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

  • Stefan Helber
Chapter

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”.

Keywords

Flow line Performance evaluation Decomposition General processing times Cox-2-distribution 

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References

  1. 1.
    Altiok T (1996) Performance analysis of manufacturing systems. Springer, Berlin Heidelberg New YorkGoogle Scholar
  2. 2.
    Artamonov G (1977) Productivity of a two-instrument discrete processing line in the presence of failures. Cybernetics 12: 464–468Google Scholar
  3. 3.
    Bronstein IN, Semendjajew KA (1983) Taschenbuch der Mathematik, 21st edn. Teubner, LeipzigGoogle Scholar
  4. 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 ProductivityGoogle Scholar
  5. 5.
    Buzacott JA (1967) Automatic transfer lines with buffer stocks. International Journal of Production Research 5(3): 183–200CrossRefGoogle Scholar
  6. 6.
    Buzacott J (1972) The effect of station breakdowns and random processing times on the capacity of flow lines. AIIE Transactions 4: 308–312Google Scholar
  7. 7.
    Buzacott JA, Hanifin LE (1978) Models of automatic transfer lines with inventory banks — a review and comparison. AIIE Transactions 10(2): 197–207Google Scholar
  8. 8.
    Buzacott JA, Kostelski D (1987) Matrix-geometric and recursive algorithm solution of a two-stage unreliable flow line. IIE Transactions 19(4): 429–438CrossRefGoogle Scholar
  9. 9.
    Buzacott JA, Liu XG, Shanthikumar JG (1995) Multistage flow line analysis with the stopped arrival queue model. IIE Transactions 27(4): 444–455CrossRefGoogle Scholar
  10. 10.
    Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  11. 11.
    Buxey G, Slack N, Wild R (1973) Production flow line system design — a review. AIIE Transactions 5: 37–48Google Scholar
  12. 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: 150–159CrossRefGoogle Scholar
  13. 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): 280–283CrossRefGoogle Scholar
  14. 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): 943–953CrossRefGoogle Scholar
  15. 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): 3–94CrossRefGoogle Scholar
  16. 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): 315–330CrossRefGoogle Scholar
  17. 17.
    Gaver DP (1962) A waiting line with interrupted service, including priorities. Journal of the Royal Statistical Society 24: 73–90zbMATHMathSciNetGoogle Scholar
  18. 18.
    Gershwin SB (1987) An efficient decomposition algorithm for the approximate evaluation of tandem queues with finite storage space and blocking. Operations Research 35: 291–305zbMATHMathSciNetCrossRefGoogle Scholar
  19. 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, AmsterdamGoogle Scholar
  20. 20.
    Gershwin SB (1991) Assembly/disassembly systems: An efficient decomposition algorithm for tree-structured networks. IIE Transactions 23(4): 302–314CrossRefGoogle Scholar
  21. 21.
    Gershwin SB (1994) Manufacturing systems engineering. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  22. 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): 2–11Google Scholar
  23. 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, MAGoogle Scholar
  24. 24.
    Gershwin SB, Schick I (1983) Modeling and analysis of three-stage transfer lines with unreliable machines and finite buffers. Operations Research 31(2): 354–380CrossRefGoogle Scholar
  25. 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): 24–42ADSzbMATHCrossRefGoogle Scholar
  26. 26.
    Helber S (1999) Performance analysis of flow lines with non-linear flow of material. Springer, Berlin Heidelberg New YorkGoogle Scholar
  27. 27.
    Hillier F, Boling RW (1967) Finite queues in series with exponential or Erlang service times — a numerical approach. Operations Research 16: 286–303CrossRefGoogle Scholar
  28. 28.
    Koenigsberg E (1959) Production lines and internal storage — a review. Management Science 5: 410–433CrossRefGoogle Scholar
  29. 29.
    Okamura K, Yamashina H (1977) Analysis of the effect of buffer storage capacity in transfer line systems. AIEE Transactions 9: 127–135Google Scholar
  30. 30.
    Papadopoulus HT, Heavey C, Browne J (1993) Queueing theory in manufacturing systems analysis and design. Chapman & Hall, LondonGoogle Scholar
  31. 31.
    Sastry BLN, Awate PG (1988) Analysis of a two-station flow line with machine processing subject to inspection and rework. Opsearch 25: 89–97Google Scholar
  32. 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: 429–438CrossRefGoogle Scholar
  33. 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): 42–47Google Scholar
  34. 34.
    Yeralan S, Muth EJ (1987) A general model of a production line with intermediate buffer and station breakdown. IIE Transactions 19(2): 130–139CrossRefGoogle Scholar
  35. 35.
    Zimmern B (1956) Etudes de la propagation des arrêts aleatoires dans les chaines de production. Review Statististical Applications 4: 85–104Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Stefan Helber
    • 1
  1. 1.Department for Production ManagementUniversity of HannoverHannoverGermany

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