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Optimizing fortification plan of capacitated facilities with maximum distance limits

  • Girish Ch. DeyEmail author
  • Mamata Jenamani
Theoretical Article


Facilities are the backbone of many supply systems and are always vulnerable to potential attacks. Considering that when disruptions occur, limits on transportation distances are essential for many important supply systems like emergency items and perishable items, this paper presents fortification plan of capacitated facilities with maximum distance limits. The problem is formulated as a tri-level mixed integer problem, which considers capacitated facilities, interdiction, and fortification budget limit simultaneously. Then it is simplified to a bi-level problem and solved by implicit enumeration algorithm performed on a binary tree. Computational results obtained from 64 randomly generated test instances are reported along with the benefit of maximum distance limits.


Fortification Interdiction Tri-level programming Maximum distance limits 



  1. 1.
    Akbari-Jafarabadi, M., Tavakkoli-Moghaddam, R., Mahmoodjanloo, M., Rahimi, Y.: A tri-level r-interdiction median model for a facility location problem under imminent attack. Comput. Ind. Eng. 114, 151–165 (2017)Google Scholar
  2. 2.
    Aksen, D., Aras, N.: A bilevel fixed charge location model for facilities under imminent attack. Comput. Oper. Res. 39(7), 1364–1381 (2012)Google Scholar
  3. 3.
    Aksen, D., Piyade, N., Aras, N.: The budget constrained r-interdiction median problem with capacity expansion. Central Eur. J. Oper. Res. 18(3), 269–291 (2010)Google Scholar
  4. 4.
    Aksen, D., Aras, N., Piyade, N.: A bilevel p-median model for the planning and protection of critical facilities. J. Heuristics 19(2), 373–398 (2013)Google Scholar
  5. 5.
    Aksen, D., Akca, S.Ş., Aras, N.: A bilevel partial interdiction problem with capacitated facilities and demand outsourcing. Comput. Oper. Res. 41, 346–358 (2014)Google Scholar
  6. 6.
    Aliakbarian, N., Dehghanian, F., Salari, M.: A bi-level programming model for protection of hierarchical facilities under imminent attacks. Comput. Oper. Res. 64, 210–224 (2015)Google Scholar
  7. 7.
    Basu, S., Sharma, M., Ghosh, P.S.: Metaheuristic applications on discrete facility location problems: a survey. OPSEARCH 52(3), 530–561 (2015)Google Scholar
  8. 8.
    Church, R.L., Scaparra, M.P.: Analysis of facility systems reliability when subject to attack or a natural disaster. In: Murray, A.T., Grubesic, T.H. (eds.) Critical Infrastructure, pp. 221–241. Springer, Berlin (2007)Google Scholar
  9. 9.
    Church, R.L., Scaparra, M.P.: Protecting critical assets: the r-interdiction median problem with fortification. Geogr. Anal. 39(2), 129–146 (2007b)Google Scholar
  10. 10.
    Church, R.L., Scaparra, M.P., Middleton, R.S.: Identifying critical infrastructure: the median and covering facility interdiction problems. Ann. Assoc. Am. Geogr. 94(3), 491–502 (2004)Google Scholar
  11. 11.
    Fathali, J.: Backup multifacility location problem with l p norm. OPSEARCH 52(2), 382–391 (2015)Google Scholar
  12. 12.
    Ghaffarinasab, N., Atayi, R.: An implicit enumeration algorithm for the hub interdiction median problem with fortification. Eur. J. Oper. Res. 267(1), 23–39 (2018)Google Scholar
  13. 13.
    He, M., Du, G., Zhang, X., Zheng, Z.: A cooperative network interdiction model and its optimization solution algorithm. Int. J. Comput. Intell. Syst. 11(1), 560–572 (2018)Google Scholar
  14. 14.
    Khanduzi, R., Maleki, H.R., Akbari, R.: Two novel combined approaches based on TLBO and PSO for a partial interdiction/fortification problem using capacitated facilities and budget constraint. Soft Comput. 22(17), 1–19 (2018)Google Scholar
  15. 15.
    Liberatore, F., Scaparra, M.P., Daskin, M.S.: Analysis of facility protection strategies against an uncertain number of attacks: the stochastic r-interdiction median problem with fortification. Comput. Oper. Res. 38(1), 357–366 (2011)Google Scholar
  16. 16.
