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The Buffer Allocation Problem

  • Chrissoleon T. Papadopoulos
  • Michael J. Vidalis
  • Michael E. J. O’Kelly
  • Diomidis Spinellis
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 31)

Abstract

The buffer allocation problem, BAP, is concerned with the allocation of a certain fixed number of buffer slots, N, among the K−1 intermediate buffer locations of a production line in order to meet some specified objective. The number of stations of the line is fixed at K, the number of servers assigned to each station is fixed and the work allocation \({\bf w} = ({w}_{1},{w}_{2}, \ldots ,{w}_{K})\) is also fixed.

The buffer allocation problem is of particular interest to operations management in that in many practical production line situations, the allocation of buffer space may be the primary flexibility available to the organization. Clearly, buffer space is an expensive resource and so, ideally models involving cost considerations are very desirable. Of course, there are also plant layout issues involved.

At least three buffer allocation problems have been identified in the literature and these are described in Section 5.1. Solutions of the buffer allocation problems are discussed in Section 5.2. Special solution approaches to buffer allocation problems in short lines are the subject of Section 5.3, whereas solution approaches to buffer allocation problems in longer lines are treated in Section 5.4.

Keywords

Production Line Tabu Search Buffer Space Buffer Allocation Longe Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Altiok, T. (1989), Approximate analysis of queues in series with phase-type service times and blocking, Operations Research, Vol. 37, pp. 601–610.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Altiok, T. and Stidham, S. Jr. (1983), The allocation of interstage buffer capacities in production lines, IIE Transactions, Vol. 15, No. 4, pp. 292–299.Google Scholar
  3. 3.
    Anderson, D.R. and Moodie, C.L. (1989), Optimal buffer storage capacity in production line systems, International Journal of Production Research, Vol. 7, No. 3, pp. 233–240.Google Scholar
  4. 4.
    Bulgak, A.A., Diwan, P.D., and Inozu, B. (1995), Buffer size optimization in asynchronous systems using genetic algorithms, Computers and Industrial Engineering, Vol. 28, No. 2, pp. 309–322.Google Scholar
  5. 5.
    Cheng, D.W. (1994), On the design of a tandem queue with blocking: Modeling analysis, and gradient estimation, Naval Research Logistics, Vol. 41, pp. 759–770.MATHCrossRefGoogle Scholar
  6. 6.
    Chow, W.-M. (1987), Buffer capacity analysis for sequential production lines with variable process times, International Journal of Production Research, Vol. 25, No. 8, pp. 1183–1196.Google Scholar
  7. 7.
    Colledani, Matta, A., Grasso, M., and Tolio, T. (2005), A new analytical method for buffer space allocation in production lines, CIRP–Journal of Manufacturing Systems, Vol. 34, No. 4.Google Scholar
  8. 8.
    Conway, R., Maxwell, W., McClain, J.O., and Thomas, L.J. (1988), The role of work-in-process inventory in serial production lines, Operations Research, Vol. 36, No. 2, pp. 229–241.Google Scholar
  9. 9.
    Dallery, Yves and Frein, Yannick (1993), On decomposition methods for tandem queueing networks with blocking, Operations Research, Vol. 41, No. 2, pp. 386–399.MATHMathSciNetGoogle Scholar
  10. 10.
    de Werra, D. and Hertz, A. (1989), Tabu Search techniques: A tutorial and an application to neural networks, OR Spektrum, pp. 131–141.Google Scholar
  11. 11.
    Enginarlar, E., Li, J., Meerkov, S., and Zhang, Q. (2002), Buffer capacity for accommodating machine downtime in serial production lines, International Journal of Production Research, Vol. 40, No. 3, pp. 601–624.MATHGoogle Scholar
