Multi-depot time dependent vehicle routing problem with heterogeneous fleet and time windows

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.