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Probability chains: A general linearization technique for modeling reliability in facility location and related problems

O'Hanley, J.R., Scaparra, M.P., García-Quiles, S. (2013) Probability chains: A general linearization technique for modeling reliability in facility location and related problems. European Journal of Operational Research, 230 (1). pp. 63-75. ISSN 0377-2217. (doi:10.1016/j.ejor.2013.03.021) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1016/j.ejor.2013.03.021

Abstract

In this paper, we propose an efficient technique for linearizing facility location problems with site-dependent failure probabilities, focusing on the unreliable p-median problem. Our approach is based on the use of a specialized flow network, which we refer to as a probability chain, to evaluate compound probability terms. The resulting linear model is compact in size. The method can be employed in a straightforward way to linearize similarly structured problems, such as the maximum expected covering problem. We further discuss how probability chains can be extended to problems with co-location and other, more general problem classes. Additional lower bounds as well as valid inequalities for use within a branch and cut algorithm are introduced to significantly speed up overall solution time. Computational results are presented for several test problems showing the efficiency of our linear model in comparison to existing problem formulations.

Item Type: Article
DOI/Identification number: 10.1016/j.ejor.2013.03.021
Uncontrolled keywords: Facility location; Reliability; Linearization; Probability chains; Probability flow networks; Valid inequalities
Subjects: H Social Sciences > HA Statistics > HA33 Management Science
Divisions: Faculties > Social Sciences > Kent Business School > Management Science
Faculties > Social Sciences > Kent Business School > Centre for Logistics and Heuristic Organisation (CLHO)
Depositing User: Jesse O'Hanley
Date Deposited: 30 May 2013 10:25 UTC
Last Modified: 20 Jun 2019 11:20 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/34015 (The current URI for this page, for reference purposes)
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