Scheduling proportionate flow shops with preventive machine maintenance

Abstract

We examine machine scheduling problems that have been inspired by the production environment of semiconductor manufacturing. In semiconductor manufacturing a job processing machine is often enforced to go through a preventive maintenance operation with an objective of minimizing the wafer quality risk. In this research such periodic machine maintenance is considered for single machine and flow shop scheduling models. For the flow shop model we focus on an important special case with proportionate processing times. We first present that the maximum lateness and the total completion time in a single machine can be minimized by a monotone scheduling rule. For the maximum lateness it is shown that the scheduling rule of a single machine special case is also optimal for a proportionate flow shop. However, for the total completion time we observe that the scheduling algorithm of a single machine is not necessarily optimal for its extension to a proportionate flow shop. We prove that the total completion time in a proportionate flow shop is solvable by an O(n2) algorithm, and even the total weighted completion time is minimized with the same computational complexity. Lastly, we discuss how these results are further generalized when setup operations are additionally considered.