Logic-based Benders decomposition to solve the permutation flowshop scheduling problem with time lags

Abstract

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). Also, a lower bound based on Moore's algorithm is developed. Then, computational results are reported.