Assistant Professor, Department of Mathematics, Nehru Institute of Technology.
In this paper we discuss the Vehicle Routing Problem (VRP), the goal is to find optimal routes for multiple vehicles visiting a set of locations. We mean by "optimal routes" for a Vehicle Routing Problem is the routes with the least total distance. However, if there are no other constraints, the optimal solution is to assign just one vehicle to visit all locations, and find the shortest route for that vehicle. This is essentially the same problem as the Transportation Salesmen Problem. A better way to define optimal routes is to minimize the length of the longest single route among all vehicles. This is the right definition if the goal is to complete all deliveries as soon as possible. The Vehicle Routing Problem finds optimal routes defined.Also in this paper we discuss,why is it a challenge to solve the Vehicle Routing Problem?