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Worst-case analyses, linear programming and the bin-packing problem

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Abstract

In this paper we consider the familiar bin-packing problem and its associated set-partitioning formulation. We show that the optimal solution to the bin-packing problem can be no larger than 4/3 ⌈Z LP⌉, whereZ LP is the optimal solution value of the linear programming relaxation of the set-partitioning formulation. An example is provided to show that the bound is tight. A by-product of our analysis is a new worst-case bound on the performance of the well studied First Fit Decreasing and Best Fit Decreasing heuristics.

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Author information

Authors and Affiliations

  1. Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong People's Republic of China

    Lap Mui Ann Chan

  2. Department of Industrial Engineering and Management Sciences, Northwestern University, MLSB 2225 North Campus Drive, 60208-3119, Evanston, IL, USA

    David Simchi-Levi

  3. Graduate School of Business, Columbia University, 10027, New York, NY, USA

    Julien Bramel

Authors
  1. Lap Mui Ann Chan
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  2. David Simchi-Levi
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  3. Julien Bramel
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Corresponding author

Correspondence to David Simchi-Levi.

Additional information

This research was supported in part by ONR Contracts N00014-90-J-1649 and N00014-95-1-0232, and NSF Contracts DDM-8922712 and DDM-9322828.

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Chan, L.M.A., Simchi-Levi, D. & Bramel, J. Worst-case analyses, linear programming and the bin-packing problem. Mathematical Programming 83, 213–227 (1998). https://doi.org/10.1007/BF02680559

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  • DOI: https://doi.org/10.1007/BF02680559

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