Online Advance Admission Scheduling for Services with Customer Preferences

TL;DR

This paper introduces new online algorithms for scheduling services with customer preferences, providing performance guarantees and demonstrating superior empirical results over existing heuristics in hospital appointment data.

Contribution

The paper develops the tightest known performance bounds for online weighted bipartite matching with non-stationary arrivals and applies these algorithms to real-world scheduling data.

Findings

Algorithms outperform existing heuristics in hospital scheduling data

Achieve at least 1-√(2/π)/√k performance ratio compared to offline optimal

Algorithms are 21% more effective than current hospital scheduling strategies

Abstract

We study web and mobile applications that are used to schedule advance service, from medical appointments to restaurant reservations. We model them as online weighted bipartite matching problems with non-stationary arrivals. We propose new algorithms with performance guarantees for this class of problems. Specifically, we show that the expected performance of our algorithms is bounded below by $1-\sqrt{\frac{2}{\pi}}\frac{1}{\sqrt{k}}+O(\frac{1}{k})$ times that of an optimal offline algorithm, which knows all future information upfront, where $k$ is the minimum capacity of a resource. This is the tightest known lower bound. This performance analysis holds for any Poisson arrival process. Our algorithms can also be applied to a number of related problems, including display ad allocation problems and revenue management problems for opaque products. We test the empirical performance of our algorithms against several well-known heuristics by using appointment scheduling data from a major academic hospital system in New York City. The results show that the algorithms exhibit the best performance among all the tested policies. In particular, our algorithms are $21\%$ more effective than the actual scheduling strategy used in the hospital system according to our performance metric.