  12. 12.
    Erel, E. (1993), Effect of discrete batch WIP transfer on the efficiency of production lines, International Journal of Production Research, Vol. 36, No. 2, pp. 343–358.Google Scholar
  13. 13.
    Faigle, U. and Kern, W. (1992), Some convergence results for probabilistic Tabu search, ORSA Journal on Computing, Vol. 4, pp. 32–37.MATHGoogle Scholar
  14. 14.
    Fox, B.L. (1993), Integrating and accelerating tabu search, simulated annealing and genetic algorithms, Annals of Operations Research, Vol. 41, pp. 46–67.Google Scholar
  15. 15.
    Glover, F. (1986), Future paths for integer programming and links to artificial intelligence, Computers and Operations Research, Vol. 13, pp. 533–549.MATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Glover, F. (1989), Tabu search, Part I, ORSA Journal on Computing, Vol. 1, pp. 190–206.MATHMathSciNetGoogle Scholar
  17. 17.
    Glover, F. (1990), Tabu search, Part II, ORSA Journal on Computing, Vol. 2, pp. 4–32.MATHGoogle Scholar
  18. 18.
    Glover, F. (1992), Private communication.Google Scholar
  19. 19.
    Glover, F. and Laguna, M. (1998), Tabu search, Kluwer Academic Publishers.Google Scholar
  20. 20.
    Glover, F., Taillard, E., Laguna, M., and de Werra, D. (1993), Tabu search, Annals of Operations Research, Vol. 41, pp. 3–28.MATHCrossRefGoogle Scholar
  21. 21.
    Grefenstette, J.J. (1986), Optimization of control parameters for genetic algorithms, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 16, No. 1, pp. 122–128.Google Scholar
  22. 22.
    Gershwin, S.B. and Schor, J.E. (2000), Efficient algorithms for buffer space allocation, Annals of Operations Research, Vol. 93, pp. 117–144.MATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Grefenstette, J. (1986), Optimization of control parameters for genetic algorithms, IEEE Transactions on Systems, Man and Cybernetics, Vol. 16, Issue 1, pp. 122–128.CrossRefGoogle Scholar
  24. 24.
    Hansen, P. (1986), The steepest ascent mildest descent heuristic for combinatorial programming, Presented at the Congress on Numerical Methods in Combinatorial Optimization, Capri, Italy.Google Scholar
  25. 25.
    Harris, J.H. and Powell, S.G. (1999), An algorithm for optimal buffer placement in reliable serial lines, IIE Transactions, Vol. 31, pp. 287–302.Google Scholar
  26. 26.
    Hatcher, J.M. (1969), The effect of internal storage on the production rate of a series of stages having exponential service times, AIIE Transactions, Vol. 1, No. 2, pp. 150–156.Google Scholar
  27. 27.
    Heavey, C., Papadopoulos, H.T., and Browne, J. (1993), The throughput rate of multistation unreliable production lines, European Journal of Operational Research, Vol. 68, No. 1, pp. 69–89.MATHGoogle Scholar
  28. 28.
    Hertz, A., Taillard, E., and de Werra, D. (1995), A tutorial on Tabu search, In Proc. of Giornate di Lavoro AIRO ’95, (Enterprise Systems: Management of Technological and Organizational Changes), pp. 13–24.Google Scholar
  29. 29.
    Hillier, F.S. and So, K.C. (1991a), The effect of machine breakdowns and interstage storage on the performance of production line systems, International Journal of Production Research, Vol. 29, No. 10, pp. 2043–2055.MATHGoogle Scholar
  30. 30.
    Hillier, F.S. and So, K.C. (1991b), The effect of the coefficient of variation of operation times on the allocation of storage space in production line systems, IIE Transactions, Vol. 23, No. 2, pp. 198–206.Google Scholar
  31. 31.
    Hillier, F.S. and So, K.C. (1995), On the optimal design of tandem queueing systems with finite buffers, Queueing Systems, Vol. 21, pp. 245–266.MATHMathSciNetCrossRefGoogle Scholar
