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

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  • O’Hanley, Jesse R.
  • Scaparra, M. Paola
  • García, Sergio

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.

Suggested Citation

  • O’Hanley, Jesse R. & Scaparra, M. Paola & García, Sergio, 2013. "Probability chains: A general linearization technique for modeling reliability in facility location and related problems," European Journal of Operational Research, Elsevier, vol. 230(1), pages 63-75.
    • Handle: RePEc:eee:ejores:v:230:y:2013:i:1:p:63-75
    DOI: 10.1016/j.ejor.2013.03.021
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    1. Mark S. Daskin, 1983. "A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution," Transportation Science, INFORMS, vol. 17(1), pages 48-70, February.
    2. Marianov, Vladimir & ReVelle, Charles, 1996. "The Queueing Maximal availability location problem: A model for the siting of emergency vehicles," European Journal of Operational Research, Elsevier, vol. 93(1), pages 110-120, August.
    3. Tingting Cui & Yanfeng Ouyang & Zuo-Jun Max Shen, 2010. "Reliable Facility Location Design Under the Risk of Disruptions," Operations Research, INFORMS, vol. 58(4-part-1), pages 998-1011, August.
    4. Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 189(1), pages 76-92, August.
    5. Kathleen Hogan & Charles ReVelle, 1986. "Concepts and Applications of Backup Coverage," Management Science, INFORMS, vol. 32(11), pages 1434-1444, November.
    6. Chaya Losada & M. Scaparra & Richard Church & Mark Daskin, 2012. "The stochastic interdiction median problem with disruption intensity levels," Annals of Operations Research, Springer, vol. 201(1), pages 345-365, December.
    7. Rajan Batta & June M. Dolan & Nirup N. Krishnamurthy, 1989. "The Maximal Expected Covering Location Problem: Revisited," Transportation Science, INFORMS, vol. 23(4), pages 277-287, November.
    8. Mozart Menezes & O. Berman & D. Krass, 2007. "Facility Reliability Issues in Network p-Median Problems: Strategic Centralization and Co-location Effects," Post-Print halshs-00170396, HAL.
    9. Lian Qi & Zuo-Jun Max Shen & Lawrence V. Snyder, 2010. "The Effect of Supply Disruptions on Supply Chain Design Decisions," Transportation Science, INFORMS, vol. 44(2), pages 274-289, May.
    10. Robert G. Haight & Charles S. Revelle & Stephanie A. Snyder, 2000. "An Integer Optimization Approach to a Probabilistic Reserve Site Selection Problem," Operations Research, INFORMS, vol. 48(5), pages 697-708, October.
    11. O'Hanley, Jesse R. & Church, Richard L., 2011. "Designing robust coverage networks to hedge against worst-case facility losses," European Journal of Operational Research, Elsevier, vol. 209(1), pages 23-36, February.
    12. Owen, Susan Hesse & Daskin, Mark S., 1998. "Strategic facility location: A review," European Journal of Operational Research, Elsevier, vol. 111(3), pages 423-447, December.
    13. Jeffrey D. Camm & Susan K. Norman & Stephen Polasky & Andrew R. Solow, 2002. "Nature Reserve Site Selection to Maximize Expected Species Covered," Operations Research, INFORMS, vol. 50(6), pages 946-955, December.
    14. Charles ReVelle & Kathleen Hogan, 1989. "The Maximum Availability Location Problem," Transportation Science, INFORMS, vol. 23(3), pages 192-200, August.
    15. Cui, Tingting & Ouyang, Yanfeng & Shen, Zuo-Jun Max J, 2010. "Reliable Facility Location Design under the Risk of Disruptions," University of California Transportation Center, Working Papers qt5sh2c7pw, University of California Transportation Center.
    16. Zuo-Jun Max Shen & Roger Lezhou Zhan & Jiawei Zhang, 2011. "The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 470-482, August.
    17. Liberatore, Federico & Scaparra, Maria P. & Daskin, Mark S., 2012. "Hedging against disruptions with ripple effects in location analysis," Omega, Elsevier, vol. 40(1), pages 21-30, January.
    18. Losada, Chaya & Scaparra, M. Paola & O’Hanley, Jesse R., 2012. "Optimizing system resilience: A facility protection model with recovery time," European Journal of Operational Research, Elsevier, vol. 217(3), pages 519-530.
    19. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    20. Lawrence V. Snyder & Mark S. Daskin, 2005. "Reliability Models for Facility Location: The Expected Failure Cost Case," Transportation Science, INFORMS, vol. 39(3), pages 400-416, August.
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