# Recommendation under Capacity Constraints

## TL;DR

This paper extends existing recommendation algorithms to incorporate capacity constraints, ensuring recommended items do not exceed their maximum capacity, which is crucial for practical applications like POI and inventory recommendations.

## Contribution

It introduces capacity-aware extensions of three state-of-the-art recommendation methods, integrating user propensity and item capacity concepts to improve recommendation feasibility.

## Key findings

- Enhanced recommendation accuracy under capacity constraints
- Effective handling of POI and inventory recommendation scenarios
- Demonstrated improvements on real-world datasets

## Abstract

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.