Developing a Mathematical Model for a Location-Routing Vehicle Problem with Customer Satisfaction and Pick up Delivery

This study considers a location-routing problem (LRP) with multiple depots and hard time windows for customers. The aim of this paper is to select optimal locations for depots and plan scheduling and routing of heterogeneous vehicle fleets. Therefore, it minimizes costs of establishment of depots and reduce transportation time by finding the optimum routs simultaneously. Customer satisfaction is important for each organization; hence, a hard time window is considered for customers. The main approach of this study is considered location-routing problem simultaneously for reducing location-routing costs and it work effectively. To validate the model, an augmented epsilon-constraint is used to solve small-sized problems. Because the problem is NP-hard, it takes too long time and needs too much space memory to solve large-sized problems optimally. Deterministic algorithms cannot solve the large-size problems. Thus, a well-known multi-objective evolutionary algorithm, namely non-dominated sorting genetic algorithm (NSGA-II), is proposed. Gap between augmented epsilon-constraint and NSGA-II show accuracy. The results are analyzed and compared in order to show the efficiency of the proposed NSGA-II.