Single vehicle scheduling problems on path/tree/cycle networks with release and handling times

In this paper, we consider the single vehicle scheduling problem (SVSP) on networks. Each job, located at some node, has a release time and a handling time. The vehicle starts from a node (depot), processes all the jobs, and then returns back to the depot. The processing of a job cannot be started before its release time, and its handling time indicates the time needed to process the job. The objective is to find a routing schedule of the vehicle that minimizes the completion time. When the underlying network is a path, we provide a simple 3/2-approximation algorithm for SVSP where the depot is arbitrarily located on the path, and a 5/3-approximation algorithm for SVSP where the vehicle's starting depot and the ending depot are not the same. For the case when the network is a tree network, we show that SVSP is polynomially approximable within 11/6 of optimal. All these results are improvements of the previous results [2,4]. The approximation ratio is improved when the tree network has constant number of leaf nodes. For cycle networks, we propose a 9/5-approximation algorithm and show that SVSP without handling times can be solved exactly in polynomial time. No such results on cycle networks were previously known.