Optimization of Routes in Pickup and Delivery Problem

In shipping services, the goal is to propose cyclical routes which ensure transport of required goods among main centers of regions. The problem is classified as a pickup and delivery problem with split demand and reloading. The objective is to minimize total shipping cost or total length of all cyclical routes. The optimum solution gives a number of vehicles going on arcs of the communication network and the amount of goods being transported on the arcs. Consequently, cyclical routes and depots are proposed for all vehicles. First, the multi-graph, in which each directed arc corresponds to exactly one vehicle, is generated. The multi-graph satisfies the condition that the number of arcs entering each node equals the number of arcs outgoing the node. Heuristic method to load goods on a vehicle in the pickup node and to transport it to the delivery node without reloading on another vehicle is proposed. The method is verified on the case study of the international company.