On the optimality conditions of the two-machine flow shop problem

Abstract

This paper tackles the makespan minimization for the well known two-machine flow shop problem. Several optimality conditions are discussed aiming at the characterization of a large set of optimal solutions. We show that our approach dominates some of the results found in the literature. We also establish a number of necessary optimality conditions and discuss the asymptotic behavior of the optimal makespan when the number of jobs goes to infinity.