: 10.1287/ijoc.2019.0929
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    References listed on IDEAS

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    1. Suvrajeet Sen & Yifan Liu, 2016. "Mitigating Uncertainty via Compromise Decisions in Two-Stage Stochastic Linear Programming: Variance Reduction," Operations Research, INFORMS, vol. 64(6), pages 1422-1437, December.
    2. Julia Higle & Suvrajeet Sen, 1999. "Statistical approximations forstochastic linear programming problems," Annals of Operations Research, Springer, vol. 85(0), pages 173-193, January.
    3. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    4. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
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