Fractional 0–1 programming and submodularity

Shaoning Han, Andrés Gómez and Oleg A. Prokopyev ()
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Shaoning Han: University of Southern California
Andrés Gómez: University of Southern California
Oleg A. Prokopyev: University of Pittsburgh

Journal of Global Optimization, 2022, vol. 84, issue 1, No 3, 77-93

Abstract: 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.

Keywords: Fractional 0–1 programming; Hyperbolic 0–1 programming; Multiple ratios; Single ratio; Submodularity; Assortment optimization; Facility location; Greedy algorithm (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01131-5

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