Heuristic algorithms for two-machine flowshop with availability constraints

The majority of the scheduling studies carry a common assumption that machines are available all the time. However, machines may not always be available in the scheduling period due to breakdown or preventive maintenance. Taking preventive maintenance activity into consideration, we dealt with the two-machine flowshop scheduling problem with makespan objective. The preventive maintenance policy in this paper was dependent on the number of finished jobs. The integer programming model was proposed. We combined two recent constructive heuristics, HI algorithm and H algorithm, with Johnson’s algorithm, and named the combined heuristic H&J algorithm. We also developed a constructive heuristic, HD, with time complexities O(n²). Based on the difference in job processing times on two machines, both H&J and HD showed good performance, and the latter was slightly better. The HD algorithm was able to obtain the optimality in 98.88% of cases. We also employed the branch and bound (B&B) algorithm to obtain the optimum. With a good upper bound and a modified lower bound, the proposed B&B algorithm performed significantly effectively.