On the allocation of exclusive-use counters for airport check-in queues: static vs. dynamic policies

In this paper we propose a static policy for the optimal allocation of a fixed number of exclusive-use check-in counters dedicated to a single flight. We first provide the motivation for considering the static policy by showing that the dynamic policy already available in the literature suffers from the curse of dimensionality. The objective is to minimize the (expected) total cost of waiting, counter operation, and passenger delay costs which we show to be convex in the number of counters allocated. In those cases where the passenger delay cost is difficult to estimate, we propose an alternative formulation and minimize the operating and waiting costs subject to a probabilistic service-level constraint. This constraint ensures that the probability of all passengers being cleared by the gate closing time exceeds a specific level. Finally, we provide a simple procedure for estimating the implied delay costs by exploiting the properties of the two optimization problems. Compared to the difficult-to-evaluate dynamic policy in other papers in the literature, the present static policy requires only a few function evaluations. This feature of the static policy makes it easy to find the optimal number of counters even when the number of booked passengers is in the hundreds.