# CONTINUOUS-TIME REVENUE MANAGEMENT IN CARPARKS

### A. Papayiannis, P. Johnson, D. Yumashev, S. Howell, N. Proudlove, P. Duck

#### 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 theMonte 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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#### Paper Citation

#### in Harvard Style

Papayiannis A., Johnson P., Yumashev D., Howell S., Proudlove N. and Duck P. (2012). **CONTINUOUS-TIME REVENUE MANAGEMENT IN CARPARKS** . In *Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-8425-97-3, pages 73-82. DOI: 10.5220/0003762800730082

#### in Bibtex Style

@conference{icores12,

author={A. Papayiannis and P. Johnson and D. Yumashev and S. Howell and N. Proudlove and P. Duck},

title={CONTINUOUS-TIME REVENUE MANAGEMENT IN CARPARKS},

booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2012},

pages={73-82},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003762800730082},

isbn={978-989-8425-97-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - CONTINUOUS-TIME REVENUE MANAGEMENT IN CARPARKS

SN - 978-989-8425-97-3

AU - Papayiannis A.

AU - Johnson P.

AU - Yumashev D.

AU - Howell S.

AU - Proudlove N.

AU - Duck P.

PY - 2012

SP - 73

EP - 82

DO - 10.5220/0003762800730082