Efficient PTAS for the euclidean capacitated vehicle routing problem with non-uniform non-splittable demand

Abstract

The Capacitated Vehicle Routing Problem (CVRP) is the well-known combinatorial optimization problem having numerous relevant applications in operations research. As known, CVRP is strongly NP-hard even in the Euclidean plane, APX-hard for an arbitrary metric, and can be approximated in polynomial time with any accuracy in the Euclidean spaces of any fixed dimension. In particular, for the several special cases of the planar Euclidean CVRP there are known Polynomial Time Approximation Schemes (PTAS) stemming from the seminal papers by M. Haimovich, A. Rinnooy Kan and S. Arora. Although, these results appear to be promising and make a solid contribution to the field of algorithmic analysis of routing problems, all of them are restricted to the special case of the CVRP, where all customers have splittable or even unit demand, which seems to be far from the practice. In this paper, to the best of our knowledge, we propose the first Efficient Polynomial Time Approximation Scheme (EPTAS) for this problem in the case of non-uniform non-splittable demand.