    Liberatore, F., Scaparra, M.P., Daskin, M.S.: Hedging against disruptions with ripple effects in location analysis. Omega 40(1), 21–30 (2012)Google Scholar
  17. 17.
    Losada, C., Scaparra, M.P., Church, R.L., Daskin, M.S.: The stochastic interdiction median problem with disruption intensity levels. Ann. Oper. Res. 201(1), 345–365 (2012)Google Scholar
  18. 18.
    Losada, C., Scaparra, M.P., OHanley, J.R.: Optimizing system resilience: a facility protection model with recovery time. Eur. J. Oper. Res. 217(3), 519–530 (2012b)Google Scholar
  19. 19.
    Medal, H.R., Pohl, E.A., Rossetti, M.D.: A multi-objective integrated facility location-hardening model: analyzing the pre-and post-disruption tradeoff. Eur. J. Oper. Res. 237(1), 257–270 (2014)Google Scholar
  20. 20.
    Moteff, J., Parfomak, P.: Critical infrastructure and key assets: definition and identification. DTIC Document (2004)Google Scholar
  21. 21.
    RFE/RL. Afghanistan: mobile-phone towers are Taliban’s new target. March 2008. Retrieved on 22 April 2016
  22. 22.
    Saharidis, G.K., Ierapetritou, M.G.: Resolution method for mixed integer bi-level linear problems based on decomposition technique. J. Glob. Optim. 44(1), 29–51 (2009)Google Scholar
  23. 23.
    Sarhadi, H., Tulett, D.M., Verma, M.: An analytical approach to the protection planning of a rail intermodal terminal network. Eur. J. Oper. Res. 257(2), 511–525 (2017)Google Scholar
  24. 24.
    Scaparra, M.P., Church, R.: Protecting supply systems to mitigate potential disaster a model to fortify capacitated facilities. Int. Reg. Sci. Rev. 35(2), 188–210 (2012)Google Scholar
  25. 25.
    Scaparra, M.P., Church, R.L.: A bilevel mixed-integer program for critical infrastructure protection planning. Comput. Oper. Res. 35(6), 1905–1923 (2008)Google Scholar
  26. 26.
    Scaparra, M.P., Starita, S., Sterle, C.: Optimizing investment decisions for railway systems protection. In: Setola, R., Sforza, A., Vittorini, V., Pragliola, C. (eds.) Railway Infrastructure Security, pp. 215–233. Springer, Cham (2015)Google Scholar
  27. 27.
    Smith, R.: Assault on California power stations raises alarm on potential for terrorism. February (2014). Retrieved on 22 April 2016
  28. 28.
    Smith, R.: U.S. risks national blackout from small-scale attack. March (2014). Retrieved on 22 April 2016
  29. 29.
    Starita, S., Paola Scaparra, M.: Passenger railway network protection: a model with variable post-disruption demand service. J. Oper. Res. Soc. 69(4), 603–618 (2018)Google Scholar
  30. 30.
    Starita, S., Scaparra, M.P.: Optimizing dynamic investment decisions for railway systems protection. Eur. J. Oper. Res. 248(2), 543–557 (2016)Google Scholar
  31. 31.
    Starita, S., Scaparra, M.P., OHanley, J.R.: A dynamic model for road protection against flooding. J. Oper. Res. Soc. 68(1), 74–88 (2017)Google Scholar
  32. 32.
    Toregas, C., Swain, R., ReVelle, C., Bergman, L.: The location of emergency service facilities. Oper. Res. 19(6), 1363–1373 (1971)Google Scholar
  33. 33.
    Wollmer, R.: Removing arcs from a network. Oper. Res. 12(6), 934–940 (1964)Google Scholar
  34. 34.
    Wood, R.K.: Bilevel Network Interdiction Models: Formulations and Solutions. Wiley Encyclopedia of Operations Research and Management Science. Wiley, Hoboken (2010)Google Scholar
  35. 35.
    Zhang, C., Ramirez-Marquez, J.E., Li, Q.: Locating and protecting facilities from intentional attacks using secrecy. Reliab. Eng. Syst. Saf. 169, 51–62 (2018)Google Scholar
  36. 36.
    Zhang, X., Zheng, Z., Zhang, S., Du, W.: Partial interdiction median models for multi-sourcing supply systems. Int. J. Adv. Manuf. Technol. 84(1–4), 165–181 (2016)Google Scholar
  37. 37.
    Zhang, X.-Y., Zheng, Z., Cai, K.-Y.: A fortification model for decentralized supply systems and its solution algorithms. IEEE Trans. Reliab. 67(1), 381–400 (2018)Google Scholar
  38. 38.
    Zhu, Y., Zheng, Z., Zhang, X., Cai, K.: The r-interdiction median problem with probabilistic protection and its solution algorithm. Comput. Oper. Res. 40(1), 451–462 (2013)Google Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringIIT KharagpurKharagpurIndia

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