New mathematical modeling for a facilities location and vehicle routing problem solving by a hybrid imperialist competitive algorithm

Document Type : Research Paper


School of Industrial Engineering, College of Engineering, University of Tehran, I.R. Iran


Increasing of the distribution efficiency is one of the most objectives of an integrated logistic system developed as a new management philosophy in the past few decades. The problem is examind in two parts: facilities location problem (FLP) for long policies and vehicle routing problem (VRP) to meet the customer demand. These two components can be solved separately; however, this solution may not be the optimum solution of the original problem. Hence, in this paper, facilities location and vehicle routing problems are considered simultaniously to visit the facilities that should be serviced. Due to the complexity of the integrated problem in large sizes, a hybrid imperialist competitive algorithm (ICA) is proposed. Furthermore, to show the efficiency of the proposed hybrid ICA, a number of test problems in small and large sizes are solved. Finally, the obtained results are evaluated with the results obtained by CPLEX. Finally, the conclusion is provided.


Main Subjects

  1. Ting, C. and Chen, C. H. (2013). “A multiple ant colony optimization algorithm for the capacitated location routing problem.” Int. J. of Production Economics, 141, 34–44.
  2. Xu, Y., Wang, L., and Yang, Y. (2012). “A new variable neighborhood search algorithm for the multi depot heterogeneous vehicle routing problem with time windows.” Electronic Notes in Discrete Mathematics, 39, 289–296.
  3. Yücenur, G. N. and Demirel, N. Ç. (2011). “A new geometric shape-based genetic clustering algorithm for the multi-depot vehicle routing problem.” Expert Systems with Applications, 38(9), 11859–11865.
  4. Baldacci, R., Mingozzi, A., and Roberti, R. (2012). “Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints.” European J. of Operational Research, 218(1), 1–6.
  5. Garcia-Najera, A. and Bullinaria, J. A. (2011). “An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows.” Computers & Operations Research, 38(1), 287–300.
  6. Kritikos, M. N. and Ioannou, G. (2013). “The heterogeneous fleet vehicle routing problem with overloads and time windows.” Int. J. of Production Economics, 144(1), 68-75.
  7. Mirabi, M., FatemiGhomi, S. M. T., and Jolai, F. (2010). “Efficient stochastic hybrid heuristics for the multi-depot vehicle routing problem.” Robotics and Computer-Integrated Manufacturing, 26, 564–569.
  8. Ruan, Q., Zhang, Z., Miao, L., and Shen, H. (2011). “A hybrid approach for the vehicle routing problem with three-dimensional loading constraints.” Computers & Operations Research, 40, 1579–1589.
  9. Fazel-Zarandi, M. H., Hemmati, A., Davari, S., and Turksen, I, B. (2012). “Capacitated location-routing problem with time windows under uncertainty.” Knowledge-Based Systems, 3, 480–489.
  10. 10.  Zhou, G., Min, H., and Gen, M. (2003). “A genetic algorithm approach to the bi-criteria allocation of customers to warehouses.” Int. J. of Production Economics, 86, 34–45.
  11. 11.  Escobar, J. W., Linfati, R., and Toth, P. (2012). “A two-phase hybrid heuristic algorithm for the capacitated location-routing problem.” Computers & Operations Research, 40, 70–79.
  12. 12.  Norouzi, N., Razmi, J., and Sadegh-Amalnick, M. (2013). “A vehicle routing problem with minimizing fuel consumption and number of vehicles by improved particle swarm optimization.” J. of Industrial Engineering, 47(1), 105-112.

13. Razmi, J., Haleh, H., and Ezzati, B. (2011). “Solving the dynamic vehicle routing problem with AntNet algorithm.” Int. J. Logistics Systems and Management, 26, 65-70.

14. Razmi, J. and Yosefi, M. (2012). “Introducing a novel mathematical model for school vehicle routing problem and proposing a new algorithm to solve it.” J. of Industrial Engineering, 46(2), 185-194.

Lucas, C., Nasiri-Gheidari, Z., and Tootoonchian, F. (2010). “Application of an imperialist competitive algorithm to the design of a linear induction motor.” Energy Conversion and Management, 51(7), 1407–1411.