Abstract
The fluctuations of the buffered flow of parts delivered by failure prone production processes are analyzed by using a fluid model. The presence of storage regions between the production centers introduces memory effects into the dynamics of the flow of parts. As a consequence, the production output delivered by the factory can be approximately described by stochastic differential equations with noises being non-markovian alternating renewal processes. The relevant probabilistic properties of the solutions of such stochastic differential equations are discussed. Using results available in the context of dam’s theory, we derive, as an illustration, an exact characterization of the output process delivered by a production dipole composed of two machines separated by a single storage zone.
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References
Y. Dallery and S. B. Gerschwin, Manufacturing flow line systems. A review of models and analytical results, Queuing Systems and Appl., 12 (1992), 3–94.
S. B. Gerschwin, Manufacturing System Engineering, Prentice Hall, 1994.
S. B. Gerschwin, Variance of the output of a tandem production system, in: R. Onvural and I. Akyldiz, Eds., Proceedings of the 2nd International Workshop on Queuing Network with Finite Capacity, Triangle Park, 1993.
G. Miltenburg, Variance of the number of units produced on a transfer line with buffer inventories during a period of length T, Naval Research Log, 34 (1987), 811–822.
K. Hendricks, The output process of serial production lines of exponential machines with finite buffers, Op. Res., 40 (1992), 1139–1147.
S. Ross, Stochastic Processes, J. Wiley, 1983.
L. Takacs, On certain sojourn time problems in the theory of stochastic processes, Acta Math Hungarica, 8 (1957), 169–191.
D. P. Gaver and R. G. Miller, Limiting distributions for some storage problems, in: K. J. Arrow, S. Karlin and H. Scarf, Eds., Studies in Applied Probability and Management Science, Stanford University Press, 1962, 110–126.
C. Terracol and R. David, Performance d’une ligne composée de machines et de stocks intermédiaires, A.P.I.I., 21 (1987), 239–262.
C. Commault and A. Semery, Taking into account delays in buffers for analytical performance of transfer lines, I.I.E. Trans., 22 (1990), 133–140.
P. Coillard and J. M. Proth, Sur l’effet de l’adjonction de stocks tampon dans une fabrication en ligne, Rev. Belge de Stat. Infor, et de R.O., 24 (1983), 1–23.
D. Dubois and J.-P. Forestier, Productivité et en-cours moyen d’un ensemble de deux machines séparées par une zone de stockage, R.A.I.R.O. Autom. Syst. Analysis and Control, 16 (1981), 105–132.
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© 1999 Springer Basel AG
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Ciprut, P., Hongler, MO., Salama, Y. (1999). Random Production Flows. An Exactly Solvable Fluid Model. In: Dalang, R.C., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 45. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8681-9_9
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DOI: https://doi.org/10.1007/978-3-0348-8681-9_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9727-3
Online ISBN: 978-3-0348-8681-9
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