  32. 32.
    Hillier, F.S., So, K.C., and Boling, R.W. (1993), Notes: Towards characterizing the optimal allocation of storage space in production line systems with variable processing times, Management Science, Vol. 39, No. 1, pp. 126–133.Google Scholar
  33. 33.
    Ho, Y.C., Eyler, M.A., and Chien, T.T. (1979), A gradient technique for general buffer storage design in a production line, International Journal of Production Research, Vol. 17, No. 6, pp. 557–580.Google Scholar
  34. 34.
    Jafari, M.A. and Shanthikumar, J.G. (1989), Determination of optimal Buffer storage capacities and optimal allocation in multistage automatic transfer lines, IIE Transactions, Vol. 21, No. 2, pp. 130–135.Google Scholar
  35. 35.
    Jensen, P.A., Pakath, R., and Wilson, J.R. (1991), Optimal buffer inventories for multistage production systems with failures, European Journal of Operational Research, Vol. 51, pp. 313–326.MATHCrossRefGoogle Scholar
  36. 36.
    Knuth, D.E. (1981), The Art of Computer Programming, Vol. 2/Seminumerical Algorithms, Second Edition, pp. 171–173, Addison-Wesley.Google Scholar
  37. 37.
    Koulamas, C.P. (1989), Optimal buffer space in two-stage machining systems with Markovian or non-Markovian tool life processes, International Journal of Production Research, Vol. 27, No. 7, pp. 1167–1178.MATHGoogle Scholar
  38. 38.
    Kraemer, S.A. and Love, R.F. (1970), A model for optimizing the buffer inventory storage size in a sequential production system, AIIE Transactions, Vol. 2, No. 1, pp. 64–69.Google Scholar
  39. 39.
    Kubat, P. and Sumita, U. (1985), Buffers and backup machines in automatic transfer lines, International Journal of Production Research, Vol. 23, pp. 1259–1270.CrossRefGoogle Scholar
  40. 40.
    Levantesi, R., Matta, A., and Tolio, T. (2001), A new algorithm for buffer allocation in production lines, Proceedings of the Third Aegean International Conference on Design and Analysis of Manufacturing Systems, May 19–22, 2001, Tinos Island, Greece, pp. 279–288.Google Scholar
  41. 41.
    Liu, C. and Tu, F.-S. (1994), Buffer allocation via genetic algorithm, Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL, December, 1994, pp. 609–610.Google Scholar
  42. 42.
    Masso, J. and Smith, M.L. (1974), Interstage storages for three stage lines subjet to stochastic failures, AIIE Transactions, Vol. 6, No. 4, pp. 354–358.Google Scholar
  43. 43.
    Martin, G.E. (1994), Optimal design of production lines, International Journal of Production Research, Vol. 32, No. 5, pp. 989–1000.MATHGoogle Scholar
  44. 44.
    Meester, L.E. and Shanthikumar, J.G. (1990), Concavity of the throughput of tandem queueing systems with finite buffer storage space, Advances in Applied Probability, Vol. 22, pp. 764–767.MATHMathSciNetCrossRefGoogle Scholar
  45. 45.
    Okamura, K. and Yamashita, H. (1977), Analysis of the effect of buffer storage capacity in transfer line systems, AIIE Transactions, Vol. 9, No. 2, pp. 127–135.Google Scholar
  46. 46.
    Papadopoulos, H.T. and Karagiannis, T.I. (2001), A genetic algorithm approach for the buffer allocation problem in unreliable production lines, International Journal of Operations and Quantitative Management, Vol. 7, No. 1, pp. 23–35.Google Scholar
  47. 47.
    Papadopoulos, H.T. and Vidalis, M.I. (1998), Optimal buffer storage allocation in balanced reliable production lines, International Transactions in Operational Research, Vol. 5, No. 4, pp. 325–339.Google Scholar
  48. 48.
    Papadopoulos, H.T. and Vidalis, M.I. (1999), Optimal buffer allocation in short μ-balanced unreliable production lines, Computers & Industrial Engineering, Vol. 37, pp. 691–710.CrossRefGoogle Scholar
