This thesis investigates the revenue management (RM) problem encountered in an airport carpark of finite capacity, where the available parking spaces should be sold optimally in advance in order to maximise the revenues on a given day. Customer demand is stochastic, where random pre-booking times and stay lengths overlap with each other, a setting that generates strong inter-dependence among consecutive days and hence leads to a complex network optimisation problem. Several mathematical models are introduced to approximate the problem; a model based on a discrete-time formulation which is solved using Monte Carlo (MC) simulations and two single-resource models, the first based on a stochastic process and the other on a deterministic one, both developed in continuous-time that lead to a partial differential equation (PDE). The optimisation for the spaces is based on the expected displacement costs which are then used in a bid-price control mechanism to optimise the value of the carpark. Numerical tests are conducted to examine the methods’ performance under the network setting. Taking into account the methods’ efficiency, the computation times and the resulting expected revenues, the stochastic PDE approach is shown to be the preferable method. Since the pricing structure among operators varies, an adjusted model based on the stochastic PDE is derived in order to facilitate the solution applicable in all settings. Further, for large carparks facing high demand levels, an alternative second-order PDE model is proposed. Finally, an attempt to incorporate more information about the network structure and the inter-dependence between consecutive days leads to a weighted PDE scheme. Given a customer staying on day T, a weighting kernel is introduced to evaluate the conditional probability of stay on a neighbouring day. Then a weighted average is applied on the expected marginal values over all neighbouring days. The weighted PDE scheme shows significant improvement in revenue for small-size carparks. The use of the weighted PDE opens the possibility for new ways to approximate network RM problems and thus motivates further research in this direction.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:603269 |
| Date | January 2014 |
| Creators | Papayiannis, Andreas |
| Contributors | Duck, Peter; Johnson, Paul |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/on-revenue-management-techniques-a-continuoustime-applicationto-airport-carparks(152e2261-1113-49ba-a846-8d6607024e11).html |
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