A Multi Echelon Location-Routing-Inventory Model for a Supply Chain Network: NSGA II and Multi-Objective Whale Optimization Algorithm

In this study, we aim to explore the modeling and solution approach for a multi-objective location-routing-inventory problem. The focus is on planned transportation with the goal of minimizing total costs and reducing the maximum working hours of drivers. To achieve these objectives, we need to consider the routing of vehicles between customers and distribution centers, as well as the optimal allocation of product transfer flow between the production center and customers. Therefore, the proposed model incorporates location, routing-inventory, and allocation simultaneously. To solve the two-objective model, we employed the Epsilon-constraint method for small-sized problems. For large-sized problems, we utilized the NSGA-II and MOWOA meta-heuristic algorithms with a new chromosome. The computational results indicate that in order to reduce the maximum working hours of drivers, it is necessary to increase the number of vehicles and minimize travel distances. However, this leads to higher costs due to vehicle utilization and the need for constructing distribution centers closer to customers, which in turn increases construction costs. Finally, based on the analysis, the NSGA-II algorithm outperformed the MOWOA algorithm with a weighted value of 0.983 compared to 0.016, making it the selected algorithm.