  49. 49.
    Papadopoulos, H.T. and Vidalis, M.I. (2001a), A heuristic algorithm for the buffer allocation in unreliable unbalanced production lines, Computers & Industrial Engineering, Vol. 41, pp. 261–277.CrossRefGoogle Scholar
  50. 50.
    Papadopoulos, H.T. and Vidalis, M.I. (2001b), Minimizing WIP inventory in reliable production lines, International Journal of Production Economics, Vol. 70, pp. 185–197.CrossRefGoogle Scholar
  51. 51.
    Park, T. (1993), A two-phase heuristic algorithm for determining buffer sizes of production lines, International Journal of Production Research, Vol. 31, No. 3, pp. 613–631.Google Scholar
  52. 52.
    Powell, S.G. (1994), Buffer allocation in unbalanced three-station serial lines, International Journal of Production Research, Vol. 32, No. 9, pp. 2201–2217.MATHGoogle Scholar
  53. 53.
    Powell, S.G. and Pyke, D.F. (1994), Optimal allocation of buffers in serial production lines with a single bottleneck, The Amos Tuck School of Business Administration, Dartmouth College, Working Paper No. 301.Google Scholar
  54. 54.
    Sevast’yanov B.A. (1962), Influence of storage bin capacity on the average standstill time of a production line, Theory of Probability and its Applications, Vol. 7, pp. 429–438.MATHCrossRefGoogle Scholar
  55. 55.
    Singh, A. and Smith, MacGregor, J. (1997), Buffer allocation for an integer nonlinear network design problem, Computers and Operations Research, Vol. 24, No. 5, pp. 453–472.Google Scholar
  56. 56.
    Smith, MacGregor, J., and Chikhale, N. (1995), Buffer allocation for a class of nonlinear stochastic knapsack problems, Annals of Operations Research, Vol. 58, pp. 323–360.Google Scholar
  57. 57.
    Smith, MacGregor, J., and Daskalaki, S. (1988), Buffer space allocation in automated assembly lines, Operations Research, Vol. 36, No. 2, pp. 343–358.Google Scholar
  58. 58.
    So, K.C. (1990), The impact of buffering strategies on the perfomance of production line systems, International Journal of Production Research, Vol. 28, No. 2, pp. 2293–2307.Google Scholar
  59. 59.
    So, K.C. (1997), Optimal buffer allocation strategy for minimizing work-in-process inventory in unpaced production lines, IIE Transactions, Vol. 29, No. 1, pp. 81–88.Google Scholar
  60. 60.
    Spinellis, D.D. and Papadopoulos, C.T. (2000a), A simulated annealing approach for buffer allocation in reliable production lines, Annals of Operations Research, Vol. 93, pp. 373–384.MATHMathSciNetCrossRefGoogle Scholar
  61. 61.
    Spinellis, D.D. and Papadopoulos, C.T. (2000b), Stochastic algorithms for buffer allocation in reliable production lines, Mathematical Problems in Engineering, Vol. 5, pp. 441–458.MATHCrossRefGoogle Scholar
  62. 62.
    Vouros, G.A. and Papadopoulos, H.T. (1998), Buffer allocation in unreliable production lines using a knowledge based system, Computers & Operations Research, Vol. 25, No. 12, pp. 1055–1067.MATHGoogle Scholar
  63. 63.
    Yamashita, H. and Altiok, T. (1998), Buffer capacity allocation for a desired throughput in production lines, IIE Transactions, Vol. 30, pp. 883–891.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Chrissoleon T. Papadopoulos
    • 1
  • Michael J. Vidalis
    • 2
  • Michael E. J. O’Kelly
    • 3
  • Diomidis Spinellis
    • 4
  1. 1.Department of EconomicsAristotle University of ThessalonikiThessalonikiGreece
  2. 2.Department of Business AdministrationUniversity of the AegeanChiosGreece
  3. 3.Department of Industrial EngineeringNational University of Ireland University College GalwayGalwayIreland
  4. 4.Department of Management ScienceUniversity of Economics & BusinessAthensGreece

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