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Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

Author

Listed:
  • Tahir Ekin

    (McCoy College of Business, Texas State University, San Marcos, Texas 78666)

  • Nicholas G. Polson

    (Booth School of Business, University of Chicago, Chicago, Illinois 60637)

  • Refik Soyer

    (School of Business, George Washington University, Washington, DC 20052)

Abstract

In this paper, we develop a simulation-based approach for two-stage stochastic programs with recourse. We construct an augmented probability model with stochastic shocks and decision variables. Simulating from the augmented probability model solves for the expected recourse function and the optimal first-stage decision. Markov chain Monte Carlo methods, together with ergodic averaging, provide a framework to compute the optimal solution. We illustrate our methodology via the two-stage newsvendor problem with unimodal and bimodal continuous uncertainty. Finally, we present performance comparisons of our algorithm and the sample average approximation method.

Suggested Citation

  • Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2014. "Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse," Decision Analysis, INFORMS, vol. 11(4), pages 250-264, December.
    • Handle: RePEc:inm:ordeca:v:11:y:2014:i:4:p:250-264
    DOI: 10.1287/deca.2014.0303
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    References listed on IDEAS

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    Cited by:

    1. Huidong Zhang & Dragan Djurdjanovic, 2022. "Integrated production and maintenance planning under uncertain demand with concurrent learning of yield rate," Flexible Services and Manufacturing Journal, Springer, vol. 34(2), pages 429-450, June.
    2. Ekin, Tahir & Aktekin, Tevfik, 2021. "Decision making under uncertain and dependent system rates in service systems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 335-348.
    3. Ekin, Tahir, 2018. "Integrated maintenance and production planning with endogenous uncertain yield," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 52-61.
    4. Tahir Ekin & Stephen Walker & Paul Damien, 2023. "Augmented simulation methods for discrete stochastic optimization with recourse," Annals of Operations Research, Springer, vol. 320(2), pages 771-793, January.
    5. Tevfik Aktekin & Tahir Ekin, 2016. "Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 460-478, September.
    6. Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2017. "Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 613-627, December.
    7. Ekin, Tahir & Naveiro, Roi & Ríos Insua, David & Torres-Barrán, Alberto, 2023. "Augmented probability simulation methods for sequential games," European Journal of Operational Research, Elsevier, vol. 306(1), pages 418-430.

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