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

Ting L. Lei, Daoqin Tong

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)491-512
Number of pages22
JournalJournal of Geographical Systems
Issue number4
StatePublished - Oct 2013
Externally publishedYes


  • Closest assignment
  • Integer linear programming
  • Location analysis
  • System vulnerability
  • p-Median problem

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes


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