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.

Centralizing and using proper transportation facilities cut down costs and traffic. Hub facilities concentrate on flows to cause economic advantage of scale and multimodal transportation helps use the advantage of another transporter. A distinctive feature of this paper is proposing a new mathematical formulation for a three-stage p-hub LOCATION ROUTING PROBLEM with simultaneous pick-ups and deliveries on time. A few studies have been devoted to this PROBLEM; however, many people are still suffering from the PROBLEMs of commuting in crowded cities. The proposed formulation controlled the tumult of each node by indirect fixed cost. Node-to-node traveling cost was followed by a vehicle ROUTING PROBLEM between nodes of each hub. A couple of datasets were solved for small and medium scales by GAMS software. But, for large-scale instances, a meta-heuristic algorithm was proposed. To validate the model, datasets were used and the results demonstrated the performance suitability of the proposed algorithm.

One of the most important and widely used PROBLEMs in the logistics part ‎of ‎any supply chain is the LOCATION-ROUTING PROBLEM (LRP) of vehicles. The ‎‎purpose is to select distribution centers to supply goods for ‎‎customers and create suitable travel routes for vehicles to serve ‎customers.‎ Studies conducted in the field of supply chain logistics systems have shown that if vehicle travel ROUTING is neglected when locating supply centers, the costs of the logistics system may increase dramatically. Therefore, in the LRP PROBLEM, the LOCATION of supply centers and the ROUTING of vehicles are considered simultaneously. In this paper, we will present a multi-objective model for vehicle LOCATION-ROUTING PROBLEMs with a flexible fuzzy ‎approach. Its' goals are to make strategic decisions to deploy ‎candidate supply centers at the beginning of the planning horizon, as well as ‎form the vehicle travel at the tactical level to serve the customers in ‎short-term periods of time. Therefore, in ‎order to adapt the mathematical model to the real conditions, the ‎constraints related to the capacity of the vehicles have been considered in a ‎flexible fuzzy state, and also the PROBLEM has been modeled in a multi-period state along with the presence of the distance limit and the ‎accessibility factor for each vehicle. The evaluation criterion is to minimize costs related to the establishment of candidate supply centers, the fixed cost of using vehicles and transportation costs, as well as maximizing customer satisfaction by reducing shortage costs and reducing harmful environmental effects. To solve the model, it is first converted into a single-objective model using the weight method and then solved using the proposed algorithm. Finally, using a numerical example in the field of waste management, the effectiveness of the proposed solution method is shown. It should be mentioned that the model was solved using GAMS software and the results are shown.