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A facility reliability problem: Formulation, properties, and algorithm

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  • Michael Lim
  • Mark S. Daskin
  • Achal Bassamboo
  • Sunil Chopra

Abstract

Having a robustly designed supply chain network is one of the most effective ways to hedge against network disruptions because contingency plans in the event of a disruption are often significantly limited. In this article, we study the facility reliability problem: how to design a reliable supply chain network in the presence of random facility disruptions with the option of hardening selected facilities. We consider a facility location problem incorporating two types of facilities, one that is unreliable and another that is reliable (which is not subject to disruption, but is more expensive). We formulate this as a mixed integer programming model and develop a Lagrangian Relaxation‐based solution algorithm. We derive structural properties of the problem and show that for some values of the disruption probability, the problem reduces to the classical uncapacitated fixed charge location problem. In addition, we show that the proposed solution algorithm is not only capable of solving large‐scale problems, but is also computationally effective. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • Michael Lim & Mark S. Daskin & Achal Bassamboo & Sunil Chopra, 2010. "A facility reliability problem: Formulation, properties, and algorithm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(1), pages 58-70, February.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:1:p:58-70
    DOI: 10.1002/nav.20385
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    References listed on IDEAS

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    1. Mark S. Daskin, 1983. "A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution," Transportation Science, INFORMS, vol. 17(1), pages 48-70, February.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. Brian Tomlin, 2006. "On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks," Management Science, INFORMS, vol. 52(5), pages 639-657, May.
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    Cited by:

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    3. Luohao Tang & Cheng Zhu & Zaili Lin & Jianmai Shi & Weiming Zhang, 2016. "Reliable Facility Location Problem with Facility Protection," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-24, September.
    4. Donya Rahmani, 2019. "Designing a robust and dynamic network for the emergency blood supply chain with the risk of disruptions," Annals of Operations Research, Springer, vol. 283(1), pages 613-641, December.
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    6. Yu, Guodong & Zhang, Jie, 2018. "Multi-dual decomposition solution for risk-averse facility location problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 70-89.
    7. Parajuli, Anubhuti & Kuzgunkaya, Onur & Vidyarthi, Navneet, 2021. "The impact of congestion on protection decisions in supply networks under disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    8. Bhuiyan, Tanveer Hossain & Medal, Hugh R. & Harun, Sarah, 2020. "A stochastic programming model with endogenous and exogenous uncertainty for reliable network design under random disruption," European Journal of Operational Research, Elsevier, vol. 285(2), pages 670-694.
    9. Dixit, Vijaya & Verma, Priyanka & Tiwari, Manoj Kumar, 2020. "Assessment of pre and post-disaster supply chain resilience based on network structural parameters with CVaR as a risk measure," International Journal of Production Economics, Elsevier, vol. 227(C).
    10. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    11. Nader Azad & Elkafi Hassini, 2019. "A Benders Decomposition Method for Designing Reliable Supply Chain Networks Accounting for Multimitigation Strategies and Demand Losses," Transportation Science, INFORMS, vol. 53(5), pages 1287-1312, September.
    12. Nader Azad & Georgios Saharidis & Hamid Davoudpour & Hooman Malekly & Seyed Yektamaram, 2013. "Strategies for protecting supply chain networks against facility and transportation disruptions: an improved Benders decomposition approach," Annals of Operations Research, Springer, vol. 210(1), pages 125-163, November.
    13. Mengshi Lu & Lun Ran & Zuo-Jun Max Shen, 2015. "Reliable Facility Location Design Under Uncertain Correlated Disruptions," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 445-455, October.
    14. Robert Aboolian & Tingting Cui & Zuo-Jun Max Shen, 2013. "An Efficient Approach for Solving Reliable Facility Location Models," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 720-729, November.
    15. Cheng, Chun & Adulyasak, Yossiri & Rousseau, Louis-Martin, 2021. "Robust facility location under demand uncertainty and facility disruptions," Omega, Elsevier, vol. 103(C).
    16. Wang, Zhaodong & Xie, Siyang & Ouyang, Yanfeng, 2022. "Planning reliable service facility location against disruption risks and last-mile congestion in a continuous space," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 123-140.
    17. Michael K. Lim & Achal Bassamboo & Sunil Chopra & Mark S. Daskin, 2013. "Facility Location Decisions with Random Disruptions and Imperfect Estimation," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 239-249, May.
    18. Arash Gourtani & Tri-Dung Nguyen & Huifu Xu, 2020. "A distributionally robust optimization approach for two-stage facility location problems," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 141-172, June.
    19. Fahimnia, Behnam & Jabbarzadeh, Armin & Sarkis, Joseph, 2018. "Greening versus resilience: A supply chain design perspective," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 119(C), pages 129-148.
    20. Aldrighetti, Riccardo & Battini, Daria & Ivanov, Dmitry & Zennaro, Ilenia, 2021. "Costs of resilience and disruptions in supply chain network design models: A review and future research directions," International Journal of Production Economics, Elsevier, vol. 235(C).
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    22. Mozhu Wang & Jianming Yao, 2023. "A reliable location design of unmanned vending machines based on customer satisfaction," Electronic Commerce Research, Springer, vol. 23(1), pages 541-575, March.

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