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Decision rule-based method for flexible multi-facility capacity expansion problem

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  • Sixiang Zhao
  • William Benjamin Haskell
  • Michel-Alexandre Cardin

Abstract

Strategic capacity planning for multiple-facility systems with flexible designs is an important topic in the area of capacity expansion problems with random demands. The difficulties of this problem lie in the multidimensional nature of its random variables and action space. For a single-facility problem, the decision rule method has been shown to be efficient in deriving desirable solutions, but for a Multiple-facility Capacity Expansion Problem (MCEP), it has not been well studied. This article designs a novel decision rule–based method for the solution of an MCEP with multiple options, discrete capacity, and a concave capacity expansion cost. An if–then decision rule is designed and the original multi-stage problem is thus transformed into a master problem and a multi-period sub-problem. As the sub-problem contains non-binding constraints, we combine a stochastic approximation algorithm with a branch-and-cut technique so that the sub-problem can be further decomposed across scenarios and be solved efficiently. The proposed decision rule–based method is also extended to solving the MCEP with fixed costs. Numerical studies in this article illustrate that the proposed method affords not only improved performance relative to an inflexible design taken as benchmark but also time savings relative to approximate dynamic programming analysis.

Suggested Citation

  • Sixiang Zhao & William Benjamin Haskell & Michel-Alexandre Cardin, 2018. "Decision rule-based method for flexible multi-facility capacity expansion problem," IISE Transactions, Taylor & Francis Journals, vol. 50(7), pages 553-569, July.
  • Handle: RePEc:taf:uiiexx:v:50:y:2018:i:7:p:553-569
    DOI: 10.1080/24725854.2018.1426135
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    Cited by:

    1. Torres-Rincón, Samuel & Bastidas-Arteaga, Emilio & Sánchez-Silva, Mauricio, 2021. "A flexibility-based approach for the design and management of floating offshore wind farms," Renewable Energy, Elsevier, vol. 175(C), pages 910-925.
    2. Torres-Rincón, Samuel & Sánchez-Silva, Mauricio & Bastidas-Arteaga, Emilio, 2021. "A multistage stochastic program for the design and management of flexible infrastructure networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    3. Sixiang Zhao, 2023. "Decision rule-based method in solving adjustable robust capacity expansion problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(2), pages 259-286, April.
    4. Zhou, Siyu & Han, Yang & Chen, Shuheng & Yang, Ping & Mahmoud, Karar & Darwish, Mohamed M.F. & Matti, Lehtonen & Zalhaf, Amr S., 2023. "A multiple uncertainty-based Bi-level expansion planning paradigm for distribution networks complying with energy storage system functionalities," Energy, Elsevier, vol. 275(C).

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