Competitive analysis of on-line stack-up algorithms

  • J. Rethmann
  • E. Wanke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1284)


Let q = (b1,...,bn) be a sequence of bins. Each bin is destined for some pallet t. For two given integers s and p, the stack-up problem is to move step by step all bins from q onto their pallets such that the position of the bin moved from q is always not greater than s and after each step there are at most p pallets for which the first bin is already stacked up but the last bin is still missing. If a bin b is moved from q then all bins to the right of b are shifted one position to the left. We determine the performance of four simple on-line algorithms called First-In, First-Done, Most-Frequently, and Greedy with respect to an optimal off-line solution for the stack-up problem.


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  1. [BNS69]
    L.A. Belady, R.A. Nelson, and G.S. Shelder. An Anomaly in Space-Time Characteristics of Certain Programs Running in a Paging Machine. Communications of the ACM, 12:349–353, 1969.Google Scholar
  2. [dK94]
    R. de Koster. Performance approximation of pick-to-belt orderpicking systems. European Journal of Operational Research, 92:558–573, 1994.Google Scholar
  3. [GJ79]
    M.R. Garey and D.S. Johnson. Computers and Intractability. W.H. Freeman and Company, San Francisco, 1979.Google Scholar
  4. [LLKS93]
    E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys. Sequencing and Scheduling: Algorithms and Complexity. In S.C. Graves, A.H.G. Rinnooy Kan, and P.H. Zipkin, editors, Handbooks in Operations Research and Management Science, vol. 4, Logistics of Production and Inventory, pages 445–522. North-Holland, Amsterdam, 1993.Google Scholar
  5. [MMS88]
    M.S. Manasse, L.A. McGeoch, and D.D. Sleator. Competitive algorithms for on-line problems. In Proceedings of the Annual ACM Symposium on Theory of Computing, pages 322–333. ACM, 1988.Google Scholar
  6. [RW97a]
    J. Rethmann and E. Wanke. Storage Controlled Pile-Up Systems, Theoretical Foundations. In Operations Research Proceedings. Springer-Verlag, 1997.Google Scholar
  7. [RW97b]
    J. Rethmann and E. Wanke. An approximation algorithm for stacking up bins from a conveyer onto pallets. In Proceedings of the Annual Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science. Springer-Verlag, to appear 1997.Google Scholar
  8. [RW97c]
    J. Rethmann and E. Wanke. Storage Controlled Pile-Up Systems. European Journal of Operational Research, to appear 1997.Google Scholar
  9. [Tan87]
    Andrew S. Tanenbaum. Operating Systems. Prentice-Hall, Englewood Cliffs, NJ, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • J. Rethmann
    • 1
  • E. Wanke
    • 1
  1. 1.Department of Computer ScienceUniversity of DüsseldorfDüsseldorfGermany

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