OR Spectrum

, Volume 34, Issue 1, pp 273–291 | Cite as

The variance of inter-departure times of the output of an assembly line with finite buffers, converging flow of material, and general service times

  • Michael Manitz
  • Horst Tempelmeier
Regular Article


In this paper, we propose an approximation for the variability of the inter-departure times of finished products in an assembly line with finite buffers, converging flow of material, and general service times. We use the coefficient of variation as the relevant measure of variability. Exact procedures are not available for that case. The quality of the proposed approximation is tested against the results of various simulation experiments.


Production Assembly lines Queueing models Variance of the output Inter-departure time 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Altıok TM (1997) Performance analysis of manufacturing systems. Springer series in operations research. Springer, New YorkGoogle Scholar
  2. Buzacott JA, Liu X-G, Shanthikumar JG (1995) Multistage flow line analysis with the stopped arrival queue model. IIE Trans 27(4): 444–455CrossRefGoogle Scholar
  3. Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems. Prentice-Hall, Englewood CliffsGoogle Scholar
  4. Carrascosa M (1995) Variance of the output in a deterministic two-machine line. Master thesis, Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, CambridgeGoogle Scholar
  5. Colledani M, Tolio T (2006) Impact of statistical process control (SPC) on the performance of production systems. Ann CIRP 55(1): 453–458CrossRefGoogle Scholar
  6. Dallery Y, Gershwin SB (1992) Manufacturing flow line systems: A review of models and analytical results. Queueing Theory 12: 3–94CrossRefGoogle Scholar
  7. Duenyas I, Hopp WJ (1990) Estimating variance of output from cyclic exponential queueing systems. Queueing Systems 7: 337–353CrossRefGoogle Scholar
  8. Gaver DP (1962) A waiting line with interrupted service, including priorities. J R Stat Soc 24(2): 73–90Google Scholar
  9. Gershwin SB (1987) An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking. Oper Res 35(2): 291–305CrossRefGoogle Scholar
  10. Gershwin SB (1993) Variance of output of a tandem production system. In: Onvural RD, Akyildiz IF (eds) Queueing networks with finite capacity. North-Holland, Elsevier Science Publishers, pp 291–304Google Scholar
  11. Gershwin SB (1994) Manufacturing systems engineering. Prentice-Hall, Englewood CliffsGoogle Scholar
  12. He X-F, Wu S, Li Q-L (2007) Production variability of production lines. Int J Prod Econ 107(1): 78–87CrossRefGoogle Scholar
  13. Helber S (1999) Performance analysis of flow lines with non-linear flow of material, vol 473 of Lecture Notes in Economics and Mathematical Systems. Berlin, Heidelberg, Springer, New YorkGoogle Scholar
  14. Hendricks KB (1992) The output processes of serial production lines of exponential machines with finite buffers. Oper Res 40(6): 1139–1147CrossRefGoogle Scholar
  15. Hendricks KB, McClain JO (1993) The output processes of serial production lines of general machines with finite buffers. Manage Sci 39(10): 1194–1201CrossRefGoogle Scholar
  16. Kalir AA, Sarin SC (2009) A method for reducing inter-departure time variability in serial production line. Int J Prod Econ 120: 340–347CrossRefGoogle Scholar
  17. Kuhn H (1998) Fließproduktionssysteme—Leistungsbewertung, Konfigurations- und Instandhaltungsplanung, Volume 67 of Physica-Schriften zur Betriebwirtschaft. Physica, HeidelbergGoogle Scholar
  18. Levantesi R, Matta A, Tolio T (2003) Performance evaluation of continuous production lines with machines having different processing times and multiple failure modes. Perform Eval 51(2–4): 247–268CrossRefGoogle Scholar
  19. Li J (2005) Overlapping decomposition: a system-theoretic method for modeling and analysis of complex manufacturing systems. IEEE Trans Autom Sci Eng 2(1): 40–54CrossRefGoogle Scholar
  20. Li J, Meerkov DM (2007) Production systems engineering. WingSpan Press, LivermoreGoogle Scholar
  21. Manitz M (2008) Queueing-model based analysis of assembly lines with finite buffers and general service times. Comput Oper Res 35(8): 2520–2536CrossRefGoogle Scholar
  22. Papadopoulos HT, Heavey C, Browne J (1993) Queueing theory in manufacturing systems analysis and design. Chapman & Hall, LondonGoogle Scholar
  23. Sabuncuoglu I, Erel E, Kok AG (2002) Analysis of assembly systems for interdeparture time variability and throughput. IIE Trans 34(1): 23–40Google Scholar
  24. Tan B (1999) Variance of the output as a function of time: production line dynamics. Eur J Oper Res 117: 470–484CrossRefGoogle Scholar
  25. Tan B (2000) Asymptotic variance rate of the output in production lines with finite buffers. Ann Oper Res 93: 385–403CrossRefGoogle Scholar
  26. Tempelmeier H, Bürger M (2001) Performance evaluation of unbalanced flow lines with general distributed processing times, failures and imperfect production. IIE Trans 33(4): 293–302Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Supply Chain Management and ProductionUniversity of CologneKölnGermany

Personalised recommendations