Dynamic Programming Algorithms for Two-Machine Hybrid Flow-Shop Scheduling With a Given Job Sequence and Deadline

In “Shared Manufacturing” environment, orders are processed in a given job sequence which is based on the time of receipt of orders. This paper studies a problem of scheduling two-task jobs in a two-machine hybrid flow-shop subject to a given job sequence which is used in production of electronic circuits under shared manufacturing. Each job has two tasks: the first one is a flexible task, which can be processed on either of the two machines, and the second one is a preassigned task, which can only be processed on the second machine after the first task is finished. Each job has a processing deadline. Three objective functions related to deadlines are considered. The computational complexity of the problem for any of three objective functions is showed to be ordinary NP-hard, a dynamic programming algorithm (DPA) is presented for each case and the time complexity of each algorithm is given. The results of computational experiments show the relationship between the running time of DPA and the parameters, and also show the advantages of DPA in dealing with this problem compared with branch-and-bound algorithm and iterated greedy algorithm.