Multi-objective Metaheuristics for a Location-Routing Problem with Simultaneous Pickup and Delivery

We address an integrated logistics system where decisions on location of depot, vehicle routing are considered simultaneously. Total cost and service quality are common criteria influencing decision-making. Literature on location routing problem (LRP) addressed the location and vehicle routing decisions with a common assumption that each vehicle can only performance pickup or delivery assignment in each dispatch. However, both demands of each customer often require be satisfied at the same time. In this paper we consider a LRP with simultaneous pickup and delivery to minimize total cost and customer waiting time. We formulate a nonlinear multi-objective integrated programming model for the problem. A heuristic algorithm based on tabu search is proposed to solve the large-size problem. We then empirically evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions or strong lower bounds, and investigate the effectiveness of the proposed heuristic approach. Results show that the proposed heuristic approach is computationally efficient in finding good quality solutions.