Deterministic chaos in a model of discrete manufacturing

Abstract

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...

Policy for Rearranging Workers for a Self-Balancing Production Line with Worker Learning

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“…There is typically assumed to be no walk-back time or hand off time in this type of line. However, Bartholdi and Eisenstein [5] consider a constant walk-back time and hand off time, and Bartholdi et al [6] and Bratcu and Dolgui [7] consider finite walk-back speeds. Additionally, Armbruster et al [8] consider the case in which there are two zones according to the speed (i.e., the worker's speed changes according to the zone).…”

Workforce reconfiguration strategies in manufacturing systems: a state of the art

“…Despite the deterministic nature of the basic bucket brigade model, it can have a chaotic behavior that negatively influences the performance of an assembly line (Bartholdi et al, 2009). Indeed, the hand-offs can be unpredictable when workers are interrupted at any time or any position of the line.…”

TECHNICAL NOTE—Cellular Bucket Brigades

“…Due to their dynamics, bucket brigades constantly seek balance and spontaneously adapt to disruptions and seasonality. For applications and related studies on bucket brigades, see Eisenstein (1996b, 2005), Bartholdi et al (1999Bartholdi et al ( , 2001Bartholdi et al ( , 2006Bartholdi et al ( , 2009, Villalobos et al (1999a,b), Eisenstein (2005), Armbruster and Gel (2006), Armbruster et al (2007), and Lim and Yang (2009). In this study, we present a novel design alternative that may provide significant improvement to the performance of a bucket brigade.…”