<P> The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?". It generalises the well - known travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John Ramser in 1959, in which first algorithmic approach was written and was applied to petrol deliveries . Often, the context is that of delivering goods located at a central depot to customers who have placed orders for such goods . The objective of the VRP is to minimize the total route cost . In 1964, Clarke and Wright improved on Dantzig and Ramser's approach using an effective greedy approach called the savings algorithm . </P> <P> Determining the optimal solution to VRP is NP - hard, so the size of problems that can be solved, optimally, using mathematical programming or combinatorial optimization may be limited . Therefore, commercial solvers tend to use heuristics due to the size and frequency of real world VRPs they need to solve . </P>

Difference between traveling salesman problem and vehicle routing problem
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