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Min-Sum Bin Packing

Author

Listed:
  • Leah Epstein

    (University of Haifa)

  • David S. Johnson

    (AT&T Labs - Research)

  • Asaf Levin

    (The Technion)

Abstract

We study min-sum bin packing (MSBP). This is a bin packing problem, where the cost of an item is the index of the bin into which it is packed. The problem is equivalent to a batch scheduling problem we define, where the total completion time is to be minimized. The problem is NP-hard in the strong sense. We show that it is not harder than this by designing a polynomial time approximation scheme for it. We also show that several natural algorithms which are based on well-known bin packing heuristics (such as First Fit Decreasing) fail to achieve an asymptotic finite approximation ratio, whereas Next Fit Increasing has an absolute approximation ratio of at most 2, and an asymptotic approximation ratio of at most 1.6188. We design a new heuristic that applies Next Fit Increasing on the relatively small items and adds the larger items using First Fit Decreasing, and show that its asymptotic approximation ratio is at most 1.5604.

Suggested Citation

  • Leah Epstein & David S. Johnson & Asaf Levin, 2018. "Min-Sum Bin Packing," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 508-531, August.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:2:d:10.1007_s10878-018-0310-x
    DOI: 10.1007/s10878-018-0310-x
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    References listed on IDEAS

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    1. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
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