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ON REVENUE MANAGEMENT TECHNIQUES: A CONTINUOUS-TIME APPLICATIONTO AIRPORT CARPARKS

Papayiannis, Andreas

[Thesis]. Manchester, UK: The University of Manchester; 2014.

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Abstract

This thesis investigates the revenue management (RM) problem encountered inan airport carpark of finite capacity, where the available parking spaces should besold optimally in advance in order to maximise the revenues on a given day. Customerdemand is stochastic, where random pre-booking times and stay lengthsoverlap with each other, a setting that generates strong inter-dependence amongconsecutive days and hence leads to a complex network optimisation problem.Several mathematical models are introduced to approximate the problem; a modelbased on a discrete-time formulation which is solved using Monte Carlo (MC) simulationsand two single-resource models, the first based on a stochastic processand the other on a deterministic one, both developed in continuous-time thatlead to a partial differential equation (PDE). The optimisation for the spaces isbased on the expected displacement costs which are then used in a bid-price con-trol mechanism to optimise the value of the carpark.Numerical tests are conducted to examine the methods’ performance under thenetwork setting. Taking into account the methods’ efficiency, the computationtimes and the resulting expected revenues, the stochastic PDE approach is shownto be the preferable method.Since the pricing structure among operators varies, an adjusted model based onthe stochastic PDE is derived in order to facilitate the solution applicable in allsettings. Further, for large carparks facing high demand levels, an alternativesecond-order PDE model is proposed.Finally, an attempt to incorporate more information about the network structureand the inter-dependence between consecutive days leads to a weighted PDEscheme. Given a customer staying on day T, a weighting kernel is introducedto evaluate the conditional probability of stay on a neighbouring day. Then aweighted average is applied on the expected marginal values over all neighbouringdays. The weighted PDE scheme shows significant improvement in revenue forsmall-size carparks. The use of the weighted PDE opens the possibility for newways to approximate network RM problems and thus motivates further researchin this direction.