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Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse

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  • Lewis Ntaimo

    (Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843)

Abstract

This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse is presented. In particular, we derive valid inequalities that allow for scenario subproblems for SIP with random recourse but deterministic technology matrix and right-hand side vector to share cut coefficients. The valid inequalities are used to derive a disjunctive decomposition method whose derivation has been motivated by real-life stochastic server location problems with random recourse, which find many applications in operations research. Computational results with large-scale instances to demonstrate the potential of the method are reported.

Suggested Citation

  • Lewis Ntaimo, 2010. "Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse," Operations Research, INFORMS, vol. 58(1), pages 229-243, February.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:229-243
    DOI: 10.1287/opre.1090.0693
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    References listed on IDEAS

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    Cited by:

    1. Chao Li & Muhong Zhang & Kory Hedman, 2021. "Extreme Ray Feasibility Cuts for Unit Commitment with Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1037-1055, July.
    2. Onur Tavaslıoğlu & Oleg A. Prokopyev & Andrew J. Schaefer, 2019. "Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function," Operations Research, INFORMS, vol. 67(6), pages 1659-1677, November.
    3. Can Li & Ignacio E. Grossmann, 2019. "A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables," Journal of Global Optimization, Springer, vol. 75(2), pages 247-272, October.
    4. Ward Romeijnders & Niels van der Laan, 2020. "Pseudo-Valid Cutting Planes for Two-Stage Mixed-Integer Stochastic Programs with Right-Hand-Side Uncertainty," Operations Research, INFORMS, vol. 68(4), pages 1199-1217, July.
    5. Andrew C. Trapp & Oleg A. Prokopyev & Andrew J. Schaefer, 2013. "On a Level-Set Characterization of the Value Function of an Integer Program and Its Application to Stochastic Programming," Operations Research, INFORMS, vol. 61(2), pages 498-511, April.
    6. Valicka, Christopher G. & Garcia, Deanna & Staid, Andrea & Watson, Jean-Paul & Hackebeil, Gabriel & Rathinam, Sivakumar & Ntaimo, Lewis, 2019. "Mixed-integer programming models for optimal constellation scheduling given cloud cover uncertainty," European Journal of Operational Research, Elsevier, vol. 275(2), pages 431-445.
    7. Brian Keller & Güzin Bayraksan, 2012. "Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Generalized Upper Bound Constraints," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 172-186, February.
    8. Nesbitt, Peter & Blake, Lewis R. & Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo K. & Newman, Alexandra & Brickey, Andrea, 2021. "Underground mine scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 294(1), pages 340-352.
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    10. Fang, Yi-Ping & Sansavini, Giovanni, 2019. "Optimum post-disruption restoration under uncertainty for enhancing critical infrastructure resilience," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 1-11.
    11. Qipeng Zheng & Jianhui Wang & Panos Pardalos & Yongpei Guan, 2013. "A decomposition approach to the two-stage stochastic unit commitment problem," Annals of Operations Research, Springer, vol. 210(1), pages 387-410, November.
    12. Qipeng P. Zheng & Panos M. Pardalos, 2010. "Stochastic and Risk Management Models and Solution Algorithm for Natural Gas Transmission Network Expansion and LNG Terminal Location Planning," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 337-357, November.
    13. Fengqi You & Ignacio Grossmann, 2013. "Multicut Benders decomposition algorithm for process supply chain planning under uncertainty," Annals of Operations Research, Springer, vol. 210(1), pages 191-211, November.
    14. Li, Xiaohong & Yang, Dong & Hu, Mengqi, 2018. "A scenario-based stochastic programming approach for the product configuration problem under uncertainties and carbon emission regulations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 126-146.
    15. Saravanan Venkatachalam & Lewis Ntaimo, 2023. "Integer set reduction for stochastic mixed-integer programming," Computational Optimization and Applications, Springer, vol. 85(1), pages 181-211, May.

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