Approximations for minimum and min-max vehicle routing problems

: We consider a variety of vehicle routing problems. The input to a problem consists of a graph G = (N, E) and edge lengths l(e) e E. Customers located at the vertices have to be visited by a set of vehicles. Two important parameters are k the number of vehicles, and the longest distance traveled by a vehicle. We consider two types of problems: (1) Given a bound on the length of each path, find a minimum sized collection of paths that cover all the vertices of the graph, or all the edges from a given subset of edges of the input graph. We also consider a variation where it is desired to cover N by a minimum number of stars of length bounded by . (2) Given a number k find a collection of k paths that cover either the vertex set of the graph or a given subset of edges. The goal here is to minimize , the maximum travel distance. For all these problems we provide constant ratio approximation algorithms and prove their NP-hardness.

• Type: Journal
• Year: 2006
• Where: JAL
• Authors: Esther M. Arkin, Refael Hassin, Asaf Levin
• Keywords: JAL 2006, Minimum Sized Collection, Problems, Vehicle