Abstract
The solution of vehicle-routing problem (VRP) determines a set of routes that starts and ends at its own depot, each performed by a single vehicle in a way that minimizes the global transportation cost and fulfills the demands of the customers and operational constraints. Researchers are interested in studying the VRP for two reasons: its practical relevance and its difficulty. Lenstra and Rinnooy Kan have analyzed the complexity of the VRP and concluded that practically all of the VRP problems are non-deterministic polynomial-time hard (NP-hard). VRP has many applications in real-world cases. Some applications are solid-waste collection, street cleaning, school bus routing, routing of salespeople and maintenance units, transportation of handicapped people, and so forth.
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