Location-Routing Problem with Fuzzy Time Windows and Traffic Time

Document Type: Research Paper

Authors

1 Department of Industrial Engineering, Elmo Honar University

2 Department of Industrial Engineering, Yazd University

Abstract

The location-routing problem is a relatively new branch of logistics system. Its objective is to determine a suitable location for constructing distribution warehouses and proper transportation routing from warehouse to the customer. In this study, the location-routing problem is investigated with considering fuzzy servicing time window for each customer. Another important issue in this regard is the existence of congested times during the service time and distributing goods to the customer. This caused a delay in providing service for customer and imposed additional costs to distribution system. Thus we have provided a mathematical model for designing optimal distributing system. Since the vehicle location-routing problem is Np-hard, thus a solution method using genetic meta-heuristic algorithm was developed and the optimal sequence of servicing for the vehicle and optimal location for the warehouses were determined through an example. 

Keywords


Ahmadi Javid A. and Azad N. (2010). Incorporating location, routing and inventory decisions in supply chain network design , Transportation Research Part E. Vol. 46, pp. 582–597.

Claudio C., Vera H. and Teodor G.C. (2012). Lower and upper bounds for the two-echelon capacitated location-routing problem. Computers & Operations Research, Vol. 39, pp. 3185–3199.

Contardo C., Hemmelmayr V. and Gabriel-Crainic T. (2012). Lower and upper bounds for the twoechelon capacitated location-routing problem. Computers & Operations Research, Vol. 39, pp. 3185–3199.

Derbel H., Jarboui B., Hanafi S. and Chabchoub H. (2010). An Iterated Local Search for Solving A Location-Routing Problem. Electronic Notes in Discrete Mathematics, Vol. 36, pp. 875–882.

Derbel H., Jarboui B., Hanafi S. and Chabchoub H. (2012). Genetic algorithm with iterated local search for solving a location-routing problem. Expert Systems with Applications, Vol. 39, pp. 2865– 2871.

Fazel-Zarandi M.H., Hemmati A., Davari S. and Turksen B. (2013). Capacitated location-routing problem with time windows under uncertainty. Knowledge-Based Systems, Vol. 37, pp. 480–489.

Fazel-Zarandi M.H., Hemmati A. and Davari S. (2011). The multi-depot capacitated locationrouting problem with fuzzy travel times. Expert Systems with Applications, Vol. 38, pp. 10075– 10084.

Caballero R., Gonzalez M., Ma Guerrero F., Molina J. and Paralera C. (2007). Solving a multi objective location routing problem with a meta-heuristic based on Tabu search. Application to a real case in Andalusia, European Journal of Operational Research, Vol. 177, pp. 1751–1763.

Homberger J. and Gehring H. (2005). A two-phase hybrid meta-heuristic for the vehicle routing problem with time windows. European Journal of Operational Research, Vol. 162, pp. 220–238.

Jabal-Ameli M.S. Ghaffari-Nasab N. (2010). Location Routing Problem with Time Window. Novel mathematicalprogramming formulations, 7th international Industrial engineering conference, Isfahan. Iran.

Lau H.C.W. and Jiang Z.Z. and Ip W.H. and Wang D. (2010). A credibility-based fuzzy location model with Hurwicz criteria for the design of distribution systems in B2C e-commerce. Computers & Industrial Engineering, Vol. 59, pp.873–886.

Lin C.K.Y. and Kwok R.C.W. (2006). Multi-objective meta-heuristics for a location-routing problem with multiple use of vehicles on real data and simulated data. European Journal of Operational Research, Vol. 175, pp. 1833–1849.

Max S.Z.J., Lian Q. (2007). Incorporating inventory and routing costs in strategic location models. European Journal of Operational Research, Vol. 179, pp. 372–389.

Nagy G. and Salhi S. (2007). Location-routing: Issues, models and methods. European Journal of Operational Research, Vol. 177, pp. 649–672.

Prodhon C. (2010). A hybrid evolutionary algorithm for the periodic location-routing problem. European Journal of Operational Research, Vol. 210, pp. 204–212.

Sexton T. and Choi Y. (1986). Pickup and delivery of partial loads with soft time windows. American Journal of Mathematical and Management, Vol. 6, pp. 369–398.

Sibel A. and Kara-Bahar Y. (2007). A new model for the hazardous waste location-routing problem. Computers & Operations Research, Vol. 34, pp. 1406–1423.

Stanciulescu C., Fortemps P., Install M. and Wertz V. (2003). Multi objective fuzzy linear programming problems with fuzzy decision variables. European Journal of Operational Research, Vol. 149, pp. 654–675.

Stenger A., Schneider M., Schwind M. and Vigo D. (2012). Location routing for small package shippers with subcontracting options. International Journal of Production Economics, Vol. 140(2), pp. 702–712.

Tang J., Pana Z., Fung R. and Lau H. (2009). Vehicle routing problem with fuzzy time windows. Fuzzy Sets and Systems, Vol. 160, pp. 683–695.

Tavakkoli-Moghaddam A. and Makuib M. (2010). A new integrated mathematical model for a biobjective multi-depot location-routing problem solved by a multi-objective scatter search algorithm. Journal of Manufacturing Systems, Vol. 29, pp. 111–119.

Ting C.J. and Chen C.H. (2013). A multiple ant colony optimization algorithm for the capacitated location routing problem. International Journal of Production Economics, Vol. 141(1), pp. 34-44.

Wang H.F. and Wen Y.P. (2002). Time-constrained Chinese postman problems, Comput. Math. Vol. 44, pp. 375–387.

Xie Y., Lu W., Wangb W. and Quadrifogliob L. (2012). A multimodal location and routing model for hazardous materials transportation. Journal of Hazardous Materials, Vol. 227– 228, pp.135– 141.

Xu J., Yan F. and Li S. (2011). Vehicle routing optimization with soft time windows in a fuzzy random environment. Transportation Research Part E, Vol. 47, pp. 1075–1091.

Yu V.F., Lin S.W., Lee W. and Ting C.J. (2010). A simulated annealing heuristic for the capacitated location routing problem. Computers & Industrial Engineering, Vol. 58, pp. 288–299.

Zadeh, L. (1965). Fuzzy sets. Information and Control, Vol. 8, pp. 338–353. Zheng Y. and Liu B. (2006). Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm. Applied Mathematics and Computation, Vol. 176, pp. 673–683.