Chaos in discrete production systems?

Schmitz, Jesse; Beek, D.A. van; Rooda, J.E.

doi:10.1016/s0278-6125(02)80164-9

Cited by 36 publications

(36 citation statements)

References 11 publications

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“…Recently Schmitz et al [21] surveyed claims of chaos in manufacturing and concluded "Realistic, non-artificial discrete-event models of discrete production systems that show chaotic behavior, as defined in the theory of chaos in dynamic systems, were not found in this study".…”

Section: Chaosmentioning

confidence: 63%

“…We offer a model of bucket brigade assembly lines that meets the criteria of Schmitz et al [21]. The model is realistic: Indeed, bucket brigades are currently used in a variety of manufacturing environments, examples of which are documented at Bartholdi and Eisenstein [4].…”

Section: Chaosmentioning

confidence: 99%

“…This model treats manufacturing as a process and the product as a fluid. In this model there are no discrete or intermediate products and therefore it did not satisfy the criteria of Schmitz et al [21]. Armbruster [2] agrees, saying "One major drawback of the switched arrival system is the fact that the chaotic dynamics are strictly internal to the production-the total throughput through the set of machines is always constant and does not reflect the chaotic dynamics".…”

mentioning

confidence: 99%

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Deterministic chaos in a model of discrete manufacturing

Bartholdi

Eisenstein

Lim

2009

Naval Research Logistics

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A natural extension of the bucket brigade model of manufacturing is capable of chaotic behavior in which the product intercompletion times are, in effect, random, even though the model is completely deterministic. This is, we believe, the first proven instance of chaos in discrete manufacturing. Chaotic behavior represents a new challenge to the traditional tools of engineering management to reduce variability in production lines. Fortunately, if configured correctly, a bucket brigade assembly line can avoid such pathologies. ChaosSome simple deterministic systems can generate surprisingly complicated behavior that has been termed "chaotic". A system that is chaotic has long-term behavior that can be hard to describe, hard to predict, and hard even to simulate. Indeed, long-term behavior of chaotic systems seems to be deeply connected to randomness. discrete-event models of discrete production systems that show chaotic behavior, as defined in the theory of chaos in dynamic systems, were not found in this study".To our knowledge, only one model of a production system has heretofore been formally shown to exhibit chaotic dynamics and that is the switched arrival system studied in Chase et al. [10]. This model treats manufacturing as a process and the product as a fluid. In this model there are no discrete or intermediate products and therefore it did not satisfy the criteria of Schmitz et al. [21]. Armbruster [2] agrees, saying "One major drawback of the switched arrival system is the fact that the chaotic dynamics are strictly internal to the production-the total throughput through the set of machines is always constant and does not reflect the chaotic dynamics". In short, it is not the strong example one would prefer to display if chaos can indeed be found in manufacturing systems.In the model of Chase et al.[10] a single switching server distributes work over n parallel machines. The amount of work in the buffer in front of each machine is assumed to be a continuous variable and the processing rate of each machine is assumed to be constant. The server continues to fill the current buffer until some other buffer empties. The rate at which the server fills a buffer is equal to the sum of the processing rates of all machines. When the system is sampled at the instants when any buffer empties, the dynamics of the system can be represented by a function that, for n = 3, maps the unit interval into itself. Chase et al.[10] showed that this function, which describes the amount of work in the buffers, can be chaotic. Others have extended the model in various ways, as may be found in Ushio et al. We offer a model of bucket brigade assembly lines that meets the criteria of Schmitz et al.[21]. The model is realistic: Indeed, bucket brigades are currently used in a variety of manufacturing environments, examples of which are documented at Bartholdi and Eisenstein [4]. Furthermore, the model explicitly represents each product as a discrete entity with start and completion times. As we show, the product intercompletion times...

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Section: Chaosmentioning

confidence: 63%

Section: Chaosmentioning

confidence: 99%

mentioning

confidence: 99%

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Deterministic chaos in a model of discrete manufacturing

Bartholdi

Eisenstein

Lim

2009

Naval Research Logistics

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“…In general, complexity is not easy to measure, since it is difficult to define precisely. Obviously, there are many useful complexity definitions related to manufacturing systems (see, e.g., [5][6][7][8][9]). In addition, several approaches were proposed during the past decades to analyze the manufacturing complexity.…”

Section: Introductionmentioning

confidence: 99%

Novel Complexity Indicator of Manufacturing Process Chains and Its Relations to Indirect Complexity Indicators

Modrák

Šoltysová

2017

Complexity

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Manufacturing systems can be considered as a network of machines/workstations, where parts are produced in flow shop or job shop environment, respectively. Such network of machines/workstations can be depicted as a graph, with machines as nodes and material flow between the nodes as links. The aim of this paper is to use sequences of operations and machine network to measure static complexity of manufacturing processes. In this order existing approaches to measure the static complexity of manufacturing systems are analyzed and subsequently compared. For this purpose, analyzed competitive complexity indicators were tested on two different manufacturing layout examples. A subsequent analysis showed relevant potential of the proposed method.

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“…Nevertheless, application of the chaos theory to production systems is considered as a relatively new area (Schmitz et al 2002). In production systems, the models considered usually involve a system of liquid tanks with a switched flow server.…”

mentioning

confidence: 99%