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A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints

Author

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  • Minjiao Zhang

    (Department of Integrated Systems Engineering, Ohio State University, Columbus, Ohio 43210)

  • Simge Küçükyavuz

    (Department of Integrated Systems Engineering, Ohio State University, Columbus, Ohio 43210)

  • Saumya Goel

    (Department of Integrated Systems Engineering, Ohio State University, Columbus, Ohio 43210)

Abstract

In this paper, we consider a finite-horizon stochastic mixed-integer program involving dynamic decisions under a constraint on the overall performance or reliability of the system. We formulate this problem as a multistage (dynamic) chance-constrained program, whose deterministic equivalent is a large-scale mixed-integer program. We study the structure of the formulation and develop a branch-and-cut method for its solution. We illustrate the efficacy of the proposed model and method on a dynamic inventory control problem with stochastic demand in which a specific service level must be met over the entire planning horizon. We compare our dynamic model with a static chance-constrained model, a dynamic risk-averse optimization model, a robust optimization model, and a pseudo-dynamic approach and show that significant cost savings can be achieved at high service levels using our model.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1822 . This paper was accepted by Dimitris Bertsimas, optimization .

Suggested Citation

  • Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    • Handle: RePEc:inm:ormnsc:v:60:y:2014:i:5:p:1317-1333
    DOI: 10.1287/mnsc.2013.1822
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    2. Yongjia Song & Minjiao Zhang, 2015. "Chance‐constrained multi‐terminal network design problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 321-334, June.
    3. Jianqiu Huang & Kai Pan & Yongpei Guan, 2021. "Multistage Stochastic Power Generation Scheduling Co-Optimizing Energy and Ancillary Services," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 352-369, January.
    4. Xiao Liu & Simge Küçükyavuz, 2018. "A polyhedral study of the static probabilistic lot-sizing problem," Annals of Operations Research, Springer, vol. 261(1), pages 233-254, February.
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    6. Bismark Singh & David P. Morton & Surya Santoso, 2018. "An adaptive model with joint chance constraints for a hybrid wind-conventional generator system," Computational Management Science, Springer, vol. 15(3), pages 563-582, October.
    7. Kai Pan & Yongpei Guan, 2016. "Strong Formulations for Multistage Stochastic Self-Scheduling Unit Commitment," Operations Research, INFORMS, vol. 64(6), pages 1482-1498, December.

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