Statistical/Quantitative

method

Quantitative methods: These types of forecasting

methods are based on mathematical (quantitative) models, and are objective in

nature. They rely heavily on mathematical computations.

In the scope of this very course,

Rooms Division Managers forecast mainly Room Demand for a future period of time

measured either in:

·

Number of Rooms

·

Number of Room Nights

·

Number of Guest Nights

· Room

Nights = Occupancy Rate * Hotel Rooms * Average Length of Stay

· Guest

Nights = Occupancy Rate * Hotel Rooms * Average Guest per Room

Forecasting demand in room nights

and/or guest nights is a better measurement compared to number of rooms. For,

room nights and /or guest nights underlies more than one demand dimension at

the same time and hence is more meaningful!

Types of Quantitative Method are

:

·

Percentage growth period

·

Moving average period

·

Weighted average period and others like

Regression analysis, econometrics etc that are more complicated

Quantitative Methods:

Jamel Hotel’s Historical Room

Nights for the past 20 years are depicted below:

Year:

Room Nights:

1989

6,520

1990

6,719

1991

7,060

1992

7,148

1993

7,612

1994

8,915

1995

5,430

1996

4,519

1997

5,029

1998

5,478

1999

6,769

2000

7,005

2001

7,345

2002

8,325

2003

8,975

2004

9,066

2005

9,125

2006

8,243

2007

9,324

2008

10,698

Could you forecast 2009 room

demand in room nights only bearing in mind the above-mentioned historical data?

1. Percentage Growth Method:

The assumption according to this

method is that data available follows either an increasing or decreasing trend.

Therefore this method shall be used for forecasting, only when data matches

this assumption. Percentage growth

between two periods i.e. first & the last year, is identified and

applied to the previous year of the year for which forecasts are to be made.

Thus

according to the above example:

During the last 20 years of

operation of Jamel Hotel:

·

The Total Percentage Change in Room

Nights is (10,698 – 6520) / 6,520 * 100 = 64.08

%.

·

The Yearly Percentage Change = 64.08 % /

20 = 3.20 %.

·

The Forecasted Room Nights for year 2009

is 10,698 * (1 + 0.03203) @ 11,041 Room Nights.

2. Moving Average Method:

The Moving Average Method similar

to the “Percentage Growth Method” assumes an increasing or decreasing trend.

This forecasting technique aims at smoothing data and adjusts it as to minimize

volatility reflected in a high standard deviation between different records in

the same data range.

The most common used moving

average is the Double moving average, which calculates a third column by taking

averages of couples of any two successive years, Later, the percentage growth

method would be applied to the smoothed data, Lastly, come up with the

forecasted value:

Year:

Room Nights:

Double Moving Average

1989

6,520

————-

1990

6,719

6,619.5

1991

7,060

6,889.5

1992

7,148

7,104

1993

7,612

7,380

1994

8,915

8,263.5

1995

5,430

7,172.5

1996

4,519

4,974.5

1997

5,029

4,774

1998

5,478

5,253.5

1999

6,769

6,123.5

2000

7,005

6,887

2001

7,345

7,175

2002

8,325

7,835

2003

8,975

8,650

2004

9,066

9,020.5

2005

9,125

9,095.5

2006

8,243

8,684

2007

9,324

8,783.5

2008

10,698

10,011

·

The Total Moving Average Percentage

Change = (10,011-6,619.5) / 6,619.5 * 100 = 51.23 %

·

The Period Moving Average Percentage

Change = 51.23 % / 19 = 2.70 %.

·

The Forecasted 2008 – 2009 Moving

Average = 10,011 * (1.026965) = 10,280.954.

·

The Forecasted 2009 Room Nights =

(10,280.954 * 2) – (10,698) @ 9,864 Room Nights.

3. Weighted Average Method:

The Weighted Average Method

assigns Certain Importance Factor or Coefficient to each historical Value.

Later, the forecasted value shall be computed by dividing the weighted data to

its coefficients by the sum of coefficients.

·

Assigning weights or coefficients is and

art that depends on experience, thorough analysis of past figures, and

performances… Yet, whatsoever coefficients chosen, there is always a certain

subjectivity factor that might affect eventually the forecasted figure!

·

One of the most common types of the

weighted average method is the simplest method, which assigns the lowest weight

to the oldest data in a sequential order.

·

Though the simplest weighted average

method is straight foreword, assigning least weight to oldest data assumes

that:

·

The factors that affects the oldest

demand diminishes through time and hence are not important as far as the future

period to be forecasted is concerned

·

The factors and hence the conditions

that created the last period’s demand are assumed to continue heavily playing

an important role in the next period to be forecasted!

·

Since the above mentioned assumptions

might not be valid, in most of the cases, hotels shall adjust the coefficients

attributed in the simplest weighted average method in a way that mostly puts

more weight on factors thought to affect next period’s demand and less weight

to those which would be considered relatively unimportant!!

·

Another possibility is that hotels

shall, after finding a forecast from the simple weighted average method, adjust

to experience, trends, and facts…

Year

Room Nights

Weight

Total

1989

6,520

1

6,520

1990

6,719

2

13,438

1991

7,060

3

21,180

1992

7,148

4

28,592

1993

7,612

5

38,060

1994

8,915

6

53,490

1995

5,430

7

38,010

1996

4,519

8

36,152

1997

5,029

9

45,261

1998

5,478

10

54,780

1999

6,769

11

74,459

2000

7,005

12

84,060

2001

7,345

13

95,485

2002

8,325

14

116,550

2003

8,975

15

134,625

2004

9,066

16

145,056

2005

9,125

17

155,125

2006

8,243

18

148,374

2007

9,324

19

177,156

2008

10,698

20

213,960

Total

210

1,680,333

The 2009 Forecasted Room Nights

is 1,680,333 / 210 @ 8,002 Room Nights

4. Time Series Analysis:

·

The Time Series Method tries through

Regression Analysis to come up with a Line that minimizes the distance between

any Actual Point on the Curve and its Corresponding Point on the Line (Least

Square Method). This Technique is refereed to as the Regression Analysis.

·

After finding the Equation of the Line

(i.e. f (x) = y = a * x + b), we try to

forecast the independent Variable (in this Case, the 2004 Forecasted Room

Nights)

·

As far as Jamel Hotel’s problem is

concerned, post to running a regression analysis, the equation of the line that

best fits the data (significant at a 95% interval level!) turned out to be:

Room Nights = 169.3692 * Year –

331,019

·

Therefore the 2009 forecasted room nights = 169.3692 * 2009 – 331,019 @ 9,244

Room Nights

III- Comparison

of Forecasting Methods:

Method:

Forecasted Room Nights:

Percentage Growth Method

11,041

Moving Average Method

9,864

Simple Weighted Average Method

8,002

Regression Analysis

9,244

·

Managers shall use forecasting methods with extreme precautions, and shall

consider first the assumptions underlying each Forecasting Method to be able to

find a good forecast.

· After

running a statistical forecast, managers shall adjust it to trends,

expectations, and opinion surveys. (I.e. shall consider judgmental forecasting)