Resilient network design in a location-allocation problem with multi-level facility hardening

Document Type : Article

Authors

1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Industrial Engineering, Shahed University, Tehran, Iran.

3 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.;Arts et Metiers ParisTech, LCFC, Metz, France.

Abstract

There are many sources of risk affecting the network elements may lead to network failure, so planners need to consider them in the network design. One of the most important strategies for disruption risk management is the static resilience. In this strategy, the network functionality is maintained after the disruption event by the prevention and hardening actions. In this paper, a resilient capacitated fixed-charge location-allocation model is proposed. Both facility hardening and equipping of the network to backup facilities for disrupted elements are considered together to avoid supply network failure due to random disruption. Facilities are decided to be hardened in multiple levels before disruption events. The problem is formulated as a non-linear integer programming model, then its equivalent linear form is presented. A Lagrangian decomposition algorithm (LDA) is developed to solve large-scale instances. Computational results confirm the efficacy of the proposed solution approach comparing to classical solution approaches in large-scale problems. Moreover, the superiority of the proposed model is confirmed by comparing to the classical models.

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Main Subjects


References:
1. Amoaning, Y. "A resiliency framework for planning in state transportation agencies", Gor. Ins. Technol., pp. 1-2 (2013).
2. Azad, N., Davoudpour, H., Saharidis, G.K.D., and Shiripour, M. "A new model to mitigating random disruption risks of facility and transportation in supply chain network design", International Journal of Advanced Manufacturing Technology, 69, pp. 1757-1774 (2013).
3. Qingwei, L. and Savachkin, A. "A heuristic approach to the design of fortified distribution networks", Transportation Research Part E, 50, pp. 138-148 (2013).
4. Church, R.L., Middleton, R.S., and Scaparra, M.P. "Identifying critical infrastructure: The median and covering facility interdiction problems", Annals of the Association of American Geographers, 94, pp. 491-502 (2004).
5. Scaparra, M.P. and Church, R.L. "A bilevel mixedinteger program for critical infrastructure protection planning", Computer and Operations Research, 35, pp. 1905-1923 (2008).
6. Aksen, D., Necati, A., and Piyade, N. "The budget constrained r-interdiction median problem with capacity expansion", Central European Journal of Operations Research, 18, pp. 269-291 (2010).
7. Daskin, M., Liberatore, F., and Scaparra, M.P. "Hedging against disruptions with ripple effects in location analysis", OMEGA, 40, pp. 21-30 (2012).
8. Medal, H.R., Pohl, E.A., and Rossetti, M.D. "A multiobjective integrated facility location-hardening model: Analyzing the pre and post-disruption tradeoff", European Journal of Operational Research, 237, pp. 257- 270 (2014).
9. Snyder, L. and Daskin, M.S. "Reliability models for facility location: the expected failure cost case", Transportation Science, 39, pp. 400-416 (2005).
10. Lim, M., Daskin, M.S., Bassamboo, A., and Chopra, S. "Facility reliability problem: formulation, properties, and algorithm", Naval Research Logistics, 57, pp. 58- 70 (2009).
11. Shishebori, D., Snyder, L.V., and Jabalameli, M.S. "A reliable budget-constrained facility location/network design problem with unreliable facilities", Networks and Spatial Economics, 14, pp. 549-580 (2014).
12. Mohammadi, M., Tavakkoli-Moghaddam, R., Siadat, A., and Dantan, J.-Y. "Design of a reliable logistics network with hub disruptions under uncertainty", Applied Mathematical Modelling, 40, pp. 5621-5642 (2016).
13. Fattahi, M., Govindan, K., and Keyvanshokooh, E. "Responsive and resilient supply chain network design under operational and disruption risks with delivery lead-time sensitive customers", Transportation Research Part E: Logistics and Transportation Review, 101, pp. 176-200 (2017).
14. Jabbarzadeh, A., Fahimnia, B., Sheu, J.B., and Shahmoradi-Moghadam, H. "Designing a supply chain resilient to major disruptions and supply/demand interruptions", Transportation Research Part B, 94, pp. 121-149 (2016).
15. Losada, C., Scaparra, M.P., and O'Hanley, J.R. "Optimizing system resilience: a facility protection model with recovery time", European Journal of Operational Research, 217, pp. 519-530 (2012).
16. Rastgoufard, P., Leevongwat, I., and Rastgoufard, R. "Electric grid hardening and resiliency: part I, resiliency and safety", Engineering & Technology Reference, 14 pages (2016).
17. Niakan, F. and Rahimi, M. "A multi-objective healthcare inventory routing problem: A fuzzy possibilistic approach", Transportation Research Part E: Logistics and Transportation Review, 80, pp. 74-94 (2015).
18. Holmberg, K., Ronnqvist, M., and Yuan, D. "An exact algorithm for the capacitated facility location problems with single sourcing", European Journal of Operational Research, 113, pp. 544-559 (1999).
19. Barcelo, J. and Casanovas, J. "A heuristic Lagrangean algorithm for the capacitated plant location problem", European Journal of Operational Research, 15, pp. 212-226 (1984).
20. Beasley, J.E. "Lagrangean heuristics for location problems", European Journal of Operational Research, 65, pp. 383-399 (1993).
21. Agar, M.C. and Salhi, S. "Lagrangean heuristics applied to a variety of large capacitated plant location problems", Journal of the Operational Research Society, 49(1), pp. 1072-1084 (1998).
22. Cortinhal, M.J. and Captivo, M.E. "Upper and lower bounds for the single source capacitated location problem", European Journal of Operational Research, 151, pp. 333-351 (2003).
23. Chen, C.H. and Ting, C.J. "Combining Lagrangian heuristic and ant colony system to solve the single source capacitated facility location problem", Transportation Research Part E: Logistics and Transportation Review, 44(6), pp. 1099-1122 (2008).
24. Jena, S.D., Cordeau, J.F., and Gendron, B. "Solving a dynamic facility location problem with partial closing and reopening", Computers and Operations Research, 67, pp. 143-154 (2016).
25. Ronnqvist, M., Tragantalerngsak, S., and Holt, J. "A repeated matching heuristic for the single-source capacitated facility location problem", European Journal of Operational Research, 116, pp. 51-68 (1999).
26. Wu, T., Chu, F., Yang, Z., and Zhou, Z. "A Lagrangean relaxation approach for a two-stage capacitated facility location problem with choice of facility size", In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 713-718 (2015).
27. Li, Q., Savachkin, A., and Zeng, B.O. "Reliable facility location design under disruptions", Computers and Operations Research, 40, pp. 901-909 (2013).
28. Li, Q. and Savachkin, A. "Reliable distribution networks design with nonlinear fortification function", International Journal of Systems Science, 47, pp. 805- 813 (2014).
29. Held, M., Crowder, D., and Wolf, H. "Validation of subgradient optimization", Mathematical Programming, 6, pp. 62-88 (1974).
30. Eskandarzadeh, S., Tavakkoli-Moghaddam, R., and Azaron, A. "An extension of the relaxation algorithm for solving a special case of capacitated arc routing problems", Journal of Combinatorial Optimization, 17(2), pp. 214-234 (2009).
31. Shishebori, D., Yousefi Babadi, A., and Noormohammadzadeh, Z.A. "Lagrangian relaxation approach to fuzzy robust multi-objective facility location network design problem", Scientia Iranica, 25, pp. 1750-1767 (2018).