The main purpose of this research is to propose a mathematics model, in which includes the random yields and process time, the rework yields and process time, the stock cost and the shortage cost. This paper also studies the optimal decisions of input quantity and timing under the technological uncertainty, which will maximize the total expected profits. Secondly, to solve the mathematical model algorithm with utilizing the numerical analysis is deeply discussed this paper. In addition, to understand the influence between the function of profits and relevant parameters, this study analyze the susceptibility of the function of the total expect profits versus relevant parameters. Furthermore, the meaning of this research theme and the verification to the inference with a numerical analysis is explained this paper. For the reference of the follow-up study, there are nine concrete conclusions summarized at the end of the paper.