Permutation flowshop scheduling problems with time lags to minimize the weighted sum of machine completion times

In this article, we consider flowshop scheduling problems with minimal and maximal time lag constraints. Such constraints extend precedence constraints between operations in the jobs and may be used to model various industrial applications. The objective is to minimize a non-classical criterion based on the weighted sum of machine completion times. We show that it generalizes makespan and we derive several complexity results for two- and three-machine problems. An exact algorithm based on a branch-and-bound procedure is developed to solve the permutation flowshop problem with m machines.