On a labeled vehicle routing problem

Abstract

In this paper, we study the complexity and (in)approximability of the minimum label vehicle routing problem. Given a simple complete graph G=(V,E) containing a special vertex 0 called the depot and where the edges are colored (labeled), the minimum label k-vehicle routing problem consists in finding a k-vehicle routing E′, i.e. a collection of cycles of size at most k+1 which all contain the depot 0, and such that every customer v ε V {0} is visited once, minimizing the number of colors used. © 2010 Springer-Verlag Berlin Heidelberg.