×

zbMATH — the first resource for mathematics

Conservation of filtering in manufacturing systems with unreliable machines and finished goods buffers. (English) Zbl 1200.91160
Summary: This paper addresses the issue of reliable satisfaction of customer demand by unreliable production systems. In the framework of a simple production-storage-customer model, we show that this can be accomplished by using an appropriate level of filtering of production randomness. The filtering is ensured by finished goods buffers (filtering in space) and shipping periods (filtering in time). The following question is considered: how are filtering in space and filtering in time interrelated? As an answer, we show that there exists a conservation law: in lean manufacturing systems, the amount of filtering in space multiplied by the amount of filteringin time (both measured in appropriate dimensionless units) ispractically constant. Along with providing an insight into the nature of manufacturing systems, this law offers a tool for selecting the smallest, that is, lean, finished goods buffering, which is necessary and sufficient to ensure the desired level ofcustomer demand satisfaction.

MSC:
91B38 Production theory, theory of the firm
91B70 Stochastic models in economics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] M. Carrascosa, Variance of the output in a deterministic two-machine line, M.S. thesis, Laboratory for Manufacturing and Productivity, MIT, Massachusetts, 1995.
[2] P. Ciprut, M.-O. Hongler, and Y. Salama, “On the variance of the production output of transfer lines,” IEEE Transactions on Robotics and Automation, vol. 15, no. 1, pp. 33-43, 1999.
[3] P. Ciprut, M.-O. Hongler, and Y. Salama, “Fluctuations of the production output of transfer lines,” Journal of Intelligent Manufacturing, vol. 11, no. 2, pp. 183-189, 2000.
[4] I. Duenyas and W. J. Hopp, “CONWIP assembly with deterministic processing and random outages,” IIE Transactions, vol. 24, no. 4, pp. 97-109, 1992.
[5] S. B. Gershwin, “Variance of output of a tandem production system,” in Queuing Networks with Finite Capacity, R. O. Onvural and I. F. Akyildiz, Eds., Elsevier, 1993.
[6] K. B. Hendricks, “The output process of serial production lines of exponential machines with finite buffers,” Operations Research.I, vol. 40, no. 6, pp. 1139-1147, 1992. · Zbl 0825.90522
[7] D. A. Jacobs and S. M. Meerkov, “System-theoretic analysis of due-time performance in production systems,” Mathematical Problems in Engineering, vol. 1, no. 3, pp. 225-243, 1995. · Zbl 0919.90083
[8] J. Li, E. Enginarlar, and S. M. Meerkov, “Random demand satisfaction in unreliable production-inventory-customer systems,” Annals of Operations Research, vol. 126, pp. 159-175, 2004. · Zbl 1040.90011
[9] J. Li and S. M. Meerkov, “Bottlenecks with respect to due-time performance in pull serial production lines,” Mathematical Problems in Engineering, vol. 5, no. 6, pp. 479-498, 2000. · Zbl 0972.90022
[10] J. Li and S. M. Meerkov, “Production variability in manufacturing systems: Bernoulli reliability case,” Annals of Operations Research, vol. 93, pp. 299-324, 2000. · Zbl 0946.90015
[11] J. Li and S. M. Meerkov, “Customer demand satisfaction in production systems: a due-time performance approach,” IEEE Transactions on Robotics and Automation, vol. 17, no. 4, pp. 472-482, 2001.
[12] J. Li and S. M. Meerkov, “Due-time performance of production systems with Markovian machines,” in Analysis and Modeling of Manufacturing Systems, S. B. Gershwin, Y. Dallery, C. T. Papadopoulos, and J. M. Smith, Eds., pp. 221-253, Kluwer Academic, Massachusetts, 2003. · Zbl 1059.90056
[13] G. J. Miltenburg, “Variance of the number of units produced on a transfer line with buffer inventories during a period of length T,” Naval Research Logistics., vol. 34, no. 6, pp. 811-822, 1987. · Zbl 0648.90034
[14] B. Tan, “Variance of the throughput of an N-station production line with no intermediate buffers and time dependent failure,” European Journal of Operational Research, vol. 101, no. 3, pp. 560-576, 1997. · Zbl 0916.90119
[15] B. Tan, “Effects of variability on the due-time performance of a continuous materials flow production system in series,” International Journal of Production Economics, vol. 54, no. 1, pp. 87-100, 1998.
[16] B. Tan, “Variance of the output as a function of time: production line dynamics,” European Journal of Operational Research, vol. 117, no. 3, pp. 470-484, 1999. · Zbl 0948.90056
[17] B. Tan, “Asymptotic variance rate of the output in production lines with finite buffers,” Annals of Operations Research., vol. 93, pp. 385-403, 2000. · Zbl 0953.90017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.