TY - GEN

T1 - Continuous-time revenue management in carparks

T2 - 2nd International Conference on Operations Research and Enterprise Systems, ICORES 2013

AU - Papayiannis, Andreas

AU - Johnson, Paul

AU - Yumashev, Dmitry

AU - Duck, Peter

PY - 2013

Y1 - 2013

N2 - 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 ΔT. The new model is compared against the Monte Carlo (MC) approach for several choices of ΔT; 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.

AB - 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 ΔT. The new model is compared against the Monte Carlo (MC) approach for several choices of ΔT; 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.

KW - Expected revenue

KW - Rejection policy

M3 - Conference contribution/Paper

AN - SCOPUS:84877932012

SN - 9789898565402

SP - 76

EP - 81

BT - ICORES 2013 - Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems

A2 - Vitoriano, Begoña

Y2 - 16 February 2013 through 18 February 2013

ER -