Scheduling with deteriorating jobs and setup times on a single machine

Abstract

This paper addresses several single-machine scheduling problems with deteriorating jobs and setup times to minimise the maximum lateness, the weighted number of tardy jobs and the total weighted completion time. The actual job processing times and setup times are both proportional functions of their starting times. For the maximum lateness problem, we first show that the general problem is -hard, which also resolves an open question on its complexity raised in the literature, and then we show that the problem with a fixed number of families is polynomially solvable. For the weighted number of tardy jobs problem, we first present a pseudo-polynomial-time algorithm when the number of families is fixed, and then we provide an O(n2)-time algorithm for the unweighted problem with uniform family due dates. For the total weighted completion time problem, we present a polynomial-time algorithm when the number of families is fixed.