Optimal Makespan for the Coupled Task Ordered Flow-Shop

Abstract

The ordered flow-shop scheduling problem deals with the case where processing times follow a specific structure. We extend the ordered flow-shop scheduling to the coupled tasks setting, i.e., the coupled task ordered flow-shop, in which an exact delay exists between the consecutive tasks of each job. The aim is to minimize the makespan. The coupled task flow-shop with distinct delays between the consecutive tasks of the jobs is known to be strongly NP-hard, even for two machines and the unit execution time tasks. We investigate the problem when delays follow the ordered structure and show that the optimal permutation schedule has the pyramidal-shaped property. We also introduce two polynomially solvable cases.

Keywords: ordered flow-shop, coupled task, exact delays, pyramidal property, makespan