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August, 1994 Probabilistic Analysis of a Capacitated Vehicle Routing Problem II
WanSoo T. Rhee
Ann. Appl. Probab. 4(3): 741-764 (August, 1994). DOI: 10.1214/aoap/1177004969

Abstract

A fleet of vehicles located at a common depot must serve customers located throughout the plane. Without loss of generality, the depot will be located at the origin. Each vehicle must start at the depot, travel in turn to each customer its serves and go back to the depot. Each vehicle can serve at most $k$ customers. The objective is to minimize the total distance traveled by the fleet. In our model, the customers $X_1, \ldots, X_n$ are independent and uniformly distributed over the unit disc. If $R'(X_1, \ldots, X_n)$ denotes the optimal solution with these customer locations, we show that with overwhelming probability we have $\big|R'(X_1, \ldots, X_n) - \frac{2}{k} \sum_{i \leq n} \|X_i\| - \xi \sqrt{n} big| \leq K(n \log n)^{1/3},$ where $\xi$ and $K$ are constants that depend on $k$ only.

Citation

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WanSoo T. Rhee. "Probabilistic Analysis of a Capacitated Vehicle Routing Problem II." Ann. Appl. Probab. 4 (3) 741 - 764, August, 1994. https://doi.org/10.1214/aoap/1177004969

Information

Published: August, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0830.90060
MathSciNet: MR1284983
Digital Object Identifier: 10.1214/aoap/1177004969

Subjects:
Primary: 60D05
Secondary: 60G17

Keywords: Matching problem , Poisson process , subadditivity‎ , subgaussian inequality , vehicle routing problem

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.4 • No. 3 • August, 1994
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