Overbooking with bounded loss

TL;DR

This paper addresses a revenue management problem involving overbooking and no-shows, proposing an online algorithm with a loss bound independent of the number of customers, improving upon previous bounds.

Contribution

It introduces an online algorithm for overbooking with bounded loss, outperforming prior methods with loss bounds that do not grow with the number of arrivals.

Findings

Algorithm achieves a uniform additive loss bound.

Expected loss is independent of total customer arrivals.

Improves upon previous guarantees of  guarantees.

Abstract

We study a classical problem in revenue management: quantity-based single-resource revenue management with no-shows. In this problem, a firm observes a sequence of $T$ customers requesting a service. Each arrival is drawn independently from a known distribution of $k$ different types, and the firm needs to decide irrevocably whether to accept or reject requests in an online fashion. The firm has a capacity of resources $B$, and wants to maximize its profit. Each accepted service request yields a type-dependent revenue and has a type-dependent probability of requiring a resource once all arrivals have occurred (or, be a no-show). If the number of accepted arrivals that require a resource at the end of the horizon is greater than $B$, the firm needs to pay a fixed compensation for each service request that it cannot fulfill. With a clairvoyant, that knows all arrivals ahead of time, as a benchmark, we provide an algorithm with a uniform additive loss bound, i.e., its expected loss is independent of $T$. This improves upon prior works achieving $\Omega(\sqrt{T})$ guarantees.