Approximability of the Vehicle Routing Problem in finite-dimensional Euclidean spaces

Abstract

The Capacitated Vehicle Routing Problem (CVRP) is a classic combinatorial optimization problem with a wide range of applications in operations research. Since the CVRP is NP-hard even in a finite-dimensional Euclidean space, special attention is traditionally paid to the issues of its approximability. A major part of the known results concerning approximation algorithms and polynomial-time approximation schemes (PTAS) for this problem are obtained for its particular statement in the Euclidean plane. In this paper, we show that the approach to the development of a PTAS for the planar problem with a single depot proposed by Haimovich and Rinnooy Kan in 1985 can be successfully extended to the more general case, for instance, in spaces of arbitrary fixed dimension and for an arbitrary number of depots.