An Optimization Model for Heterogeneous Vehicle Routing and Scheduling Problem with Fixed Cost and Green Reverse Logistics Network Using Genetic Algorithm

Vehicle routing problem aims to find the optimal routes that must be traveled by a fleet of vehicles to satisfy the demand of the customers. In this research, the vehicle routing and scheduling problem is developed for a heterogeneous fleet with the fixed cost of applying vehicles and earliness and tardiness costs in a green reverse logistics network. Since the complexity order of these problems is higher than that of the polynomial ones, this problem is known as NP-hard. As the problem dimensions increase, the exact solving time of the problem increases considerably. Thus, metaheuristic methods are proposed to approximately solve these problems. After developing mixed integer nonlinear model, the Genetic Algorithm (GA) is used to find the near-optimal solutions for the large-scale cases. Finally, the performance of the GA is investigated for several examples by comparing its computation time and solution quality with the computation time and exact solution of the LINGO software. According to the results, the developed GA has an acceptable performance in providing solutions with minimum error in a rational time.