Authors: Behrouz Afshar-Nadjafi; Alireza Afshar-Nadjafi
Addresses: Faculty of Industrial and Mechanical Engineering, Islamic Azad University, Qazvin Branch, P.O. Box 34185-1416, Qazvin, Iran ' Department of Business Management, Islamic Azad University, Qazvin Branch, P.O. Box 34185-1416, Qazvin, Iran
Abstract: Extensive research has been devoted to the vehicle routing problem (VRP). Most of these researches assume a homogenous fleet with constant travel times and single depot. In this paper, we consider the time dependent multi-depot vehicle routing problem. The objective is to minimise the total heterogeneous fleet cost assuming that the travel time between two locations depends on the departure time of vehicles. Also, hard time window constraints for the customers and transit restrictions should be satisfied. The problem is formulated as a mixed integer programming model. Due to NP-hardness of the problem a parameters-tuned simulated annealing (SA) is proposed to obtain a satisfying solution. The efficiency of the proposed SA is evaluated on 180 test problems. The obtained computational results indicate that the proposed procedure is efficient.
Keywords: vehicle routing problem; VRP; time dependent; hard time windows; heterogeneous fleet; simulated annealing; multiple depots; mixed integer programming; MIP.
International Journal of Operational Research, 2016 Vol.26 No.1, pp.88 - 103
Received: 16 Dec 2013
Accepted: 29 Mar 2014
Published online: 31 Mar 2016 *