A Contribution to the Reentrant Flow-Shop Scheduling Problem

Abstract

This paper considers a flow-shop scheduling problem which is characterized by reentrants and aims on the minimization of makespan. Reentrants are events of a repeated processing of a specific job on a machine, which can occur due to, e.g., quality reasons. In the following, we focus on missing operations which did not receive adequate attention in the literature so far. After describing different types of reentrants, a specific level formulation is given in order to cope with processing times equal to zero in an appropriate way. Finally, we perform first computational tests with different problem sizes and compare our results with an already existing formulation with respect to solution quality and computation times. Our main results are as follows: (i) it turns out that our formulation is well suitable when zero processing times occur, as we derive better objective values for makespan; (ii) however, longer computation times have to be accepted compared to traditional formulations; (iii) the computation times are mainly influenced by the total number of jobs.