Better Approximation Ratios For The Single-Vehicle Scheduling Problems On Tree/Cycle Networks

We investigate the single vehicle scheduling problems based on tree/cycle networks. Each customer, assumed as a vertex on the given network, has a release time and a service time requirements. The single vehicle starts from the depot and aims to serve all the customers. The objective of the problem is to find the relatively optimal routing schedule so as to minimize the makespan. We provide a 16/9-approximation algorithm and a 48/25-approximation algorithm for the tour-version and the path-version of single vehicle scheduling problem on a tree, respectively. For the tour-version of single vehicle scheduling problem on a cycle, we present a 5/3-approximation algorithm.