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Analysis of flow lines with Cox-2-distributed processing times and limited buffer capacity

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Stochastic Modeling of Manufacturing Systems

Abstract

We describe a flow line model consisting of machines with Cox-2-distributed processing times and limited buffer capacities. A two-machine subsystem is analyzed exactly and a larger flow lines are evaluated through a decomposition into a set of coupled two-machine lines. Our results are compared to those given by Buzacott, Liu and Shantikumar for their “Stopped Arrival Queue Modell”.

The author thanks the anonymous referees for their helpful comments and suggestions.

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References

  1. Altiok T (1996) Performance analysis of manufacturing systems. Springer, Berlin Heidelberg New York

    Google Scholar 

  2. Artamonov G (1977) Productivity of a two-instrument discrete processing line in the presence of failures. Cybernetics 12: 464–468

    Google Scholar 

  3. Bronstein IN, Semendjajew KA (1983) Taschenbuch der Mathematik, 21st edn. Teubner, Leipzig

    Google Scholar 

  4. Burman MH (1995) New results in flow line analysis. PhD thesis, Massachusetts Institute of Technology. Also available as Report LMP-95-007, MIT Laboratory for Manufacturing and Productivity

    Google Scholar 

  5. Buzacott JA (1967) Automatic transfer lines with buffer stocks. International Journal of Production Research 5(3): 183–200

    Article  Google Scholar 

  6. Buzacott J (1972) The effect of station breakdowns and random processing times on the capacity of flow lines. AIIE Transactions 4: 308–312

    Google Scholar 

  7. Buzacott JA, Hanifin LE (1978) Models of automatic transfer lines with inventory banks — a review and comparison. AIIE Transactions 10(2): 197–207

    Google Scholar 

  8. Buzacott JA, Kostelski D (1987) Matrix-geometric and recursive algorithm solution of a two-stage unreliable flow line. IIE Transactions 19(4): 429–438

    Article  Google Scholar 

  9. Buzacott JA, Liu XG, Shanthikumar JG (1995) Multistage flow line analysis with the stopped arrival queue model. IIE Transactions 27(4): 444–455

    Article  Google Scholar 

  10. Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  11. Buxey G, Slack N, Wild R (1973) Production flow line system design — a review. AIIE Transactions 5: 37–48

    Google Scholar 

  12. Choong Y, Gershwin SB (1987) A decomposition method for the approximate evaluation of capacitated transfer lines with unreliable machines and random processing times. IIE Transactions 19: 150–159

    Article  Google Scholar 

  13. Dallery Y, David R, Xie XL (1988) An efficient algorithm for analysis of transfer lines with unreliable machines and finite buffers. IIE Transactions 20(3): 280–283

    Article  Google Scholar 

  14. Dallery Y, David R, Xie XL (1989) Approximate analysis of transfer lines with unreliable machines and finite buffers. IEEE Transactions on Automatic Control 34(9): 943–953

    Article  Google Scholar 

  15. Dallery Y, Gershwin SB (1992) Manufacturing flow line systems: a review of models and analytical results. Queuing Systems Theory and Applications 12(1–2): 3–94

    Article  Google Scholar 

  16. Di Mascolo M, David R, Dallery Y (1991) Modeling and analysis of assembly systems with unreliable machines and finite buffers. IIE Transactions 23(4): 315–330

    Article  Google Scholar 

  17. Gaver DP (1962) A waiting line with interrupted service, including priorities. Journal of the Royal Statistical Society 24: 73–90

    MATH  MathSciNet  Google Scholar 

  18. Gershwin SB (1987) An efficient decomposition algorithm for the approximate evaluation of tandem queues with finite storage space and blocking. Operations Research 35: 291–305

    Article  MATH  MathSciNet  Google Scholar 

  19. Gershwin SB (1989) An efficient decomposition algorithm for unreliable tandem queueing systems with finite buffers. In: Perros G, Altiok T (eds) Queueing networks with blocking, pp 127–146. North Holland, Amsterdam

    Google Scholar 

  20. Gershwin SB (1991) Assembly/disassembly systems: An efficient decomposition algorithm for tree-structured networks. IIE Transactions 23(4): 302–314

    Article  Google Scholar 

  21. Gershwin SB (1994) Manufacturing systems engineering. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  22. Gershwin SB, Berman O (1981) Analysis of transfer lines consisting of two unreliable machines with random processing times and finite storage buffers. AIIE Transactions 13(1): 2–11

    Google Scholar 

  23. Gershwin SB, Schick I (1980) Continuous model of an unreliable two-stage material flow system with a finite interstage buffer. Technical Report LIDS-R-1039, Massachusetts Institute of Technology, Cambridge, MA

    Google Scholar 

  24. Gershwin SB, Schick I (1983) Modeling and analysis of three-stage transfer lines with unreliable machines and finite buffers. Operations Research 31(2): 354–380

    Article  Google Scholar 

  25. Helber S (1998) Decomposition of unreliable assembly/dissassembly networks with limited buffer capacity and random processing times. European Journal of Operational Research 109(1): 24–42

    Article  ADS  MATH  Google Scholar 

  26. Helber S (1999) Performance analysis of flow lines with non-linear flow of material. Springer, Berlin Heidelberg New York

    Google Scholar 

  27. Hillier F, Boling RW (1967) Finite queues in series with exponential or Erlang service times — a numerical approach. Operations Research 16: 286–303

    Article  Google Scholar 

  28. Koenigsberg E (1959) Production lines and internal storage — a review. Management Science 5: 410–433

    Article  Google Scholar 

  29. Okamura K, Yamashina H (1977) Analysis of the effect of buffer storage capacity in transfer line systems. AIEE Transactions 9: 127–135

    Google Scholar 

  30. Papadopoulus HT, Heavey C, Browne J (1993) Queueing theory in manufacturing systems analysis and design. Chapman & Hall, London

    Google Scholar 

  31. Sastry BLN, Awate PG (1988) Analysis of a two-station flow line with machine processing subject to inspection and rework. Opsearch 25: 89–97

    Google Scholar 

  32. Sevast’yanov BA (1962) Influence of storage bin capacity on the average standstill time of a production line. Theory of Probability and Its Applications 7: 429–438

    Article  Google Scholar 

  33. Wijngaard J (1979) The effect of interstage buffer storage on the output of two unreliable production units in series, with different production rates. AIIE Transactions 11(1): 42–47

    Google Scholar 

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

    Article  Google Scholar 

  35. Zimmern B (1956) Etudes de la propagation des arrêts aleatoires dans les chaines de production. Review Statististical Applications 4: 85–104

    Google Scholar 

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Helber, S. (2006). Analysis of flow lines with Cox-2-distributed processing times and limited buffer capacity. In: Liberopoulos, G., Papadopoulos, C.T., Tan, B., Smith, J.M., Gershwin, S.B. (eds) Stochastic Modeling of Manufacturing Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29057-5_3

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