Green vehicle routing and scheduling problem with heterogeneous fleet including reverse logistics in the form of collecting returned goods

Abstract

Vehicle routing problem (VRP) is about finding optimal routes for a fixed fleet of vehicles in order that they can meet the demands for a set of given customers by traveling through those paths. This problem and its numerous expansions are one of the most important and most applicable transportation and logistics problems. In this study, the 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 and to minimize both simultaneously. In this regard, a mixed integer non-linear programming (MINLP) model is proposed. Since the problem is categorized as NP-hard, two meta-heuristics, a simulated annealing (SA) and a genetic algorithm (GA) are suggested in order to find near-optimal solutions for large instances in a reasonable computational time. The performances of the proposed algorithms are evaluated in comparison with the mathematical model for small-sized problems and with each other for problems of all size using a set of defined test problems. Analysis of the results considering two criteria: solutions quality and computational times, indicates the satisfactory performance of the presented algorithms in a proper computational time. Meanwhile, a statistical hypothesis testing (T-test) is conducted. It can generally be observed that SA achieves relatively better results in terms of solution quality, while GA spends less computational time for all-sized test problems. Eventually, sensitivity analysis is conducted to investigate the effect of collecting returned goods on the cost of total CO2 emissions, variable costs of the fleet and the objective function value.