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Complexity of Buffer Capacity Allocation Problems for Production Lines with Unreliable Machines

  • A. DolguiEmail author
  • A. Eremeev
  • M. Y. Kovalyov
  • V. Sigaev
Article

Abstract

Buffer capacity allocation problems for flow-line manufacturing systems with unreliable machines are studied. These problems arise in a wide range of manufacturing systems and concern determining buffer capacities with respect to a given optimality criterion which can depend on the average production rate of the line, buffer cost, inventory cost, etc. Here, this problem is proven to be NP-hard for a tandem production line and oracle representation of the revenue and cost functions, and NP-hard for a series-parallel line and stepwise revenue function.

Keywords

Flow-line Unreliable machines Buffer allocation Optimization Computational complexity 

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References

  1. 1.
    Cheng, T.C.E., Kovalyov, M.Y.: An unconstrained optimization problem is NP-hard given an oracle representation of its objective function: a technical note. Comput. Oper. Res. 29, 2087–2091 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Coillard, P., Proth, J.M.: Effet des stocks tampons dans une fabrication en ligne. Rev. Belge Stat. Inform. Rech. Opér. 24(2), 3–27 (1984)zbMATHGoogle Scholar
  3. 3.
    Dallery, Y., Gershwin, S.B.: Manufacturing flow line systems: a review of models and analytical results. Queueing Syst. 12(1–2), 3–94 (1992)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dolgui, A.: Analyse de performances d’un atelier de production discontinue: méthode et logiciel. Research Report INRIA 1949, 4 pp. (1993)Google Scholar
  5. 5.
    Dolgui, A., Eremeev, A.V., Kolokolov, A.A., Sigaev, V.S.: A genetic algorithm for allocation of buffer storage capacities in production line with unreliable machines. J. Math. Model. Algorithm. 2, 89–104 (2002)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dolgui, A., Eremeev, A.V., Sigaev, V.S.: HBBA: hybrid algorithm for buffer allocation in tandem production lines. J. Intell. Manuf. 18(3), 411–420 (2007)CrossRefGoogle Scholar
  7. 7.
    Dolgui, A.B., Svirin, Y.P.: Models of evaluation of probabilistic productivity of automated technological complexes. Vesti AN Belarusi: ser. phys.-tech. nav. 40(1), 59–67 (1995, in Russian)Google Scholar
  8. 8.
    Dubois, D., Forestier, J.P.: Productivité et en-cours moyens d’un ensemble de deux machines séparées par une zone de stockage. RAIRO Autom. 16(2), 105–132 (1982)zbMATHGoogle Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco (1979)zbMATHGoogle Scholar
  10. 10.
    Gershwin, S.B.: Manufacturing Systems Engineering. Prentice Hall (1993)Google Scholar
  11. 11.
    Gershwin, S.B., Schor, J.E.: Efficient algorithms for buffer space allocation. Ann. Oper. Res. 93, 117–144 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Gnedenko, B.V.: Theory of Probability. Gordon and Breach, Amsterdam (1997)zbMATHGoogle Scholar
  13. 13.
    Heavey, C., Papadopoulos, H.T., Browne, J.: The throughput rate of multistation unreliable production lines. Eur. J. Oper. Res. 68, 69–89 (1993)zbMATHCrossRefGoogle Scholar
  14. 14.
    Levin, A.A., Pasjko, N.I.: Calculating the output of transfer lines. Stanki & Instrum. 40(8), 8–10 (1969, in Russian)Google Scholar
  15. 15.
    Li, J., Meerkov, S.M.: Production Systems Engineering. Springer (2008)Google Scholar
  16. 16.
    Sevast’yanov, B.A.: Influence of storage bin capacity on the average standstill time of a production line. Theory Probab. Appl. 7(4), 429–455 (1962)CrossRefGoogle Scholar
  17. 17.
    So, K.C.: Optimal buffer allocation strategy for minimizing work-in-process inventory in unpaced production lines. IIE Trans. 29, 81–88 (1997)CrossRefGoogle Scholar
  18. 18.
    Shi, C., Gershwin, S.B.: An efficient buffer design algorithm for production line profit maximization original research. Int. J. Prod. Econ. 122(2), 725–740 (2009)CrossRefGoogle Scholar
  19. 19.
    Smith, J.M., Daskalaki, S.: Buffer space-allocation in automated assembly lines. Oper. Res. 36, 343–358 (1988)CrossRefGoogle Scholar
  20. 20.
    Tan, B., Gershwin, S.B.: Analysis of a general Markovian two-stage continuous-flow production system with a finite buffer. Int. J. Prod. Econ. 120(2), 327–339 (2009)CrossRefGoogle Scholar
  21. 21.
    Terracol, C., David, R.: An aggregation method for performance valuation of transfer lines with unreliable machines and finite buffers. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1333–1338 (1987)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • A. Dolgui
    • 1
    Email author
  • A. Eremeev
    • 2
  • M. Y. Kovalyov
    • 3
  • V. Sigaev
    • 2
  1. 1.Ecole Nationale Supérieure des Mines, FAYOL-EMSE, CNRS UMR 6158, LIMOSSaint-Etienne cedex 2France
  2. 2.Omsk Branch of Sobolev Institute of MathematicsOmskRussia
  3. 3.United Institute of Informatics Problems, National Academy of Sciences of BelarusMinskBelarus

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