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

Ting L. Lei, Daoqin Tong

Research output: Contribution to journalArticle

10 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)491-512
Number of pages22
JournalJournal of Geographical Systems
Volume15
Issue number4
DOIs
StatePublished - Oct 2013

Fingerprint

p-median
linear programing
programming
location-allocation model
facility location
software
weaver
services
church
demand

Keywords

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

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes

Cite this

Hedging against service disruptions : An expected median location problem with site-dependent failure probabilities. / Lei, Ting L.; Tong, Daoqin.

In: Journal of Geographical Systems, Vol. 15, No. 4, 10.2013, p. 491-512.

Research output: Contribution to journalArticle

@article{62ebe2748d25417a96b1a7f0e54eaca6,
title = "Hedging against service disruptions: An expected median location problem with site-dependent failure probabilities",
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.",
keywords = "Closest assignment, Integer linear programming, Location analysis, p-Median problem, System vulnerability",
author = "Lei, {Ting L.} and Daoqin Tong",
year = "2013",
month = "10",
doi = "10.1007/s10109-012-0175-y",
language = "English (US)",
volume = "15",
pages = "491--512",
journal = "Journal of Geographical Systems",
issn = "1435-5930",
publisher = "Springer Verlag",
number = "4",

}

TY - JOUR

T1 - Hedging against service disruptions

T2 - An expected median location problem with site-dependent failure probabilities

AU - Lei, Ting L.

AU - Tong, Daoqin

PY - 2013/10

Y1 - 2013/10

N2 - 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.

AB - 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.

KW - Closest assignment

KW - Integer linear programming

KW - Location analysis

KW - p-Median problem

KW - System vulnerability

UR - http://www.scopus.com/inward/record.url?scp=84885650212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885650212&partnerID=8YFLogxK

U2 - 10.1007/s10109-012-0175-y

DO - 10.1007/s10109-012-0175-y

M3 - Article

AN - SCOPUS:84885650212

VL - 15

SP - 491

EP - 512

JO - Journal of Geographical Systems

JF - Journal of Geographical Systems

SN - 1435-5930

IS - 4

ER -