Min-Max Regret Version of an m-Machine Ordered Flow Shop with Uncertain Processing Times

Abstract

We consider an m-machine flow shop scheduling problem to minimize the latest completion time, where processing times are uncertain. Processing time uncertainty is described through a finite set of processing time vectors. The objective is to minimize maximum deviation from optimality for all scenarios. Since this problem is known to be NPhard, we consider it with an ordered property. We discuss optimality properties and develop a pseudo-polynomial time approach for the problem with a fixed number of machines and scenarios. Furthermore, we find two special structures for processing time uncertainty that keep the problem NP-hard, even for two machines and two scenarios. Finally, we investigate a special structure for uncertain processing times that makes the problem polynomially solvable.

Makespan minimization for the m-machine ordered flow shop scheduling problem

“…They showed that only one case is polynomially solvable and the other two cases are NP-hard. Park and Choi (2015) considered uncertain processing times in the m-machine flow shop scheduling problem. Since the general problem with the objective function of minimizing the maximum deviation from the optimality for all scenarios is proved to be NP-hard (Kouvelis and Daniels, 2000), they studied the problem with ordered processing times.…”