An Ordered Flow Shop with Two Agents

Abstract

In this paper, we consider a two-agent scheduling problem in an [Formula: see text]-machine ordered flow shop where each agent is responsible for his own set of jobs and wishes to minimize the makespan. Since the problem is NP-hard, we develop a pseudo-polynomial time approach for the case with a fixed number of machines and investigate the conditions that make the problem polynomially solvable. Finally, we consider a three-machine problem with a special processing time structure, and demonstrate its polynomiality.