论文标题
在不变歧管方法的上下文中清除功能
Clearing function in the context of the invariant manifold method
论文作者
论文摘要
清除功能（CFS）在计划期内的生产设施的预期吞吐量与在此期间的工作量（或工作中的工作量）之间的数学关系显示出了相当大的希望，可以在生产计划中建模WIP依赖性周期时间。虽然稳态排队模型通常用于得出CFS的分析表达式，但计划期限的有限长度将其有效性提出了质疑。我们采用另一种方法，根据机器和酶分子的操作之间的类比，为单资源，单产品工厂商店提出机械模型。该模型分别简化为一个慢速（WIP）和快速（繁忙的机器）变量的两个微分方程的奇异扰动系统。对这种慢速系统的分析发现，CF不过是慢速流形的渐近扩展的结果。 CF的有效性最终取决于参数将快速变量的衍生物乘以乘以的效率。结果表明，“工作机器：WIP”的特征比率足够小，可以保证CF近似在不稳定状态操作中的适用性。
Clearing functions (CFs), which express a mathematical relationship between the expected throughput of a production facility in a planning period and its workload (or work-in-progress, WIP) in that period have shown considerable promise for modeling WIP-dependent cycle times in production planning. While steady-state queueing models are commonly used to derive analytic expressions for CFs, the finite length of planning periods calls their validity into question. We apply a different approach to propose a mechanistic model for one-resource, one-product factory shop based on the analogy between the operation of machine and enzyme molecule. The model is reduced to a singularly perturbed system of two differential equations for slow (WIP) and fast (busy machines) variables, respectively. The analysis of this slow-fast system finds that CF is nothing but a result of the asymptotic expansion of the slow invariant manifold. The validity of CF is ultimately determined by how small is the parameter multiplying the derivative of the fast variable. It is shown that sufficiently small characteristic ratio 'working machines : WIP' guarantees the applicability of CF approximation in unsteady-state operation.
