Solving a bi-objective multi-commodity two-echelon capacitated location routing problem

Planning the freight flow from the plants to the customer zones is one of the most challenging problems in the field of supply chain management. Because of many traffic regulations, oversize/overweight vehicles often are not permitted to enter city boundaries. Therefore, intermediate facilities (city distribution centers) play a very important role in distribution networks. Accordingly, in this paper, transportation of goods from the plants to the customers is considered an integrated process containing two phases, namely, transportation from plant to distribution centers and distribution from city distribution centers to customers using small and environmentally-friendly vehicles. The Transportation Location Routing Problem (TLRP) studied can be considered as an extension of the two-echelon location routing problem. Minimizing the operational costs, and the workload balancing of the heterogeneous fleet in the distribution phase are considered as the two objective functions. A Mixed Integer Programming (MIP) model, as well as two solution approaches, based on Multi-objective Particle Swarm Optimization Algorithm, and Non-dominated Sorting Genetic Algorithm, is presented for the problem. In order to illustrate the efficacy of the proposed methods, they have been implemented on test problems of different sizes. The results show the methods are able to produce efficient solutions in a reasonable amount of time.