a mixed integer programming formulation for the heterogeneous fixed fleet open vehicle routing problem

the heterogeneous fixed fleet open vehicle routing problem (hffovrp) is one of the most significant extension problems of the open vehicle routing problem (ovrp). the hffovrp is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. in this problem, the vehicle doesn’t return to the depot after serving the last customer. because of its numerous applications in industrial and service problems, a new model of the hffovrp based on mixed integer programming is proposed in this paper. furthermore, due to its np-hard nature, an ant colony system (acs) algorithm was proposed. since there were no existing benchmarks, this study generated some test problems. from the comparison with the results of exact algorithm, the proposed algorithm showed that it can provide better solutions within a comparatively shorter period of time.