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Solving Contextual Stochastic Optimization Problems through Contextual Distribution Estimation

Author

Listed:
  • Xuecheng Tian

    (Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

  • Bo Jiang

    (Institute of Data and Information, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China)

  • King-Wah Pang

    (Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

  • Yu Guo

    (Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

  • Yong Jin

    (Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

  • Shuaian Wang

    (Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China)

Abstract

Stochastic optimization models always assume known probability distributions about uncertain parameters. However, it is unrealistic to know the true distributions. In the era of big data, with the knowledge of informative features related to uncertain parameters, this study aims to estimate the conditional distributions of uncertain parameters directly and solve the resulting contextual stochastic optimization problem by using a set of realizations drawn from estimated distributions, which is called the contextual distribution estimation method. We use an energy scheduling problem as the case study and conduct numerical experiments with real-world data. The results demonstrate that the proposed contextual distribution estimation method offers specific benefits in particular scenarios, resulting in improved decisions. This study contributes to the literature on contextual stochastic optimization problems by introducing the contextual distribution estimation method, which holds practical significance for addressing data-driven uncertain decision problems.

Suggested Citation

  • Xuecheng Tian & Bo Jiang & King-Wah Pang & Yu Guo & Yong Jin & Shuaian Wang, 2024. "Solving Contextual Stochastic Optimization Problems through Contextual Distribution Estimation," Mathematics, MDPI, vol. 12(11), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1612-:d:1398702
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    References listed on IDEAS

    as
    1. Zhen, Lu, 2016. "Modeling of yard congestion and optimization of yard template in container ports," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 83-104.
    2. Dimitris Bertsimas & Nathan Kallus, 2020. "From Predictive to Prescriptive Analytics," Management Science, INFORMS, vol. 66(3), pages 1025-1044, March.
    3. Zhen, Lu & Xu, Zhou & Wang, Kai & Ding, Yi, 2016. "Multi-period yard template planning in container terminals," Transportation Research Part B: Methodological, Elsevier, vol. 93(PB), pages 700-719.
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