An approximation algorithm for stacking up bins from a conveyer onto pallets

  • J. Rethmann
  • E. Wanke
Session 11B: Invited Lecture
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1272)


Given sequence of bins q = (b1,. . . , bn) and a positive integer p. Each bin is destined for. We consider the problem to remove step by step all bins from q such the positions of the bins removed from q are as less as possible and after each removal there are at most p open (A pallet t is called open if the first bin for t is already removed from q but the last bin for t is still contained in q. If a bin b is removed from q then all bins to the right of b are shifted one position to the left.)

The maximal position of the removed bins and the maximal number of open pallets are called the storage capacity and the number of stack-up places, respectively. We introduce an O(n · log(p)) time approximation algorithm that processes each sequence q with a storage capacity of at most smin(q, p) · [log2(p + 1)] bins and p + 1 stack-up places, where smin(q,p) is the minimum storage capacity necessary to process q with p stack-up places.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AHU74]
    A.V. Aho, J.E. Hopcroft, and J.D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, Massachusetts, 1974.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, A Guide to the Theory of NP-Completeness. 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 Re search and Management Science, Vol. 4. Logistics of Production and Inventory, pages 445–522. North-Holland, Amsterdam, 1993.Google Scholar
  5. [Meh84]
    K. Mehlhorn. Data Structures and Algorithms I: Sorting and Searching. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1984.Google Scholar
  6. [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
  7. [RW97a]
    J. Rethmann and E. Wanke. Competitive analysis of on-line stack-up algorithms. In Proceedings of the Annual European Symposium on Algorithms, LNCS. Springer-Verlag, 1997. To appear.Google Scholar
  8. [RW97b]
    J. Rethmann and E. Wanke. Storage controlled pile-up systems, theoretical foundations. European Journal of Operational Research, to appear, 1997. A short abstract of this paper will also appear in the Proceedings of SOR '96.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

Personalised recommendations