Two-critical-number control policy for a stochastic production inventory system with partial backlogging
研究部分积压情形下由反射布朗运动描述库存水平的生产库存系统，提出双参数(m, M)控制策略，通过最小化长期期望总成本确定最优参数，并用数值例子和敏感性分析展示结果。
This paper deals with a production–inventory control model with partial backlogging, in which a reflected Brownian motion governs the inventory level variation. We consider a single storage facility with infinite capacity and assume that shortages are allowed and the total amount of stock-out is a mixture of backordering and lost sales. In addition, the production facility is controlled by a two-parameter (m, M) policy, which switches the production rate when the inventory level reaches the threshold values. The aim is to determine the optimal control parameters m and M by minimising the long-run total expected cost of the system. Some results are illustrated using numerical examples. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.