製造リードタイムに関する数理解析考察

—生産系におけるデッドラインスケジューリングの応用—

抄録

In this present paper, we apply a stochastic differential equation(SDE) for mathematical model which describes manufacturing process from input materials to an end of manufacturing process. We utilize a risk-neutral principal in stochastic calculus based on the SDE. We extend the mathematical model to allow for objective evaluation. In order to improve a lead-time in manufacturing process, we introduce a evaluation equation which satisfy a certain compatibility constraint with lead-time. A certain compatibility constraint with lead-time means a strategy, that is, “Cut off irrelevant process in entire process, and Bring back its improved the process”.
It is assumed that the probability density function of log-normal type which is a probability density function from input materials to an end of process. This present paper evaluate a certain compatibility constraint with lead-time by applying the risk neutrality and martingale measure of stochastic integral under this assumption.
After its evaluation value calculated by a evaluation equation, a process control system evaluates the each sub-process, and reschedules to improve the utilization efficiency of the entire manufacturing process.
Thus, a front-end-process is to cancel the request to the process, and follows the instructions on the process control systems. But, this present paper gives only simulation evaluation calculated the parameter, the paper does not discuss a compatibility between a evaluation value of calculated manufacturing lead-time compatibility constraint and a the real system.
However, this present paper gives a idea to search bottleneck sub-process in the manufacturing process, and gives a idea of software tool for process synchronization.