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Optimal Design of Process Flexibility for General Production Systems

Author

Listed:
  • Xi Chen

    (Stern School of Business, New York University, New York, New York 10012;)

  • Tengyu Ma

    (Facebook AI Research, Menlo Park, California 94025;)

  • Jiawei Zhang

    (Department of Information, Operations, and Management Sciences, New York University, New York, New York 10012; NYU Shanghai, 200122 Shanghai, China;)

  • Yuan Zhou

    (Indiana University at Bloomington, Bloomington, Indiana 47405; University of Illinois Urbana–Champaign, Urbana, Illinois 61801)

Abstract

Process flexibility is widely adopted as an effective strategy for responding to uncertain demand. Many algorithms for constructing sparse flexibility designs with good theoretical guarantees have been developed for balanced and symmetrical production systems. These systems assume that the number of plants equals the number of products, that supplies have the same capacity, and that demands are independently and identically distributed. In this paper we relax these assumptions and consider a general class of production systems. We construct a simple flexibility design to fulfill (1 - ɛ)-fraction of expected demand with high probability where the average degree is O (ln(1/ɛ)) . To motivate our construction, we first consider a natural weighted probabilistic construction from the existing literature where the degree of each node is proportional to its expected capacity. However, this strategy is shown to be suboptimal. To obtain an optimal construction, we develop a simple yet effective thresholding scheme. The analysis of our approach extends the classic analysis of expander graphs by overcoming several technical difficulties. Our approach may prove useful in other applications that require expansion properties of graphs with nonuniform degree sequences.

Suggested Citation

  • Xi Chen & Tengyu Ma & Jiawei Zhang & Yuan Zhou, 2019. "Optimal Design of Process Flexibility for General Production Systems," Operations Research, INFORMS, vol. 67(2), pages 516-531, March.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:2:p:516-531
    DOI: 10.1287/opre.2018.1780
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    References listed on IDEAS

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    1. Mabel C. Chou & Geoffrey A. Chua & Chung-Piaw Teo & Huan Zheng, 2011. "Process Flexibility Revisited: The Graph Expander and Its Applications," Operations Research, INFORMS, vol. 59(5), pages 1090-1105, October.
    2. Antoine Désir & Vineet Goyal & Yehua Wei & Jiawei Zhang, 2016. "Sparse Process Flexibility Designs: Is the Long Chain Really Optimal?," Operations Research, INFORMS, vol. 64(2), pages 416-431, April.
    3. Xuan Wang & Jiawei Zhang, 2015. "Process Flexibility: A Distribution-Free Bound on the Performance of k -Chain," Operations Research, INFORMS, vol. 63(3), pages 555-571, June.
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    7. Mabel C. Chou & Geoffrey A. Chua & Chung-Piaw Teo & Huan Zheng, 2010. "Design for Process Flexibility: Efficiency of the Long Chain and Sparse Structure," Operations Research, INFORMS, vol. 58(1), pages 43-58, February.
    8. Xi Chen & Jiawei Zhang & Yuan Zhou, 2015. "Optimal Sparse Designs for Process Flexibility via Probabilistic Expanders," Operations Research, INFORMS, vol. 63(5), pages 1159-1176, October.
    9. David Simchi-Levi & Yehua Wei, 2015. "Worst-Case Analysis of Process Flexibility Designs," Operations Research, INFORMS, vol. 63(1), pages 166-185, February.
    10. Cong Shi & Yehua Wei & Yuan Zhong, 2019. "Process Flexibility for Multiperiod Production Systems," Operations Research, INFORMS, vol. 67(5), pages 1300-1320, September.
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    Cited by:

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    2. Zhen Xu & Hailun Zhang & Jiheng Zhang & Rachel Q. Zhang, 2020. "Online Demand Fulfillment Under Limited Flexibility," Management Science, INFORMS, vol. 66(10), pages 4667-4685, October.
    3. Liu, Hongda & Zhao, Haifeng & Li, Shiyuan, 2023. "Future social change of manufacturing and service industries: Service-oriented manufacturing under the integration of innovation-flows drive," Technological Forecasting and Social Change, Elsevier, vol. 196(C).
    4. Cong Shi & Yehua Wei & Yuan Zhong, 2019. "Process Flexibility for Multiperiod Production Systems," Operations Research, INFORMS, vol. 67(5), pages 1300-1320, September.
    5. Shixin Wang & Xuan Wang & Jiawei Zhang, 2021. "A Review of Flexible Processes and Operations," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1804-1824, June.
    6. Timothy C. Y. Chan & Daniel Letourneau & Benjamin G. Potter, 2022. "Sparse flexible design: a machine learning approach," Flexible Services and Manufacturing Journal, Springer, vol. 34(4), pages 1066-1116, December.

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