Online Advance Admission Scheduling for Services with Customer Preferences

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 1times 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.

Dynamic Pricing under a Static Calendar

“…In doing so, we are treating c i as an acceptance threshold instead of a bid price. Our policy is similar to those of Wang et al (2015), Gallego et al (2016), in that it probabilistically imitates the LP solution and independently determines for each item i when to discard it from the assortment. However, our discarding rule is static and based on a fixed c i , whereas their discarding rule is dynamic and based on the realized inventory levels.…”

“…Moving to non-stationary demand, the lower bound of 1/2 which improves to 1 as b → ∞ has been previously established using dynamic policies, in the assignment problem of Wang et al (2015) and the more general assortment problem of Gallego et al (2016). We establish the same bounds using static policies, with an extremely simple analysis based on prophet inequalities from optimal stopping theory.…”

A Competitive Analysis of Online Knapsack Problems with Unit Density

“…For other variants, Truong (2015) have studied a two-class advance-scheduling model and computed the optimal scheduling policy. Wang et al (2018) have studied a simpler problem where each patient only consumes one unit of resource. 4.…”

Online matching with its applications to ridesharing

“…Wang et al [34] modeled an online advance-scheduling problem as an online weighted bipartite matching problem. The arrival process follows a non-homogeneous Poisson distribution.…”