Best Possible Approximation Algorithms for Single Machine Scheduling with Increasing Linear Maintenance Durations

Abstract

We consider a single machine scheduling problem with multiple maintenance activities, where the maintenance duration function is of the linear form ft=a+bt with a≥0 and b>1. We propose an approximation algorithm named FFD-LS2I with a worst-case bound of 2 for problem. We also show that there is no polynomial time approximation algorithm with a worst-case bound less than 2 for the problem with b≥0 unless P=NP, which implies that the FFD-LS2I algorithm is the best possible algorithm for the case b>1 and that the FFD-LS algorithm, which is proposed in the literature, is the best possible algorithm for the case b≤1 both from the worst-case bound point of view.