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Hedging against service disruptions: an expected median location problem with site-dependent failure probabilities

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  • Ting Lei
  • Daoqin Tong

Abstract

The vector assignment p-median problem (VAPMP) (Weaver and Church in Transp Sci 19(1):58–74, 1985 ) was one of the first location-allocation models developed to handle split assignment of a demand to multiple facilities. The underlying construct of the VAPMP has been subsequently used in a number of reliable facility location and backup location models. Although in many applications the chance that a facility fails may vary substantially with locations, many existing models have assumed a uniform failure probability across all sites. As an improvement, this paper proposes a new model, the expected p-median problem as a generalization of existing approaches by explicitly considering site-dependent failure probabilities. Multi-level closest assignment constraints and two efficient integer linear programming (ILP) formulations are introduced. While prior research generally concludes that similar problems are not integer-friendly and cannot be solved by ILP software, computational results show that our model can be used to solve medium-sized location problems optimally using existing ILP software. Moreover, the new model can be used to formulate other reliable or expected location problems with consideration of site-dependent failure probabilities. Copyright Springer-Verlag 2013

Suggested Citation

  • Ting Lei & Daoqin Tong, 2013. "Hedging against service disruptions: an expected median location problem with site-dependent failure probabilities," Journal of Geographical Systems, Springer, vol. 15(4), pages 491-512, October.
  • Handle: RePEc:kap:jgeosy:v:15:y:2013:i:4:p:491-512
    DOI: 10.1007/s10109-012-0175-y
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    Cited by:

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    2. Bangjun Wang & Guoqiang Shen & Xingshen Wang & Yunwen Dong & Ziyu Li, 2024. "Hub-and-Spoke Network Optimization with Flow Delay Cost: The Case of Goods Delivery on Urban Logistics Networks in Eastern China," Mathematics, MDPI, vol. 12(10), pages 1-19, May.
    3. Dimitrov, Nedialko B. & Solow, Daniel & Szmerekovsky, Joseph & Guo, Jia, 2017. "Emergency relocation of items using single trips: Special cases of the Multiple Knapsack Assignment Problem," European Journal of Operational Research, Elsevier, vol. 258(3), pages 938-942.
    4. Hyun Kim & Megan S. Ryerson, 2017. "The q-Ad Hoc Hub Location Problem for Multi-modal Networks," Networks and Spatial Economics, Springer, vol. 17(3), pages 1015-1041, September.
    5. 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.
    6. 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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    More about this item

    Keywords

    Location analysis; System vulnerability; Integer linear programming; p-Median problem; Closest assignment; C61; C44;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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