Minimizing the weighted flow time on a single machine with the resumable availability constraint: worst case of the WSPT heuristic

In this paper we study the single machine scheduling problem with the aim of minimizing the weighted flow time. The machine is unavailable during a given period. We consider the resumable case. We propose new properties of the worst-case performance of the WSPT heuristic. We give a tighter approximation of the worst-case error, and we show that the worst-case bound is equal to 2 under certain conditions. The results obtained complete the previous analysis of Lee (1996).