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Fractional 0–1 programming and submodularity

Author

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  • Shaoning Han

    (University of Southern California)

  • Andrés Gómez

    (University of Southern California)

  • Oleg A. Prokopyev

    (University of Pittsburgh)

Abstract

In this note we study multiple-ratio fractional 0–1 programs, a broad class of $$\mathcal {NP}$$ NP -hard combinatorial optimization problems. In particular, under some relatively mild assumptions we provide a complete characterization of the conditions, which ensure that a single-ratio function is submodular. Then we illustrate our theoretical results with the assortment optimization and facility location problems, and discuss practical situations that guarantee submodularity in the considered application settings. In such cases, near-optimal solutions for multiple-ratio fractional 0–1 programs can be found via simple greedy algorithms.

Suggested Citation

  • Shaoning Han & Andrés Gómez & Oleg A. Prokopyev, 2022. "Fractional 0–1 programming and submodularity," Journal of Global Optimization, Springer, vol. 84(1), pages 77-93, September.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:1:d:10.1007_s10898-022-01131-5
    DOI: 10.1007/s10898-022-01131-5
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