Hedging against service disruptions: an expected median location problem with site-dependent failure probabilities |
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| Authors: | Ting L Lei Daoqin Tong |
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| Institution: | 1. University of California, Santa Barbara, Santa Barbara, CA, 93106, USA
2. School of Geography and Development, University of Arizona, 408 Harvill Building, Box#2, Tucson, AZ, 85721, USA
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| 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. |
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