  In this paper, we investigate the common scenario where every candidate item
for recommendation is characterized by a maximum capacity, i.e., number of
seats in a Point-of-Interest (POI) or size of an item's inventory. Despite the
prevalence of the task of recommending items under capacity constraints in a
variety of settings, to the best of our knowledge, none of the known
recommender methods is designed to respect capacity constraints. To close this
gap, we extend three state-of-the art latent factor recommendation approaches:
probabilistic matrix factorization (PMF), geographical matrix factorization
(GeoMF), and bayesian personalized ranking (BPR), to optimize for both
recommendation accuracy and expected item usage that respects the capacity
constraints. We introduce the useful concepts of user propensity to listen and
item capacity. Our experimental results in real-world datasets, both for the
domain of item recommendation and POI recommendation, highlight the benefit of
our method for the setting of recommendation under capacity constraints.
