  In this note we study multiple-ratio fractional 0--1 programs, a broad class
of 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.
