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A Sequential Sampling Procedure for Stochastic Programming

Author

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  • Güzin Bayraksan

    (Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona 85721)

  • David P. Morton

    (Graduate Program in Operations Research and Industrial Engineering, The University of Texas at Austin, Austin, Texas 78712)

Abstract

We develop a sequential sampling procedure for a class of stochastic programs. We assume that a sequence of feasible solutions with an optimal limit point is given as input to our procedure. Such a sequence can be generated by solving a series of sampling problems with increasing sample size, or it can be found by any other viable method. Our procedure estimates the optimality gap of a candidate solution from this sequence. If the point estimate of the optimality gap is sufficiently small according to our termination criterion, then we stop. Otherwise, we repeat with the next candidate solution from the sequence under an increased sample size. We provide conditions under which this procedure (i) terminates with probability one and (ii) terminates with a solution that has a small optimality gap with a prespecified probability.

Suggested Citation

  • Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:4:p:898-913
    DOI: 10.1287/opre.1110.0926
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    References listed on IDEAS

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    Cited by:

    1. Saurabh Bansal & James S. Dyer, 2017. "Technical Note—Multivariate Partial-Expectation Results for Exact Solutions of Two-Stage Problems," Operations Research, INFORMS, vol. 65(6), pages 1526-1534, December.
    2. Václav Kozmík, 2015. "On variance reduction of mean-CVaR Monte Carlo estimators," Computational Management Science, Springer, vol. 12(2), pages 221-242, April.
    3. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    4. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    5. Yunxiao Deng & Suvrajeet Sen, 2022. "Predictive stochastic programming," Computational Management Science, Springer, vol. 19(1), pages 65-98, January.
    6. Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Spectral projected gradient method for stochastic optimization," Journal of Global Optimization, Springer, vol. 73(1), pages 59-81, January.
    7. Xiaotie Chen & David L. Woodruff, 2024. "Distributions and bootstrap for data-based stochastic programming," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    8. Jangho Park & Rebecca Stockbridge & Güzin Bayraksan, 2021. "Variance reduction for sequential sampling in stochastic programming," Annals of Operations Research, Springer, vol. 300(1), pages 171-204, May.
    9. Rebecca Stockbridge & Güzin Bayraksan, 2016. "Variance reduction in Monte Carlo sampling-based optimality gap estimators for two-stage stochastic linear programming," Computational Optimization and Applications, Springer, vol. 64(2), pages 407-431, June.
    10. Panos Parpas & Berk Ustun & Mort Webster & Quang Kha Tran, 2015. "Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 358-377, May.
    11. 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.
    12. Martin Šmíd & Václav Kozmík, 2024. "Approximation of multistage stochastic programming problems by smoothed quantization," Review of Managerial Science, Springer, vol. 18(7), pages 2079-2114, July.
    13. 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.
    14. Wu, Fei & Sioshansi, Ramteen, 2017. "A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 55-82.
    15. Johannes Royset, 2013. "On sample size control in sample average approximations for solving smooth stochastic programs," Computational Optimization and Applications, Springer, vol. 55(2), pages 265-309, June.
    16. Xiaotie Chen & David L. Woodruff, 2023. "Software for Data-Based Stochastic Programming Using Bootstrap Estimation," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1218-1224, November.
    17. Vitor L. de Matos & David P. Morton & Erlon C. Finardi, 2017. "Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling," Annals of Operations Research, Springer, vol. 253(2), pages 713-731, June.
    18. Anand Deo & Karthyek Murthy & Tirtho Sarker, 2022. "Combining Retrospective Approximation with Importance Sampling for Optimising Conditional Value at Risk," Papers 2206.12835, arXiv.org.
    19. Johannes O. Royset & Roberto Szechtman, 2013. "Optimal Budget Allocation for Sample Average Approximation," Operations Research, INFORMS, vol. 61(3), pages 762-776, June.

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