Vehicle scheduling on a graph revisited

Abstract

We consider a generalization of the well-known Traveling Salesman Problem, called the Vehicle Scheduling Problem (VSP), in which each city is associated with a release time and a service time. The salesman has to visit each city at or after its release time. Our main results are three-fold. First, we devise an approximation algorithm for VSP with performance ratio less than 5/2 when the number of distinct release times is fixed, improving the previous algorithm proposed by Nagamochi et al. [12]. Then we analyze a natural class of algorithms and show that no performance ratio better than 5/2 is possible unless the Metric TSP can be approximated with a ratio strictly less than 3/2, which is a well-known longstanding open question. Finally, we consider a special case of VSP, that has a heavy edge, and present an approximation algorithm with performance ratio less than 5/2 as well. © Springer-Verlag 2012.