Skip to main content

Modeling and Analysis of Output Variability in Discrete Material Flow Production Systems

  • Chapter
  • First Online:
Handbook of Stochastic Models and Analysis of Manufacturing System Operations

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 192))

Abstract

Developing analytical models for performance evaluation of production systems has been subject to numerous studies in the literature [4, 15, 24]. The main focus in most of these studies has been on utilizing Markovian models and deriving various first-order performance measures from the steady-state probabilities. The most commonly used performance measure in these studies is the throughput that is defined as the number of products produced per unit time in the long run. In addition average inventory levels, the average time spent in the system, probability of stock-out, probability of blocking and starvation are also used to design and control production systems by using these analytical models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Angius, A., Horvath, A., & Colledani, M. (2011). Moments of cumulated output and completion time of unreliable general Markovian machines. In Proceeding of the 18th World congress of the international federation of automatic control (IFAC), Milan, Italy.

    Google Scholar 

  2. Assaf, R. (2012). Analysis of the output variability in multi-stage manufacturing systems, PhD Thesis, Politecnico di Milano, Department of Mechanical Engineering, Milano, Italy.

    Google Scholar 

  3. Buzacott, J. A., & Kostelski, D. (1987). Matrix-geometric and recursive algorithm solution of a two-stage unreliable flow line. IIE Transactions, 19, 429–438.

    Article  Google Scholar 

  4. Buzacott, J. A., & Shanthikumar, J. G. (1993). Stochastic models of manufacturing systems. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  5. Carrascosa, M. (1995). Variance of the output in a deterministic two-machine line, Master’s thesis, Massachusetts Institute of Technology, Cambridge, MA.

    Google Scholar 

  6. Chen, C. T., & Yuan, J. (2004). Transient throughput analysis for a series type system of machines in terms of alternating renewal processes. European Journal of Operational Research, 155, 178–197.

    Article  Google Scholar 

  7. Ciprut, P., Hongler, M. O., & Salama, Y. (2000). Fluctuations of the production output of transfer lines. Journal of Intelligent Manufacturing, 11, 183–189.

    Article  Google Scholar 

  8. Colledani, M., Matta, A., & Tolio, T. (2008). Analysis of the production variability in manufacturing correct lines. ASME Conference Proceedings, 2008(48357), 381–390.

    Google Scholar 

  9. Colledani, M., Matta, A., & Tolio, T. (2010). Analysis of the production variability in multi-stage manufacturing systems. CIRP Annals - Manufacturing Technology, 59, 449–452.

    Article  Google Scholar 

  10. Dallery, Y., David, R., & Xie, X. L. (1988). An efficient algorithm for analysis of transfer lines with unreliable machines and finite buffers. IIE Transactions, 20, 280–283.

    Article  Google Scholar 

  11. Dallery, Y., & Gershwin, S. B. (1992). Manufacturing flow line systems: A review of models and analytical results. Queueing Systems Theory and Applications, 12, 3–94.

    Article  Google Scholar 

  12. Dincer, C., & Deler, B. (2000). On the distribution of throughput of transfer lines. The Journal of the Operational Research Society, 51(10), 1170–1178.

    Google Scholar 

  13. Gershwin, S. B. (1987). An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking. Operations Research, 35(2), 291–305.

    Article  Google Scholar 

  14. Gershwin, S. B. (1993) Variance of output of a tandem production system. In: R. Onvural, I. Akyildiz (Eds.),Queueing Networks with Finite Capacity. Proceedings of the Second International Conference on Queueing Networks with Finite Capacity. Amsterdam:Elsevier.

    Google Scholar 

  15. Gershwin, S. B. (1994). Manufacturing systems engineering. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  16. Grassman, W. K. (1993). Means and variances in markov reward systems. In C. D. Meyer, & R. J. Plemmons (Eds.), Linear algebra, Markov chains and queueing models. The IMA volumes in mathematics and its applications (Vol. 48, pp. 193–204). New York: Springer.

    Google Scholar 

  17. He, X. F., Wu, S., & Li, Q. L. (2007). Production variability of production lines. International Journal of Production Economics, 107, 78–87.

    Article  Google Scholar 

  18. Hendricks, K. B. (1992). The output processes of serial production lines of exponential machines with finite buffers. Operations Research, 40(6), 1139–1147.

    Article  Google Scholar 

  19. Hendricks, K. B., & McClain, J. O. (1993). The output processes of serial production lines of general machines with finite buffers. Management Science, 39(10), 1194–1201.

    Article  Google Scholar 

  20. Jacobs, D. A., & Meerkov, S. M. (1995). System-theoretic analysis of due-time performance in production systems. Mathematical Problems in Engineering, 1, 225–243.

    Article  Google Scholar 

  21. Li, J. (2000). Production variability in manufacturing systems: a systems approach, PhD Thesis, Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA.

