Stochastic processes and their network representations associated with a production line queuing model

Muth, Eginhard J.

doi:10.1016/0377-2217(84)90049-3

Cited by 51 publications

(31 citation statements)

References 8 publications

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“…In the case of asynchronous transfer, the analysis is much more complex. The case of three machine flow lines was deeply investigated by Hunt (1956), Hillier and Boling (1967), Hildebrand (1968), Muth (1973Muth ( , 1977Muth ( , 1984, Muth and Alkaff (1987), Rao (1976aRao ( , 1976b.…”

Section: Flow Lines With No Intermediate Storagementioning

confidence: 99%

“…It is the sum of the processing time and possibly some blocking time. The holding time at Machine M 1 , H 1 , can be expressed as (Muth, 1984)…”

Section: Flow Lines With No Intermediate Storagementioning

confidence: 99%

“…Numerical solutions have been obtained by Muth (1977Muth ( , 1984 and Rao (1976aRao ( , 1976b for specific distributions of the processing times. A unifying solution is provided by Muth and Alkaff (1987) under the following assumptions: Machines M 1 and M 3 have special phase-type distributions, while Machine M 2 has a Laplace transformable distribution.…”

Section: Flow Lines With No Intermediate Storagementioning

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: Flow Lines With No Intermediate Storagementioning

confidence: 99%

“…It is the sum of the processing time and possibly some blocking time. The holding time at Machine M 1 , H 1 , can be expressed as (Muth, 1984)…”

Section: Flow Lines With No Intermediate Storagementioning

confidence: 99%

Section: Flow Lines With No Intermediate Storagementioning

confidence: 99%

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

1992

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“…Muth (1984) models a production line of k stations, where the service time at each station is given by a random variable. Weber and Weiss (1994) describe an interesting problem called the "cafeteria problem."…”

mentioning

confidence: 99%

The effects of pick density on order picking areas with narrow aisles

2006

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The cost and service performance of an order fulfillment center are determined partly by how workers are organized into an order picking system. One common approach is batch picking, in which workers circumnavigate a picking area with other workers, gathering items on a pick list. In some systems with high space utilization, narrow aisles prohibit workers from passing one another when in the same aisle, and this leads to congestion. We build analytical and simulation models of these systems to investigate their behavior under different levels of activity. Among other things, our results suggest that when the system is busier and pick density is high -that is, when workers stop often to make picks -congestion is less of a problem and workers are more productive.

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“…Processing times at the service stations are independent exponential random variables, possibly with different means. This study is an extension of the work started in Muth [166] to provide an algorithm that allows for the efficient computation of longer lines and to provide results for the non-identical server case. The results provides the distribution function of the holding time at the stations.…”

Section: Steady-state Behaviormentioning

confidence: 99%