Heterogeneous Vehicle Routing Problem with Simultaneous Pickup and Delivery: Mathematical Formulations and A Heuristic Algorithm

Abstract

One of the most important operational decisions in the logistics management is to determine the vehicle routes serving the customers. The Vehicle Routing Problem (VRP) can be defined as the determination of the optimal routes which meet the delivery (or pickup) demands from the depot to the customers. In the real life applications of logistics, vehicles in a fleet may differ from each other. In addition, the requirements arising from customers/goods may reveal the necessity to use different vehicles. Besides, companies do care more about the management of reverse flow of products, semi-finished and raw materials because of their economic benefits and as well as legal and environmental liabilities. In this paper, a variant of the VRP is considered with heterogeneous fleet of vehicles and simultaneous pickup and delivery. This problem is referred to Heterogeneous Vehicle Routing Problem with Simultaneous Pickup and Delivery (HVRPSPD). The HVRPSPD can be defined as determining the routes and the vehicle types on each route while minimizing the total cost. In this paper, a polynomial sized flow-based mathematical model is proposed for the HVRPSPD. Since the HVRPSPD is in the class of NP-hard problems, it is difficult to find the optimal solution in a reasonable time even for the moderate size problems. Therefore, a simple and constructive heuristic algorithm is proposed to solve the medium and large scale HVRPSPD s. This algorithm is the adaptation of very well-known Clarke-Wright Savings approach, which has originally developed for the VRP, to the HVRPSPD. The performances of the proposed mathematical model and the heuristic algorithm have been examined on the test problems.