A makespan study of the two-machine flowshop scheduling problem with a learning effect

Abstract

This paper studies the problem of minimizing the makespan in a two-machine flowshop scheduling problem with learning considerations. Johnson’s rule might not provide the optimal solution for this problem. Thus, this paper not only develops several dominance relations and proposes a branch-and-bound algorithm based on them but also establishes two heuristic algorithms. Computational experiments show the accuracy of Johnson’s rule and both proposed heuristics, and a comparison of the results to the optimal solution obtained by a branch-and-bound technique is provided for small job sizes. In addition, the performances of the three heuristics, including Johnson’s rule, are also reported for large job sizes.