Consider the problem of transporting a set of objects between the vertices of a simple graph by a vehicle that traverses the edges of the graph. The problem of finding a shortest tour for the vehicle to transport all objects from their initial vertices to their destination vertices is called the vehicle routing problem. The problem is multiple capacity if the vehicle can handle more than one objects at a time. The problem is preemptive if objects can be unloaded at the intermediate vertices. In this paper, we present an O(kn + n 2 ) time algorithms for multiple capacity preemptive vehicle routing problem on paths, where k is the number of objects to be moved and n is the number of vertices in the path.
Indeed, the problem has been shown to be feasible in polynomial time on paths, formally in O((k + n) × n) where k is the number of objects and n is the number of vertices REF .
Multiple Capacity Vehicle Routing on Paths
Mathematics Computer Science