Flow shops with reentry: Reversibility properties and makespan optimal schedules

Abstract

We consider flow shops with job reentry. We first discuss how reversibility properties of conventional flow shops can be generalized to flow shop models with job reentry. We show under which conditions the makespan and job flow times are reversible. Second, we examine the problem of minimizing the makespan in ordered flow shops with job reentry. In particular, we focus on two special cases of the ordered flow shop that are referred to as machine-ordered and proportionate flow shops. We specify a class of cyclic schedules that have a makespan invariance property and minimize the makespan when each job follows the same route. We then examine makespan optimal schedules in a more generalized processing environment with loop effects on job processing times for which the makespan invariance property does not hold. Lastly, we present a dispatching rule that minimizes the makespan when considering a more general form of job recirculation with the route of each job not necessarily being the same.