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Abstract: In a social system or production line, the restrictions of the cost and the due-time exist in each period. Generally, whether these restrictions are satisfied is dependent not only on the risks of this period, but also on the risks generated beforehand. We consider controlling the production process by switching the processing rate to a faster one at a given period. This paper deals with the optimal switching period to minimize the total expected cost of the production process. We first propose the optimal switching period model, and then the mathematic formulation of the total expectation is presented. Finally, the policy of optimal switching period is investigated in detail by numerical experiments.

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