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Lower bounds and algorithms for the minimum cardinality bin covering problem

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  • Walter, Rico
  • Lawrinenko, Alexander

Abstract

This paper introduces the minimum cardinality bin covering problem where we are given m identical bins with capacity C and n indivisible items with integer weights wj(j=1,…,n). The objective is to minimize the number of items packed into the m bins so that the total weight of each bin is at least equal to C. We discuss reduction criteria, derive several lower bound arguments and propose construction heuristics as well as a powerful subset sum-based improvement algorithm that is even optimal when m=2. Moreover, we present a tailored branch-and-bound method which is able to solve instances with up to 20 bins and several hundreds of items within a reasonable amount of time. In a comprehensive computational study on a wide range of randomly generated instances, our algorithmic approach proved to be much more effective than a commercial solver.

Suggested Citation

  • Walter, Rico & Lawrinenko, Alexander, 2017. "Lower bounds and algorithms for the minimum cardinality bin covering problem," European Journal of Operational Research, Elsevier, vol. 256(2), pages 392-403.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:2:p:392-403
    DOI: 10.1016/j.ejor.2016.06.068
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    References listed on IDEAS

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    1. Fleszar, Krzysztof & Charalambous, Christoforos, 2011. "Average-weight-controlled bin-oriented heuristics for the one-dimensional bin-packing problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 176-184, April.
    2. Vijayakumar, Bharathwaj & Parikh, Pratik J. & Scott, Rosalyn & Barnes, April & Gallimore, Jennie, 2013. "A dual bin-packing approach to scheduling surgical cases at a publicly-funded hospital," European Journal of Operational Research, Elsevier, vol. 224(3), pages 583-591.
    3. Labbe, Martine & Laporte, Gilbert & Martello, Silvano, 2003. "Upper bounds and algorithms for the maximum cardinality bin packing problem," European Journal of Operational Research, Elsevier, vol. 149(3), pages 490-498, September.
    4. Scheithauer, Guntram & Terno, Johannes, 1995. "The modified integer round-up property of the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 84(3), pages 562-571, August.
    5. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    6. Gregory Dobson, 1982. "Worst-Case Analysis of Greedy Heuristics for Integer Programming with Nonnegative Data," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 515-531, November.
    7. Peeters, Marc & Degraeve, Zeger, 2006. "Branch-and-price algorithms for the dual bin packing and maximum cardinality bin packing problem," European Journal of Operational Research, Elsevier, vol. 170(2), pages 416-439, April.
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