Probabilistic analysis for a multiple depot vehicle routing problem

We give a probabilistic analysis of the Multiple Depot Vehicle Routing Problem (MDVRP) where k depots and n customers are given by i.i.d. random variables in [0,1]d, d ≥ 2. The tour length divided by n(d−1)/d tends to α∫  [0,1] df(x)(d−1)/d dx, where f is the density of the absolutely continuous part of the law of the random variables giving the depots and customers and where the constant α depends on the number of depots. If k = o(n), α is the constant of the TSP problem. For k = λn, λ > 0, we prove lower and upper bounds on α, which decrease as fast as (1 + λ)−1/d.© 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

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