Fractional 0–1 programming and submodularity

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