A Decomposition Approach with Inserted Idle Time Scheduling Subproblems in Group Scheduling

This paper focuses on minimizing the makespan of a multi-machine flowshop group-scheduling problem that is typically found in the assembly of printed circuit boards, which is characterized as one with carryover sequencedependent setup times. The intent is to minimize the makespan of schedules comprised of the sequence of board groups as well as the sequence of board types within each group. Specifically, the models and algorithms developed for identifying strong lower bounds on the optimal/near optimal solutions within a reasonable computation time are emphasized. The efficacy of the lower bound developed is demonstrated by using it to quantify the quality of a heuristic solution for the same problem, developed based on tabu search. To obtain strong lower bounds, the problem is decomposed into a master problem and single-machine subproblems which, except for the subproblem on the first machine, are inserted idle time scheduling problems. A tabu search based heuristic is developed to solve the subproblems approximately. Each solution found during the tabu search process is evaluated using a timetabling problem that is formulated as a simple integer program for identifying the inserted optimal idle times on the machine in order to minimize the subproblem objective function. The column generation algorithm developed for the decomposed problem is demonstrated on a real problem obtained from the industry.