The last class of demand forecasting methods are advanced bookings called additive and multiplicative pick-up models. The basic concept behind those methods is identifying increase of booking in different periods and then accumulating it into total demand that is expected in the future. The main advantages of those methods is taking all available bookings information, forecast is more responsive to shifts in demand and is easy to track increase in bookings. Moreover, studies conducted by: Wickham (1995) and Weatherford and Kimes (2003) reported this method to have the best results (best accuracy or lower error than other methods).

First type – additive pick up model – assumes independency between number of rooms booked in any time before arrival date and total number of rooms successfully sold. It forecasts the future bookings of rooms by calculating average from increment demand from the same period in the past. The forecast number of bookings by time for the date of stay is computed by:

where *x(ij*) is the number of reservation already booked by time for the date of stay *i*, *A(ij)=x(ij) – x(ij-1)* is the increased bookings occurred during time *j-1* to time *j* for the date of stay *i*, *Aj* is the average increased bookings during time *j-1* to time *j* (Phumchusri and Mongkolkul, 2012).

The second type – multiplicative pickup model – forecast future bookings of rooms by averaging the rate of increased demand from the same period in the past. The forecast number of bookings by time for the date of stay is computed then by:

where is the rate of increased bookings during time *j-1* to time *j* and *Mj* is the average rate of increased bookings during time *j -1* to time *j* and *T* is booking horizon. (Phumchusri and Mongkolkul, 2012).

In literature, e.g. Wickham (1995), Chen and Kochani (2007) divided pick up methods into classical and advanced Pick up. Classical methods takes data only from finished booking curves, hence ignores information about incomplete arrival dates. While advanced uses all available information about bookings, and therefore uses reservation data of arrivals that still did not occur. The other expansion of this method is to use exponential averaging instead of simple average (Zakhary et. al. 2008).

The application of this method on our data set is available here: Additive Pick-up

Explanation

First of all, we couldn’t use Multplicative Pick Up as some of the days prior to arrival had no bookings.

Secondly, we conducted three versions of method:

- 1D forecast demand for the next day
- 3D forecast demand three days ahead
- 7D forecast demand seven days ahead

Formula for forecast 3D on D1099 (1.01.2013) is as follows: =AQ1099+AVERAGE(K$3:K1098)+AVERAGE(J$3:J1098)+AVERAGE(I$3:I1098) , where:

- AQ1099 – number of bookings we held 3 days before 1.01.2013
- AVERAGE(K$3:K1098) – the usual number of bookings that appears 2 days before arrival
- AVERAGE(J$3:J1098) – the usual number of bookings that appears 1 days before arrival
- AVERAGE(I$3:I1098) – the usual number of bookings that appears during arrival date

The MAPE of respectively model 1D, 3D, 7D were: 6,6%; 7,9%; 8%

Example

This method also gave very good results when demand is unstable and hard to predict.

References:

- Chen, C. and Kachani, S. (2007) Forecasting and optimisation for hotel revenue management.
*Journal of Revenue & Pricing Management*, vol. 6, no. 3, pp. 163-174. - Phumchusri, D., Mongkolkul, J. (2012) Hotel Room Demand via Observed Reservation Information.
*Proceedings of the Asia Pacific Industrial Engineering & Management Systems Conference 2012,*pp. 1978-1985 - Weatherford, L.R. & Kimes, S.E. (2003). A comparison of forecasting methods for hotel revenue management
*. International Journal of Forecasting*, vol. 19, no. 3, pp. 401-415. - Wickham, R. (1995) Evaluation of forecasting techniques for short-term demand of air transportation. Master’s thesis, Massachusetts Institute of Technology
- Zakhary, A., El Gayar, N. and Atiya, A. (2008) A comparative Study of the Pickup Method and its Variations Using a Simulated Hotel Reservation Data.
*The International Journal of Artificial Intelligence and Machine Learning*, 8 (Special Issue on Computational Methods for the Tourism Industry).