A Mathematical Modeling for Location-Routing Problem in Critical Situations with considering to Path Security

Document Type : Original Article

Authors

1 Faculty member in Department of Industrial Engineering, Faculty of Engineering and Basic Sciences, Kosar University of Bojnord, Bojnord, Iran.

2 Assistant Prof. in Kosar University of Bojnord, Iran

Abstract

The occurrence of natural and unnatural disasters threatens the lives of many people around the world every year. Disaster response consists of some elements such as transferring of healthy people from the affected areas to the camps. The purpose of this study is to provide a mixed-integer linear mathematical programming model for determining the best location of camps and the route of vehicles between affected points and camps. In the transfer operation, fuzzy uncertainties of transportation time, the amount of affected points' demand, the time of service, and the time window are considered. In this research, the optimal amount of arrival time of vehicles to camps is calculated in pessimistic conditions. Then this amount is considered as the time limitation in a model to minimize the expected cost of damage to people and vehicles. The cost has been calculated with regard to the security of each route from the warehouse to the affected points and from the points to the camps. To illustrate the performance of the proposed model, the model is implemented on a random example. The results of this research can be used as a model for planning the response of the possible crisis of the operating defense.

Keywords

References

  • Barbarosoglu, G. & Arda, Y. (2004). A two-stage stochastic programming framework for transportation planning in disaster response, Journal of the Operational Research Society, 55 (1): 43-53.
  • Bruni, M. E., Beraldi, P. & Khodaparasti, S. (2018). A fast heuristic for routing in post-disaster humanitarian relief logistics. Transportation Research Procedia, 30: 304-313.
  • Cheng, C.H. (1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy sets and systems, 95 (3): 307-317.
  • Dehghan, M., Hashemi, B. & Ghatee, M. (2006). Computational methods for solving fully fuzzy linear systems, Applied mathematics and Computation, 179 (1): 328-43.
  • Gendreau, M., Laporte, G. & Semet, F. (1997). Solving an ambulance location model by tabu search, Location Science, 5 (2): 75-88.
  • Kumar, A., Kuar, J. & Singh, P. (2011). A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling, 35: 817-823.
  • Loree, N. & Aros-vera, F. (2018). Points of distribution location and inventory management model for Post-Disaster Humanitarian Logistics. Transportation Research Part E: Logistics and Transportation Review, 116: 1-24.
  • Lotfi, F.H., Allahviranloo, T., Jondabeh, M.A. & Alizadeh, L. (2009). Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution, Applied Mathematical Modelling, 33 (7): 3151-3156.
  • Nasseri, S.H., Behmanesh, E., Taleshian, F., Abdolalipoor, M. & TaghiNezhad, N.A. (2013). Fully fuzzy linear programming with inequality constraints. International Journal of Industrial Mathematics, 5 (4): 309-316.
  • Qiang, L., Xuejing, R. & Pilong, S. (2011). Selection of emergency shelter sites for seismic disasters in mountainous regions: Lesson from the 2008 Wenchuan Ms 8.0 Earthquake, China, Journal of Asian Earth Sciences, 40 (4): 926-934.
  • Safaei, A. S., Farsad, S. & Paydar, M. M. (2018). Robust bi-level optimization of relief logistics operations. Applied Mathematical Modelling, 56: 359-380.
  • Saffarian, M., Barzinpour, F. & Eghbali, M.A. (2015). A Robust Programming Approach to Bi-objective Optimization Model in the Disaster Relief Logistics Response Phase, International Journal of Supply Operations Management, 2 (1): 595-616.
  • Sakawa, M. (1993). ‎‎Fuzzy sets and interactive multiobjective optimization, Plenum press, New Yorkand london.

Zanjirani Farahani, R. & Asgari, N. (2007). Combination of MCDM and Covering Techniques in a Hierarchical Model for Facility Location: A Case Study, European Journal of Operational Research, 176: 1839-1858.

Defensive Future Studies
Volume 4, Issue 13
September 2019
Pages 89-110

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