Recommendation with capacity constraints

In many recommendation settings, the candidate items for recommendation are associated with a maximum capacity, i e., number of seats in a Point-of-Interest (POI) or number of item copies in the inventory. However, despite the prevalence of the capacity constraint in the recommendation process, the existing recommendation methods are not designed to optimize for respecting such a constraint. Towards closing this gap, we propose Recommendation with Capacity Constraints - a framework that optimizes for both recommendation accuracy and expected item usage that respects the capacity constraints. We show how to apply our method to three state-of-the-art latent factor recommendation models: probabilistic matrix factorization (PMF), bayesian personalized ranking (BPR) for item recommendation, and geographical matrix factorization (GeoMF) for POI recommendation. Our experiments indicate that our framework is effective for providing good recommendations while taking the limited resources into consideration. Interestingly, our methods are shown in some cases to further improve the top-N recommendation quality of the respective unconstrained models.