Scheduling Two-machine Flowshop with Limited Waiting Times to Minimize Makespan

There are numerous instances of flowshop in the production process of process industry. When such characteristics as continuous production resulted from high-temperature environment or deteriorate intermediate products are took into consideration, it should be ensured that the waiting time of any job between two consecutive machines is not greater than a given value, which results in the flowshop scheduling problem with limited waiting time constraints. The problem with two-machine environment to minimize makespan is studied. Based on the discussion of the lower bound of the minimal makespan and some properties of the optimal schedule, a two-stage search algorithm is proposed, in which the initial schedule is generated by a modified LK heuristic in the first stage and the excellent solution can be obtained by constructing inserting neighborhood in the second stage. The numerical results demonstrate the effectiveness of the algorithm.