Abstract
Nowadays, using a rental fleet to transport goods for delivering to customers at a particular time frame is very important in the services and industry. That is why, in this study, we consider the heterogeneous fixed fleet open vehicle routing problem with time windows, which is one version of the vehicle routing problem with time windows. The problem has not attracted attention so much in the operational research literature than the usual vehicle routing problem. The problem consists of determining the minimum cost routes for a fleet of a fixed number of vehicles with various capacities in order to fulfil the demands of the customer population. Moreover, the vehicles start at the headquarters and terminate at one of the customers. In this study, we introduce a mixed integer programming model and then integrate an exact algorithm to solve this model. Furthermore, a hybrid algorithm (HA) based on modified rank-based ant system is developed and then its efficiency is compared with the exact method and some metaheuristic methods on some standard instances in literature. The results proved the effectiveness of our proposed HA.