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The total flow-time problem of two machine open-shop is NP-hard in strong sense. For the above problem without constrains, an explicit solution is constructed in this paper from the optimal schedule under the non-idle machine constraint, its total flow-time is reductive. The explicit solution under non-idle machine constraints must not be the explicit solution without constraints is proved under the consideration. Keywords-Total flow-time, Open-shop, Efficient algorithm, Scheduling

The Improvement of The Total Flow-Time Problem under The Non-Idle Machine Constraint of Two Machine Open-Shop