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Worst-Case Analysis of Process Flexibility Designs

Author

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  • David Simchi-Levi

    (Engineering Systems Division, Department of Civil and Environmental Engineering, and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Yehua Wei

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708-0120)

Abstract

Theoretical studies of process flexibility designs have mostly focused on expected sales. In this paper, we take a different approach by studying process flexibility designs from the worst-case point of view. To study the worst-case performances, we introduce the plant cover indices (PCIs), defined by bottlenecks in flexibility designs containing a fixed number of products. We prove that given a flexibility design, a general class of worst-case performance measures can be expressed as functions of the design’s PCIs and the given uncertainty set. This result has several major implications. First, it suggests a method to compare the worst-case performances of different flexibility designs without the need to know the specifics of the uncertainty sets. Second, we prove that under symmetric uncertainty sets and a large class of worst-case performance measures, the long chain, a celebrated sparse design, is superior to a large class of sparse flexibility designs, including any design that has a degree of two on each of its product nodes. Third, we show that under stochastic demand, the classical Jordan and Graves (JG) index can be expressed as a function of the PCIs. Furthermore, the PCIs motivate a modified JG index that is shown to be more effective in our numerical study. Finally, the PCIs lead to a heuristic for finding sparse flexibility designs that perform well under expected sales and have lower risk measures in our computational study.

Suggested Citation

  • David Simchi-Levi & Yehua Wei, 2015. "Worst-Case Analysis of Process Flexibility Designs," Operations Research, INFORMS, vol. 63(1), pages 166-185, February.
  • Handle: RePEc:inm:oropre:v:63:y:2015:i:1:p:166-185
    DOI: 10.1287/opre.2014.1334
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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.
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    5. David Simchi-Levi & Yehua Wei, 2012. "Understanding the Performance of the Long Chain and Sparse Designs in Process Flexibility," Operations Research, INFORMS, vol. 60(5), pages 1125-1141, October.
    6. Tianhu Deng & Zuo-Jun Max Shen, 2013. "Process Flexibility Design in Unbalanced Networks," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 24-32, April.
    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.
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    Citations

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    Cited by:

    1. 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.
    2. Timothy C. Y. Chan & Douglas Fearing, 2019. "Process Flexibility in Baseball: The Value of Positional Flexibility," Management Science, INFORMS, vol. 65(4), pages 1642-1666, April.
    3. Lingxiu Dong & Duo Shi & Fuqiang Zhang, 2022. "3D Printing and Product Assortment Strategy," Management Science, INFORMS, vol. 68(8), pages 5724-5744, August.
    4. Jingui Xie & Yiming Fan & Mabel C. Chou, 2017. "Flexibility design in loss and queueing systems: efficiency of k-chain configuration," Flexible Services and Manufacturing Journal, Springer, vol. 29(2), pages 286-308, June.
    5. Cong Shi & Yehua Wei & Yuan Zhong, 2019. "Process Flexibility for Multiperiod Production Systems," Operations Research, INFORMS, vol. 67(5), pages 1300-1320, September.
    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.
    7. 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.
    8. Zhenzhen Yan & Sarah Yini Gao & Chung Piaw Teo, 2018. "On the Design of Sparse but Efficient Structures in Operations," Management Science, INFORMS, vol. 64(7), pages 3421-3445, July.
    9. Shixin Wang, 2023. "The Power of Simple Menus in Robust Selling Mechanisms," Papers 2310.17392, arXiv.org, revised Sep 2024.
    10. 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.
    11. Henao, César Augusto & Mercado, Yessica Andrea & González, Virginia I. & Lüer-Villagra, Armin, 2023. "Multiskilled personnel assignment with k-chaining considering the learning-forgetting phenomena," International Journal of Production Economics, Elsevier, vol. 265(C).
    12. Rujeerapaiboon, Napat & Zhong, Yuanguang & Zhu, Dan, 2023. "Resilience of long chain under disruption," European Journal of Operational Research, Elsevier, vol. 309(2), pages 597-615.
    13. Guodong Lyu & Wang-Chi Cheung & Mabel C. Chou & Chung-Piaw Teo & Zhichao Zheng & Yuanguang Zhong, 2019. "Capacity Allocation in Flexible Production Networks: Theory and Applications," Management Science, INFORMS, vol. 65(11), pages 5091-5109, November.
    14. 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.
    15. Dipankar Bose & A. K. Chatterjee & Samir Barman, 2016. "Towards dominant flexibility configurations in strategic capacity planning under demand uncertainty," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 604-619, September.
    16. 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.

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