On a Labeled Vehicle Routing Problem

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 epsilon V \ {0} is visited once, minimizing the number of colors used.