A NSGA-II Approach to the Bi-objective Multi-vehicle Allocation of Customers to Distribution Centers

This study proposes a bi-objective model for capacitated multi-vehicle allocation of customers to potential distribution centers (DCs).The optimization objectives are to minimize transit time and total cost including opening cost, assumed for opening potential DCs and shipping cost from DCs to the customers where considering heterogeneous vehicles lead to a more realistic model and cause more conflicting in the two objectives. An evolutionary algorithm named non-dominated sorting genetic algorithm (NSGA-II) is used as the optimization tool. To aid the decision maker choosing the best compromise solution from the Pareto front, the fuzzy-based mechanism is employed. For ensuring the robustness of the proposed method and giving a practical sense of this study, the computational results in some small cases are compared with those obtained by LP-metric method. Results show the percentage errors of objective functions compared to the LP-metric method are less than 2%. Furthermore, it can be seen that with increasing size of the problems, while the time of problem solving increases exponentially by using the LP-metric method, the running time of NSGA-II is more stable, so these show the advantages and effectiveness of NSGA-II in reporting the Pareto optimal solutions in large scale. Key-Words:bi-objective optimization; capacitated location-allocation; multi-vehicle; LP-metric; evolutionary algorithm; non-dominated sorting genetic algorithm II;