标题： 不变流形方法中的清除函数 显示英文标题

标题： Clearing function in the context of the invariant manifold method

摘要： 清除函数（CFs），它们表达了在计划期内生产设施的预期吞吐量与其工作量（或在制品，WIP）之间的数学关系，已显示出在生产计划中对依赖于在制品的周期时间进行建模的显著前景。 虽然稳态排队模型常用于推导CFs的解析表达式，但计划期的有限长度对其有效性提出了质疑。 我们采用一种不同的方法，基于机器和酶分子操作之间的类比，为单资源、单产品工厂车间提出一个机制模型。 该模型被简化为两个微分方程的奇异摄动系统，分别对应于慢变量（WIP）和快变量（运行中的机器）。 对该慢-快系统的分析发现，CF只不过是慢不变流形渐近展开的结果。 CF的有效性最终取决于乘以快变量导数的参数有多小。 结果表明，足够小的特征比例“运行机器 : WIP”保证了在非稳态操作中CF近似的适用性。 显示英文摘要

摘要： 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.