Polynomial time approximation scheme for single-depot euclidean capacitated vehicle routing problem

Abstract

We consider the classic setting of Capacitated Vehicle Routing Problem (CVRP): single product, single depot, demands of all customers are identical. It is known that this problem remains strongly NP-hard even being formulated in Euclidean spaces of fixed dimension. Although the problem is intractable, it can be approximated well in such a special case. For instance, in the Euclidean plane, the problem (and it’s several modifications) have polynomial time approximation schemes (PTAS). We propose polynomial time approximation scheme for the case of ℝ3.