Control of a discrete parts production system with random part production times to meet a given schedule

A production system is modeled as a stochastic discrete-event process. The production system produces discrete parts from an infinite supply of raw materials. The production time for a part is exponentially distributed and can be affected by a control variable-the production rate, which can be adjusted only at production initiation epochs for the discrete parts. A short-term cost criterion is introduced to accommodate two primary economic factors: cost due to the control effort and cost based on missing production deadlines. This short-term cost function depends only on quantities in the production of a single part, but with a correction term to achieve better long-term performance. Two cases are considered in detail: one case where the penalty on missing the part production deadline is asymmetric and another case where the penalty is symmetric. In each case, the optimal operating policy is determined by minimizing the short-term cost function. Properties of the resultant optimal control policy are investigated; the closed-loop behavior of the production system under the optimal control policy is discussed for each case