Lower bounds and algorithms for flowtime minimization on a single machine with set-up times

Abstract

SUMMARY A recent trend in the analysis of scheduling models integrates batching decisions with sequencing decisions. The interplay between batching and sequencing reects the realities of the small-volume, high-variety manufacturing environment and adds a new feature to traditional scheduling problems. Practical interest in this topic has given rise to new research eorts, and there has been a series of articles in the research literature surveying the rapidly developing state of knowledge. Exam- ples include Ghosh (1), Liaee and Emmons (2), Potts and Van Wassenhove (3), and Webster and Baker (4). This paper deals with an important theoretical and practical problem in this area. We examine the single-machine model with family (or group) set-up times and a criterion of minimizing total weighted job completion time (weighted owtime). We propose new lower bounds for this problem, and then turn our attention to renement of a previously proposed branch-and-bound algorithm. The benets of our renements are illustrated by computational experiments.