A hybrid simulated annealing for capacitated vehicle routing problems with the independent route length

This paper presents a linear integer model of capacitated vehicle routing problems (VRP) with the independent route length to minimize the heterogeneous fleet cost and maximize the capacity utilization. In the proposed model, the fleet cost is independent on the route length and there is a hard time window over depot. In some real-world situations, the cost of routes is independent on their length, but it is dependent to type and capacity of vehicles allocated to routes where the fleet is mainly heterogeneous. In this case, the route length or travel time is expressed as restriction, which implies a hard time window in depot. The proposed model is solved by a hybrid simulated annealing (SA) based on the nearest neighborhood. It is shown that the proposed model enables to establish routes to serve all given customers by the minimum number of vehicles and the maximum capacity used. Also, the proposed heuristic can find good solutions in reasonable time. A number of small and large-scale problems in little and large scale are solved and the associated results are reported.