The Reversibility Property of Production Lines.

Muth, Eginhard J.

doi:10.21236/ada050043

Cited by 14 publications

(24 citation statements)

References 2 publications

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“…Then, the following reversibility property has been established by Yamazaki and Sakasegawa (1975), Dattatreya (1978), and Muth (1979): the production rate of the reversed line L r is the same as that of the original line L. The proof is based on the comparison of the sample paths of the two systems again using the evolution equations introduced in Section 3.3. (Note that they actually used equation (19).)…”

Section: Reversibility and Duality Propertiesmentioning

confidence: 99%

“…They have proved to be very useful in flow line analysis, mainly for establishing qualitative properties such as monotonicity and reversibility. These equations have been used in many papers under various forms, e.g., Hildebrand (1967Hildebrand ( , 1968, Yamazaki and Sakasegawa (1975), Muth (1979), Shanthikumar and Yao (1989), Dallery, Liu, and Towsley, (1990).…”

Section: Evolution Equationsmentioning

confidence: 99%

“…This trick is due to Avi-Itzhak (1965). Evolution equations of this simpler form were used, among others, by Hildebrand (1967Hildebrand ( , 1968, Yamazaki and Sakasegawa (1975), and Muth (1979).…”

Section: Evolution Equationsmentioning

confidence: 99%

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Manufacturing flow line systems: a review of models and analytical results

1992

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The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.

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Section: Reversibility and Duality Propertiesmentioning

confidence: 99%

Section: Evolution Equationsmentioning

confidence: 99%

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Manufacturing flow line systems: a review of models and analytical results

1992

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“…We assume that the processing times of a job on all the machines are identically distributed. We extend an important result by Muth (1979), which states that the makespan for any sequence of jobs 1,2, ••• ,n is stochastically the same as the makespan for the reversed sequence n, ••• ,2,1. The author required that processing time of the job ion all the machines be independent and identically distributed.…”

Section: mentioning

confidence: 74%

“…The results can be obtained using the duality. Muth (1979) shows that with Assumption IIJ the makespan for any sequence of machines is stochastically the same as the makespan if the sequence of machines is reversed. This is an extremely important result, since it holds regardless of the storage capacity.…”

Section: Stochastic Flow Shopsmentioning

confidence: 99%