Mathematical Analysis of Manufacturing Lead Time: Applications to Deadline Scheduling in Manufacturing Systems

SUMMARY In this paper, we apply a stochastic differential equation (SDE) as a mathematical model that describes the manufacturing process from input of materials to the end of the process. We utilize the risk‐neutral principle in stochastic calculus based on the SDE. We extend the mathematical model to allow for objective evaluation. In order to improve the lead time in a manufacturing process, we introduce an evaluation equation that satisfies a certain compatibility constraint with respect to the lead time; this compatibility constraint with lead time refers to a strategy that eliminates irrelevant processes from the overall process, and results in improvements to the process. We assume a probability density function of log‐normal type, which is the probability density function from the input materials to the end of the process. The present paper evaluates a certain compatibility constraint with lead time by applying risk neutrality and the martingale measure of the stochastic integral under this assumption. After the evaluation value is calculated by the evaluation equation, a process control system evaluates each subprocess and performs rescheduling to improve the utilization efficiency of the entire manufacturing process. Thus, a front‐end process is used to cancel requests to the process, and follows the instructions in the process control systems. However, the present paper gives only a simulation evaluation in which the parameters are calculated, and does not discuss compatibility between an evaluation value based on the calculated manufacturing lead time compatibility constraint and a real system. However, the paper offers an idea for finding bottleneck subprocesses in a manufacturing process, and for use as a software tool for process synchronization.