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An exact approach for the r-interdiction covering problem with fortification

  • Marcos Costa RoboredoEmail author
  • Luiz Aizemberg
  • Artur Alves Pessoa
Original Paper
  • 95 Downloads

Abstract

In this paper we treat the r-interdiction covering problem with fortification (RICF). The environment of this problem is composed of a set of customers J and a set of facilities I. For each customer j, there is set of facilities containing the facilities that can cover the demand of j. The system efficiency is given by the sum of the total covered demand. The facilities are subject to interdictions. When a facility is interdicted, it can not cover the demand of any customer. To mitigate the negative impact of the interdictions on the system efficiency, the system planner can fortify a subset of facilities. If a facility is fortified then it can not be interdicted. The RICF consists of choosing q facilities to be fortified knowing that r not fortified facilities will be interdicted at the worst case. We propose a branch-and-cut algorithm for the problem. Our results are compared with the exact method found in the literature, being faster for the most instances, mainly the large ones.

Keywords

Integer programming Branch-and-cut algorithm r-Interdiction covering problem with fortification 

References

  1. Alderson DL, Brown GG, Carlyle WM (2014) Assessing and improving operational resilience of critical infrastructures and other systems. In: Bridging Data and Decisions. Informs, pp 180–215Google Scholar
  2. Altner DS, Ergun Ö, Uhan NA (2010) The maximum flow network interdiction problem: valid inequalities, integrality gaps, and approximability. Oper Res Lett 38(1):33–38CrossRefGoogle Scholar
  3. Berman O, Drezner T, Drezner Z, Wesolowsky G (2009) A defensive maximal covering problem on a network. Int Trans Oper Res 16(1):69–86CrossRefGoogle Scholar
  4. Brown G, Carlyle M, Salmerón J, Wood K (2006) Defending critical infrastructure. Interfaces 36(6):530–544CrossRefGoogle Scholar
  5. Choi Y, Suzuki T (2013) Protection strategies for critical retail facilities: applying interdiction median and maximal covering problems with fortification. J Oper Res Soc Japan 56(1):38–55Google Scholar
  6. Church RL, Scaparra MP (2007) Protecting critical assets: the r-interdiction median problem with fortification. Geogr Anal 39(2):129–146CrossRefGoogle Scholar
  7. Church RL, Scaparra MP, Middleton RS (2004) Identifying critical infrastructure: the median and covering facility interdiction problems. Ann Assoc Am Geogr 94(3):491–502CrossRefGoogle Scholar
  8. Dong L, Xu-Chen L, Xiang-Tao Y, Fei W (2010) A model for allocating protection resources in military logistics distribution system based on maximal covering problem. In: 2010 international conference on logistics systems and intelligent management, vol 1. IEEE, pp 98–101Google Scholar
  9. Fischetti M, Ljubic I, Monaci M, Sinnl M (2016) Interdiction games and monotonicity. Tech repGoogle Scholar
  10. Israeli E, Wood RK (2002) Shortest-path network interdiction. Networks 40(2):97–111CrossRefGoogle Scholar
  11. Keçici S, Aras N, Verter V (2012) Incorporating the threat of terrorist attacks in the design of public service facility networks. Optim Lett 6(6):1101–1121CrossRefGoogle Scholar
  12. Lei TL (2013) Identifying critical facilities in hub-and-spoke networks: a hub interdiction median problem. Geogr Anal 45(2):105–122CrossRefGoogle Scholar
  13. Nandi AK, Medal HR, Vadlamani S (2016) Interdicting attack graphs to protect organizations from cyber attacks: a bi-level defender-attacker model. Comput Oper Res 75:118–131CrossRefGoogle Scholar
  14. O’Hanley JR, Church RL (2011) Designing robust coverage networks to hedge against worst-case facility losses. Eur J Oper Res 209(1):23–36CrossRefGoogle Scholar
  15. O’Hanley JR, Church RL, Gilless JK (2007a) The importance of in situ site loss in nature reserve selection: balancing notions of complementarity and robustness. Biol Conserv 135(2):170–180CrossRefGoogle Scholar
  16. O’Hanley JR, Church RL, Gilless JK (2007b) Locating and protecting critical reserve sites to minimize expected and worst-case losses. Biol Conserv 134(1):130–141CrossRefGoogle Scholar
  17. Pereira MA, Coelho LC, Lorena LA, de Souza LC (2015) A hybrid method for the probabilistic maximal covering locationallocation problem. Comput Oper Res 57:51–59CrossRefGoogle Scholar
  18. Pessoa AA, Poss M, Roboredo MC, Aizemberg L (2013) Solving bilevel combinatorial optimization as bilinear min–max optimization via a branch-and-cut algorithm. Ann XLV Braz Symp Oper Res 2:2497–2508Google Scholar
  19. Roboredo MC, Pessoa AA (2013) A branch-and-cut algorithm for the discrete (r/p)-centroid problem. Eur J Oper Res 224(1):101–109CrossRefGoogle Scholar
  20. Sarhadi H, Tulett DM, Verma M (2015) A defender-attacker-defender approach to the optimal fortification of a rail intermodal terminal network. J Transp Secur 8(1–2):17–32CrossRefGoogle Scholar
  21. Scaparra MP, Church RL (2008a) A bilevel mixed-integer program for critical infrastructure protection planning. Comput Oper Res 35(6):1905–1923CrossRefGoogle Scholar
  22. Scaparra MP, Church RL (2008b) An exact solution approach for the interdiction median problem with fortification. Eur J Oper Res 189(1):76–92CrossRefGoogle Scholar
  23. Snyder LV, Atan Z, Peng P, Rong Y, Schmitt AJ, Sinsoysal B (2016) Or/ms models for supply chain disruptions: a review. IIE Trans 48(2):89–109CrossRefGoogle Scholar
  24. Yuan W, Zhao L, Zeng B (2014) Optimal power grid protection through a defender-attacker-defender model. Reliab Eng Syst Saf 121:83–89CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Departamento de Engenharia de ProduçãoUniversidade Federal FluminenseNiteróiBrazil
  2. 2.Banco Nacional do DesenvolvimentoRio de JaneiroBrazil

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