Bounds and Heuristics for Capacitated Routing Problems

In a capacitated routing problem, the objective is to minimize the total distance travelled by vehicles of limited capacity to serve a set of customers that are located in the Euclidean plane. We develop asymptotically optimal bounds and heuristics for this problem, under the assumption that the capacity of a vehicle is expressed in terms of an upper bound on the number of customers that it can serve. The analysis culminates in an algorithm that, for a given capacity and given (epsilon), will find a solution with relative error at most (epsilon) in time polynomial in the number of customers.

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