Generalized preemption models for single-machine dynamic scheduling problems

Abstract

In the extensive scheduling literature, job preemption, if allowed, implies that the processing of a partly completed job is temporarily halted and later resumed at the same point. However, little attention has been given to problems where job preemption is allowed under the condition that either some startup time delay must be incurred or some fraction of work must be repeated if preemption occurs. We generalize the notion of job preemption by using models representing these conditions. The models are applied to studying the dynamic single-machine scheduling problems of minimizing total flow time, and of minimizing maximum lateness, subject to arbitrary and unknown job ready dates. On-line optimal dispatching rules, which consider only available – as opposed to look-ahead – information, are developed. These rules determine, on arrival or completion of each job, which available job should next be processed by the machine. A special case of our models, the preempt-repeat scenario, where preempted jobs must be totally repeated, is suggested as heuristic for the equivalent non-preemptive static problem where all ready dates are known and given. A computational study is performed to determine the potential benefits of reducing startup time delays or work repetition fractions in the context of continuous improvement of manufacturing systems.