Permutation flowshop problem with time lags scheduling by logic-based Benders decomposition

In this paper, we consider the problem of scheduling n jobs in an m-machine permutation flowshop with time lags between consecutive operations of each job. The processing order of jobs is the same for each machine. The time lag is defined as the waiting time between consecutive operations. We use logic-based Benders decomposition to minimize the total number of tardy jobs with long time horizon defined on the last machine. We combine Mixed Integer Linear programming (MILP) to allocate jobs to time intervals of the time horizon and scheduled using Constraint Programming (CP). Then, computational results are reported.