A new optimization procedure for a re-entrant flowshop scheduling problem is proposed to plan a medium sized production schedule by mixed integer programming. Flow time is an index used to evaluate production work-in-process. The flow time is calculated from the total required cycle terms after a feasible schedule is planned. In the present paper, the reverse procedure is performed: the total cycle term is assumed before the scheduling, and the feasible schedule is planned under the assumed terms. The assumption of the total cycle term restricts the pre-assignment of every process into a corresponding cycle term. Therefore some pre-assignments never yield a feasible schedule and are eliminated from the evaluation. Methods for the assumption of the total cycle terms and for the examination of the pre-assignment of the processes are described here. The amount of times required to plan the optimal schedule is evaluated for different sizes of problems in order to validate the proposed procedures.

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