Trade-off between Time Complexity and Makespan for Flexible Flow-Shop Group Scheduling Problems with Two Machine Centers

The flexible flow-shop group scheduling problem is investigated in this paper to minimize the makespan. Two algorithms have been proposed to solve the problem with two machine centers, which have the same number of parallel machines. The first one is a heuristic algorithm. It first determines the sequence of jobs in each group by Sriskandarajah and Sethi’s approach of solving the flexible flow-shop problems of two machine centers. It then determines the sequence of groups by the Johnson algorithm. The second one is a nearly optimal algorithm based on the search-and-prune technique, but can get better solutions. It can also be used to measure the performance of the first algorithm. Experimental results show that the 1400 Tzung-Pei Hong, Pei-Ying Huang and Gwoboa Horng second approach can solve the problem with only a very limited size due to its high time complexity. The heuristic approach can, however, quickly obtain the approximate results, with much less computation time than that by the nearly optimal algorithm and with a similar quality of solutions. The proposed heuristic algorithm thus provides a feasible solution to large group scheduling problems that cannot be solved by the nearly optimal one. A trade-off can be easily achieved between accuracy and time complexity. Mathematics Subject Classification: 90B35