Overbooking with bounded loss

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.