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Designing robust coverage networks to hedge against worst-case facility losses

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  • O'Hanley, Jesse R.
  • Church, Richard L.

Abstract

In order to design a coverage-type service network that is robust to the worst instances of long-term facility loss, we develop a facility location-interdiction model that maximizes a combination of initial coverage by p facilities and the minimum coverage level following the loss of the most critical r facilities. The problem is formulated both as a mixed-integer program and as a bilevel mixed-integer program. To solve the bilevel program optimally, a decomposition algorithm is presented, whereby the original bilevel program is decoupled into an upper level master problem and a lower level subproblem. After sequentially solving these problems, supervalid inequalities can be generated and appended to the upper level master in an attempt to force it away from clearly dominated solutions. Computational results show that when solved to optimality, the bilevel decomposition algorithm is up to several orders of magnitude faster than performing branch and bound on the mixed-integer program.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:209:y:2011:i:1:p:23-36
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    References listed on IDEAS

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    1. Lukac, Zrinka & Soric, Kristina & Rosenzweig, Visnja Vojvodic, 2008. "Production planning problem with sequence dependent setups as a bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1504-1512, June.
    2. 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.
    3. Kathleen Hogan & Charles ReVelle, 1986. "Concepts and Applications of Backup Coverage," Management Science, INFORMS, vol. 32(11), pages 1434-1444, November.
    4. 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.
    5. Uno, Takeshi & Katagiri, Hideki, 2008. "Single- and multi-objective defensive location problems on a network," European Journal of Operational Research, Elsevier, vol. 188(1), pages 76-84, July.
    6. Wen, U. P. & Huang, A. D., 1996. "A simple Tabu Search method to solve the mixed-integer linear bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 563-571, February.
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    Citations

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    Cited by:

    1. Sarhadi, Hassan & Tulett, David M. & Verma, Manish, 2017. "An analytical approach to the protection planning of a rail intermodal terminal network," European Journal of Operational Research, Elsevier, vol. 257(2), pages 511-525.
    2. F. Parvaresh & S. Hashemi Golpayegany & S. Moattar Husseini & B. Karimi, 2013. "Solving the p-hub Median Problem Under Intentional Disruptions Using Simulated Annealing," Networks and Spatial Economics, Springer, vol. 13(4), pages 445-470, December.
    3. repec:eee:transe:v:102:y:2017:i:c:p:13-37 is not listed on IDEAS
    4. Zhang, Ying & Snyder, Lawrence V. & Ralphs, Ted K. & Xue, Zhaojie, 2016. "The competitive facility location problem under disruption risks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 453-473.
    5. repec:eee:reensy:v:169:y:2018:i:c:p:51-62 is not listed on IDEAS
    6. Medal, Hugh R. & Pohl, Edward A. & Rossetti, Manuel D., 2014. "A multi-objective integrated facility location-hardening model: Analyzing the pre- and post-disruption tradeoff," European Journal of Operational Research, Elsevier, vol. 237(1), pages 257-270.
    7. repec:eee:ejores:v:267:y:2018:i:2:p:496-512 is not listed on IDEAS
    8. Davood Shishebori & Lawrence Snyder & Mohammad Jabalameli, 2014. "A Reliable Budget-Constrained FL/ND Problem with Unreliable Facilities," Networks and Spatial Economics, Springer, vol. 14(3), pages 549-580, December.
    9. repec:eee:transe:v:114:y:2018:i:c:p:196-219 is not listed on IDEAS
    10. Starita, Stefano & Scaparra, Maria Paola, 2016. "Optimizing dynamic investment decisions for railway systems protection," European Journal of Operational Research, Elsevier, vol. 248(2), pages 543-557.
    11. Albareda-Sambola, Maria & Hinojosa, Yolanda & Puerto, Justo, 2015. "The reliable p-median problem with at-facility service," European Journal of Operational Research, Elsevier, vol. 245(3), pages 656-666.
    12. 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.
    13. Shishebori, Davood & Yousefi Babadi, Abolghasem, 2015. "Robust and reliable medical services network design under uncertain environment and system disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 77(C), pages 268-288.
    14. Espejo, Inmaculada & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2015. "Capacitated p-center problem with failure foresight," European Journal of Operational Research, Elsevier, vol. 247(1), pages 229-244.
    15. repec:eee:ejores:v:265:y:2018:i:3:p:872-881 is not listed on IDEAS
    16. Karabulut, Ezgi & Aras, Necati & Kuban Altınel, İ., 2017. "Optimal sensor deployment to increase the security of the maximal breach path in border surveillance," European Journal of Operational Research, Elsevier, vol. 259(1), pages 19-36.
    17. 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.
    18. repec:eee:ejores:v:267:y:2018:i:1:p:23-39 is not listed on IDEAS
    19. Mohammadi, M. & Dehbari, S. & Vahdani, Behnam, 2014. "Design of a bi-objective reliable healthcare network with finite capacity queue under service covering uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 15-41.

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