A Tagging Mechanism for Solving the Capacitated Vehicle Routing Problem

Abstract

The Vehicle Routing Problem (VRP) is one of the difficult problems in combinatorial optimization and has wide applications in all aspects of our lives. In this research, a tag-based mechanism is proposed to prevent the formation of subtours in constructing the routing sequences, while each tour does not exceed the capacity of the vehicles and the total distance travelled is minimized. For each node, two tags are applied, one on each end, and to be assigned with different values. Two nodes can be connected, only if the tag value at one end of a node matches one of the end tag values of another node. The model is formulated as a mixed integer linear programming problem. Some variations of the vehicle routing problems can also be formulated in a similar manner. If the capacity of the vehicles is infinite, i.e., capacity restrictions are removed, the VRP reduces to the multiple Travelling Salesman Problem (mTSP). Computational results indicate that the proposed model is quite efficient for small sized problems.