A new theoretical formulation for re-entrant flow shop scheduling problem is derived to plan an optimum production schedule by mixed integer programming. Flow time, which is an index of the evaluation of the planned schedule, is minimized to decrease amount of work-in-process. Cycle time, which is another important index, is determined by the total load time on a bottleneck machine to manufacture the products at the highest productivity. Both objective function and constraint conditions are described in linear expressions and a general optimization tool is adopted to solve the formulated scheduling problems. Another objective function is also introduced in order to shorten the time for the optimization. Computational scheduling results obtained by the optimization are evaluated and discussed in the present paper.
