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In this note we study multiple-ratio fractional 0--1 programs, a broad classof NP-hard combinatorial optimization problems. In particular, under somerelatively mild assumptions we provide a complete characterization of theconditions, which ensure that a single-ratio function is submodular. Then weillustrate our theoretical results with the assortment optimization andfacility location problems, and discuss practical situations that guaranteesubmodularity in the considered application settings. In such cases,near-optimal solutions for multiple-ratio fractional 0--1 programs can be foundvia simple greedy algorithms.

Fractional 0-1 programming and submodularity