供应链事件管理的正式建模方法

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"一种供应链的正式建模方法" 在供应链管理领域,随着供应链变得越来越动态,对实时感知并响应事件的能力需求日益增强。这篇研究论文提出了一个结合时间与颜色(用于表示案例数据)扩展的Petrinet形式化模型,用于管理供应链中的事件。作者Rong Liu、Akhil Kumar和Wil van der Aalst分别来自IBM Research、Smeal College of Business以及Eindhoven Technical University,他们在2005年9月首次提交,经过修订后于2006年11月再次提交,并于同年12月被接受,最终于2006年12月20日在线发布。 文章的核心在于,研究者设计了七种基础模式来捕获供应链建模中常见的概念。这些基础模式不仅可以单独使用,也可以组合起来创建新的模式。通过这种方式,他们展示了如何构建一个完整的Petrinet,并利用依赖图和模拟进行分析。依赖图作为一种工具,可以用来分析各种事件及其原因之间的关系,而模拟则进一步提供了对供应链流程性能的洞察。 Petrinet是一种图形建模语言,通常用于建模和分析并发系统的行为。在这个扩展版本中,时间元素的引入使得模型能够考虑事件发生的顺序和持续时间,而颜色(或案例数据)的添加则允许模型包含具体业务数据,如库存量、订单状态等。 供应链事件管理的关键在于理解和预测事件的影响。通过使用扩展的Petrinet,研究人员和管理者能够更准确地识别关键事件,预测潜在问题,并制定相应的应对策略。依赖图的分析揭示了事件之间的因果关系,有助于提前识别可能的风险和瓶颈。模拟则提供了一个测试不同场景的平台,可以在实际操作之前评估各种决策的可能结果。 这项工作为供应链的事件管理提供了一种严谨且实用的方法,它强调了实时响应能力和模型的灵活性,对于优化供应链的运行效率和应变能力具有重要意义。通过结合形式化建模、依赖图分析和模拟,供应链的决策过程变得更加科学,从而能够更好地适应快速变化的市场环境。

For macroscopically anisotropic media in which the variations in the phase stiffness tensor are small, formal solutions to the boundary-value problem have been developed in the form of perturbation series (Dederichs and Zeller, 1973; Gubernatis and Krumhansl, 1975 ; Willis, 1981). Due to the nature of the integral operator, one must contend with conditionally convergent integrals. One approach to this problem is to carry out a “renormalization” procedure which amounts to identifying physically what the conditionally convergent terms ought to contribute and replacing them by convergent terms that make this contribution (McCoy, 1979). For the special case of macroscopically isotropic media, the first few terms of this perturbation expansion have been explicitly given in terms of certain statistical correlation functions for both three-dimensional media (Beran and Molyneux, 1966 ; Milton and Phan-Thien, 1982) and two-dimensional media (Silnutzer, 1972 ; Milton, 1982). A drawback of all of these classical perturbation expansions is that they are only valid for media in which the moduli of the phases are nearly the same, albeit applicable for arbitrary volume fractions. In this paper we develop new, exact perturbation expansions for the effective stiffness tensor of macroscopically anisotropic composite media consisting of two isotropic phases by introducing an integral equation for the so-called “cavity” strain field. The expansions are not formal but rather the nth-order tensor coefficients are given explicitly in terms of integrals over products of certain tensor fields and a determinant involving n-point statistical correlation functions that render the integrals absolutely convergent in the infinite-volume limit. Thus, no renormalization analysis is required because the procedure used to solve the integral equation systematically leads to absolutely convergent integrals. Another useful feature of the expansions is that they converge rapidly for a class of dispersions for all volume fractions, even when the phase moduli differ significantly.

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