Solving Green Vehicle Routing and Scheduling Problem with Heterogeneous Fleet Including Reverse Logistics in the Form of Collecting Returned Goods using Genetic Algorithm

Vehicle routing problem (VRP) is about finding optimal routes for a fleet of vehicles in order that they can meet the demands for a set of given customers by traveling through those paths. This problem is one of the most important and most applicable problems of transportation and logistics scope. In this paper, green vehicle routing and scheduling problem with heterogeneous fleet including reverse logistics in the form of collecting returned goods along with weighted earliness and tardiness costs is studied to establish a trade-off between operational and environmental costs. In this regard, a mixed integer non-linear programming (MINLP) model is proposed at the first stage; then its accuracy and correct functioning are evaluated by solving some examples. Since this problem is categorized as a NP-hard problem, a genetic algorithm (GA) is suggested in order to find near-optimal solutions for large instances in a rational computational time. Eventually, the performance of the GA is evaluated in comparison with solving the mathematical model for small-sized problems. Analysis of the results considering two criteria, solutions quality and computational times, indicates the satisfactory operation of the proposed algorithm in a proper computational time.