Some underlying mathematical definitions and principles for cellular manufacturing
Some underlying mathematical definitions and principles for cellular manufacturing
复制标题
细胞制造的一些基本数学定义和原理
DOI：
10.1142/s0217595914500080
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Ikou Kaku
中科院分区：
文献类型：
--
作者：
Yong Yin;ChenGuang Liu;Ikou Kaku
本文利用集合论对单元化制造系统进行分析。我们开发了一个结构体系结构来调查以前的文献。我们将所有的研究问题分为三类--什么、为什么和如何。我们主张从哲学和科学两个角度来研究这三类问题。要全面深入地理解细胞制造，三个问题和两个视角都是重要的。我们使用开发的体系结构回顾了细胞制造的文献，并指出了以前研究中的弱点。这一综述推动了本文的研究。我们用简单而严谨的集合论来分析两个什么问题。定义了零件族、机械单元、单元化制造系统、瓶颈机床等基本概念。根据这些定义，我们推导出了完全划分单元制造系统的充要条件。发现了完全划分的两个充要条件--先验完全划分定理检验任意制造系统中潜在的独立制造单元；相反，后验完美划分定理检验完全划分的单元制造系统。据我们所知，我们是第一批将严格的数学模型应用于这两类细胞制造问题的公司之一。我们试图提供数学词汇来讨论细胞制造系统设计中固有的常见问题。
This paper uses set theory to analyze cellular manufacturing systems. We develop a structural architecture to investigate the previous literature. We divide all research problems into three types —what,why, andhow. We advocate studying these three types of problems from two managerial perspectives —philosophyandscience. To fully and deeply understand cellular manufacturing, boththree-problemsandtwo-perspectivesare important. We use the developed architecture to review cellular manufacturing literature and point out the weakness in the previous studies. This review motivates the research of this paper. We use simple but rigorous set theory to analyze twowhat-problems. Underlying concepts, such as part family, machine cell, cellular manufacturing system, bottleneck machine are defined. Following these definitions, we deduce sufficient and necessary conditions for perfectly partitioned cellular manufacturing systems. Two sufficient and necessary conditions of perfect partition have been discovered —prior perfect partition theoremscheck the potential independent manufacturing cells within an arbitrary manufacturing system; in contrast,posterior perfect partition theoremverifies a perfectly partitioned cellular manufacturing system. To our knowledge, we are among the first to apply rigorous mathematical models to these two types ofwhat-problems for cellular manufacturing. We try to provide mathematical vocabularies to discuss common problems inherent in the design of cellular manufacturing systems.