A branch and bound approach to minimize the total completion time in a k-stage hybrid flowshop

The aim of this paper is to present a branch and bound approach to solve a k-stage hybrid flowshop scheduling problem in order to minimize the total completion time. This scheduling problem encloses three subproblems: lot sizing, scheduling and assignment problems. In this paper only scheduling and assignment are taken into account because we suppose that the lot sizing problem has already been solved. The method we propose is an optimal method, based on a special architecture of search tree which allows us to solve the two subproblems considered. Some lower bounds are proposed. Then computational results are given and proved that results are acceptable. Finally, two theorems demonstrate some dominance relations.