We study the revenue management (RM) problem encountered in airport carparks, with the primary objective to maximize revenues under a continuous-time framework. The implementation of pre-booking systems for airport carparks has spread rapidly around the world and pre-booking is now available in most major airports. Currently, most RM practices in carparks are simple adjustments of those developed for hotels, exploiting the similarities between the two industries. However, airport carparks have a distinct setting where the price-per-day of a parking space is heavily discounted by the length-of-stay of the booking. This is because the customer decision tends to be made after the length of the trip is already set, and it becomes a choice between parking or alternative modes of transport. Consequently, the length-of-stay becomes a critical variable for revenue optimization. Since customers are able to book the parking by the minute, the resulting state space is very large, making a conventional network solution intractable. Instead, decomposed single-resource problems need to be considered. Here we develop a bid-price control strategy to manage the bookings and propose novel approaches to define such bidprices depending on the length of stay, which could be utilized in real-time RM algorithms. Managing stochastic carpark bookings by length-of-stay in the decomposed single-resource approximation allowed us to achieve within 5% of the expected revenues for a multi-resource approximation, with a fraction of the computational effort. When expected demand exceeds the available parking capacity, the method increases the revenues by up to 45% relative to the first-come-first-serve acceptance policy.

Abstract:In this paper, we study optimal revenue management applied to carparks, with primary objective to maximize revenues under a continuous-time framework. We develop a stochastic discrete-time model and propose a rejection algorithm that makes optimal decisions (accept/reject) according to the future expected revenues generated and on the opportunity cost that arises before each sale. For this aspect of the problem, a Monte Carlo approach is used to derive optimal rejection policies. We then extend this approach to show that there exists an equivalent continuous-time methodology that yields to a partial differential equation (PDE). The nature of the PDE, as opposed to the Monte Carlo approach, generates the rejection policies quicker and causes the optimal surfaces to be significantly smoother. However, because the solution to the PDE is considered not to solve the 'full' problem, we propose an approach to generate optimal revenues using the discrete-time model by exploiting the information coming from the PDE. We give a worked example of how to generate near-optimal revenues with an order of magnitude decrease in computation speed.

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Abstract:In this paper, we study optimal revenue management applied to carparks, with the primary objective to maximize revenues under a continuous-time framework. This work is an extension to (Papayiannis et al., 2012) where the authors developed a Partial Differential Equation (PDE) model that could solve for the rate at which cash is generated through an infinitesimal time. However, in practice, carpark managers charge customers per day or per hour which is a finite period of time. Unfortunately, this situation was currently not captured by this previous work. Therefore, our current work attempts to reformulate the existing PDE in a way that it does capture the revenue that is generated within any finite time interval of length ∆T . The new model is compared against the Monte Carlo (MC) approach for several choices of ∆T ; the results are remarkable as the improvement in computation speed and efficiency are significant. Since, the algorithm in the PDE still does not solve the 'exact' problem, a method is proposed to marry the benefits of the PDE with those of the MC approach. Our results are prominent as the optimal values generated in this case have shown to be extremely close to the MC ones while the computation times are kept to a minimum.