A branch-and-bound approach to the no-idle flowshop scheduling problem

This paper addresses to the problem of flowshop scheduling under no-idle constraints with respect to the total completion time criterion. A branch and bound algorithm is proposed and a machine based lower bound is developed for the first time in the literature of this problem. Moreover, an Iterated Local Search (ILS) algorithm is used to provide the upper bounds of the problem. The computational results are promising, and the proposed algorithm appears able to find optimal solutions to problems with up to 20 jobs and 4 machines.