Location Problem - Routing a vehicle with a specified fuel capacity based on a tough time window and customer satisfaction

Multi-objective location-routing problem is one of the most important research areas in the field of transportation and distribution management. The aim of this study is to optimize a multi-objective problem. Combining two routing and location problems, considering a set of warehouses, meeting the customer’s requirements from each warehouse, and designing an optimal route for the vehicle that brings the lowest cost to the transportation system are the main objectives of this research. Although factors such as customer satisfaction with receiving services, fuel constraints in vehicles and the existence of important time intervals, which are referred to as hard time window, are of great importance in location and routing problems, less has been paid to them. In this research, efforts have been made to address these issues. To achieve the best priority by finding the shortest route and to reach the least deviation from the time window is some of the objectives of this research. Combining variables related to vehicle fuel capacity and fuel consumption speed has also been applied in this study. In this research, first, a mixed integer linear programming model is presented and then metaheuristic method based on Non-dominated Sorting Genetic Algorithm is proposed to find the optimal solution. To evaluate the proposed performance, an example is mentioned in this framework. The result of computational experiments, shows the efficiency of the existing research methodology and its strengths and weaknesses.