Capacitated Vehicle Routing with NonUniform Speeds
Abstract
The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having nonuniform speeds (that we call Heterogenous CVRP), and present a constantfactor approximation algorithm. The technical heart of our result lies in achieving a constant approximation to the following TSP variant (called Heterogenous TSP). Given a metric denoting distances between vertices, a depot r containing k vehicles with possibly different speeds, the goal is to find a tour for each vehicle (starting and ending at r), so that every vertex is covered in some tour and the maximum completion time is minimized. This problem is precisely Heterogenous CVRP when vehicles are uncapacitated. The presence of nonuniform speeds introduces difficulties for employing standard toursplitting techniques. In order to get a better understanding of this technique in our context, we appeal to ideas from the 2approximation for scheduling in parallel machine of Lenstra et al.. This motivates the introduction of a new approximate MST construction called LevelPrim, which is related to Light Approximate Shortestpath Trees. The last component of our algorithm involves partitioning the LevelPrim tree and matching the resulting parts to vehicles. This decomposition is more subtle than usual since now we need to enforce correlation between the size of the parts and their distances to the depot.
 Publication:

arXiv eprints
 Pub Date:
 December 2010
 arXiv:
 arXiv:1012.1850
 Bibcode:
 2010arXiv1012.1850G
 Keywords:

 Computer Science  Data Structures and Algorithms