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Exact Solution of the Two-Dimensional Finite Bin Packing Problem

Author

Listed:
  • Silvano Martello

    (Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna, Bologna, Italy)

  • Daniele Vigo

    (Dipartimento di Elettronica, Informatica e Sistemistica, University of Bologna, Bologna, Italy)

Abstract

Given a set of rectangular pieces to be cut from an unlimited number of standardized stock pieces (bins), the Two-Dimensional Finite Bin Packing Problem is to determine the minimum number of stock pieces that provide all the pieces. The problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. We analyze a well-known lower bound and determine its worst-case performance. We propose new lower bounds which are used within a branch-and-bound algorithm for the exact solution of the problem. Extensive computational testing on problem instances from the literature involving up to 120 pieces shows the effectiveness of the proposed approach.

Suggested Citation

  • Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:3:p:388-399
    DOI: 10.1287/mnsc.44.3.388
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    References listed on IDEAS

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    1. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    2. Frenk, J.B.G. & Galambos, G., 1987. "Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem," Econometric Institute Research Papers 11691, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
    4. Dowsland, Kathryn A. & Dowsland, William B., 1992. "Packing problems," European Journal of Operational Research, Elsevier, vol. 56(1), pages 2-14, January.
    5. Hadjiconstantinou, Eleni & Christofides, Nicos, 1995. "An exact algorithm for general, orthogonal, two-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 83(1), pages 39-56, May.
    6. Mauro Dell’Amico & Silvano Martello, 1995. "Optimal Scheduling of Tasks on Identical Parallel Processors," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 191-200, May.
    7. Coffman, E. G. & Shor, P. W., 1990. "Average-case analysis of cutting and packing in two dimensions," European Journal of Operational Research, Elsevier, vol. 44(2), pages 134-144, January.
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