    Google Scholar 

  22. Li, J., & Meerkov, S. M. (2000). Production variability in manufacturing systems: Bernoulli reliability case. Annals of Operations Research, 93(1), 299–324.

    Article  Google Scholar 

  23. Li, J., & Meerkov, S. M. (2001). Customer demand satisfaction in production systems: A due-time performance approach. IEEE Transactions on Robotics and Automation, 17, 472–382.

    Article  Google Scholar 

  24. Li, J., & Meerkov, S. (2009). Production systems engineering. New York: Springer.

    Book  Google Scholar 

  25. Li, J., Enginarlar, E., & Meerkov, S. M. (2004). Random demand satisfaction in unreliable production-inventory-customer systems. Annals of Operations Research, 126(1–4), 159–175.

    Article  Google Scholar 

  26. Kemeny, J.G. and J.L. Snell, Finite Markov Chains, Springer-Verlag, New York, 1976

    Google Scholar 

  27. Manitz, M., & Tempelmeier, H. (2010). The variance of interdeparture times of the output of an assembly line with finite buffers, converging flow of material, and general service times. OR Spectrum, 34, 1–19.

    Google Scholar 

  28. Miltenburg, G. J. (1987). Variance of the number of units produced on a transfer line with buffer inventories during a period of length t. Naval Research Logistics, 34(6), 811–822.

    Article  Google Scholar 

  29. Muth, E. J. (1984). Stochastic processes and their network representations associated with a production line queueing model. European Journal of Operational Research, 15, 63–83.

    Article  Google Scholar 

  30. Neuts, M. F. (1981). Matrix-geometric solutions in stochastic models. Baltimore: Johns Hopkins University Press.

    Google Scholar 

  31. Ou, J., & Gershwin, S. B. (1989). The variance of the lead time of a two machine transfer line with a finite buffer. Techical report LMP-90- 028, Laboratory for Manufacturing and Productivity, MIT.

    Google Scholar 

  32. Papadopoulos, H. T. (1998). An approximate method for calculating the mean sojourn time of K-station production lines with no intermediate buffers. International Journal of Production Economics, 54(3), 297–305.

    Article  Google Scholar 

  33. Sabuncuoglu, I., Erel, E., & Kok, A. G. (2002). Analysis of assembly systems for interdeparture time variability and throughput. IIE Transactions, 34, 23–40.

    Google Scholar 

  34. Shi, C, & Gerhswin, S. B. (2011). Part waiting time distribution in a two-machine line. In VIIIth conference on stochastic models of manufacturing and service operations (pp.261–268), Kusadasi, Turkey.

    Google Scholar 

  35. Stewart, W. J. (1994). Introduction to the numerical solution of markov chains. Princeton: Princeton University Press.

    Google Scholar 

  36. Tan, B. (1997). Variance of the throughput of an n-station production line with no intermediate buffers and time dependent failures. European Journal of Operational Research, 101(3), 560–576.

    Article  Google Scholar 

  37. Tan, B. (1998). Effects of variability on the due-time performance of a continuous materials flow production system in series. International Journal of Production Economics, 54, 87–100.

    Article  Google Scholar 

  38. Tan, B. (1998). An analytical formula for variance of output from a series-parallel production system with no interstation buffers and timedependent failures. Mathematical and Computer Modelling, 27(6), 95–112.

    Article  Google Scholar 

  39. Tan, B. (1999). Asymptotic variance rate of the output of a transfer line with no buffer storage and cycle-dependent failures. Mathematical and Computer Modelling, 29(7), 97–112.

    Article  Google Scholar 

  40. Tan, B. (1999). Variance of the output as a function of time: Production line dynamics. European Journal of Operational Research, 117(3), 470–484.

    Article  Google Scholar 

  41. Tan, B. (2000). Asymptotic variance rate of the output in production lines with finite buffers. Annals of Operations Research, 93, 385–403.

    Article  Google Scholar 

  42. Tan, B. (2003). State-space modeling and analysis of pull controlled production systems. In S. Gershwin, Y. Dallery, C. Papadopoulos, & J. Smith (Eds.), Analysis and modeling of manufacturing systems. Kluwers international series in operations research and management science, Chapter 15 (pp. 363–398). Berlin: Springer.

  43. Yeralan, S., & Muth, E. J. (1987). A general model of a production line with intermediate buffer and station breakdown. IIE Transactions, 19(2), 130–139.

    Article  Google Scholar 

  44. Yeralan, S., & Tan, B. (1997). Analysis of multistation production systems with limited buffer capacity, part I. Mathematical and Computer Modelling, 25(7), 109–122.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Barış Tan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Tan, B. (2013). Modeling and Analysis of Output Variability in Discrete Material Flow Production Systems. In: Smith, J., Tan, B. (eds) Handbook of Stochastic Models and Analysis of Manufacturing System Operations. International Series in Operations Research & Management Science, vol 192. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6777-9_9

Download citation

Publish with us

Policies and ethics