Abstract An adaptive production control structure for failure-prone manufacturing systems under inventory and demand uncertainty is proposed. It contains estimation and forecasting modules incorporated into a control loop. The customer demand is unknown and its rate is composed of ramp-type, seasonal and random components. Information available to decision maker consists of imprecise inventory records, and the Kalman filter technique is used for estimating the inventory level and demand rate online from noisy inventory measurements. Estimates obtained are shown to converge to the actual values in stochastic sense. They are subsequently used for demand component forecasting, once the estimation errors become sufficiently small. A forecasting algorithm allows estimating ramp-type and seasonal demand components, together with their potential errors. Obtained estimates are incorporated into production control procedures, recently developed for manufacturing systems under variable and uncertain demand. Optimality conditions in the form of Hamilton-Jacobi-Bellman equations are obtained. A constructive numerical method for computing sub-optimal production policies is proposed and validated through numerical simulations.

中文翻译：

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基于卡尔曼滤波器的需求和库存信息不精确的单机单产品制造系统的生产控制

摘要 提出了一种在库存和需求不确定的情况下易发生故障的制造系统的自适应生产控制结构。它包含合并到控制回路中的估计和预测模块。客户需求未知，其费率由斜坡型、季节性和随机分量组成。决策者可用的信息包括不精确的库存记录，卡尔曼滤波器技术用于根据嘈杂的库存测量在线估计库存水平和需求率。显示获得的估计值会收敛到随机意义上的实际值。一旦估计误差变得足够小，它们随后将用于需求成分预测。预测算法允许估计斜坡类型和季节性需求分量，以及它们的潜在错误。获得的估计被纳入生产控制程序，最近为可变和不确定需求下的制造系统开发。获得了 Hamilton-Jacobi-Bellman 方程形式的最优条件。提出了一种用于计算次优生产策略的构造性数值方法，并通过数值模拟进行了验证。