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Forecasting Demand for

Services

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Learning Objectives

Recommend the appropriate forecasting

model for a given situation.

Conduct a Delphi forecasting exercise. Describe the features of exponential

smoothing.

Conduct time series forecasting usingexponential smoothing with trend and

seasonal adjustments.

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Forecasting Models

Subjective Models

Delphi Methods

Causal ModelsRegression Models

Time Series Models

Moving AveragesExponential Smoothing

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N Period Moving Average

Let : MAT = The N period moving average at the end of period T

AT = Actual observation for period T

Then: MAT = (AT + AT-1 + AT-2+ ..+ AT-N+1)/N

Characteristics:

Need N observations to make a forecast

Very inexpensive and easy to understand

Gives equal weight to all observationsDoes not consider observations older than N periods

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Moving Average Example

Saturday Occupancy at a 100-room Hotel

Three-period

Saturday Period Occupancy Moving Average Forecast

Aug. 1 1 79

8 2 84

15 3 83 82

22 4 81 83 82

29 5 98 87 83Sept. 5 6 100 93 87

12 7 93

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Exponential Smoothing

Let : ST = Smoothed value at endof period T

AT = Actual observation for period T

FT+1 = Forecast for period T+1

Feedback control nature of exponential smoothing

New value (ST ) = Old value (ST-1 ) + [ observed error ]

S S A S

S A S

F S

T T- T T

T T T

T T

1 1

1

1

1

[ ]( )or :

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Exponential SmoothingHotel Example

Saturday Hotel Occupancy ( =0.5)

Actual Smoothed Forecast

Period Occupancy Value Forecast Error

Saturday t At St Ft |At - Ft|Aug. 1 1 79 79.00

8 2 84 81.50 79 5

15 3 83 82.25 82 1

22 4 81 81.63 82 1

29 5 98 89.81 82 16

Sept. 5 6 100 94.91 90 10MAD = 6.6

Forecast Error (Mean Absolute Deviation) = lAt Ftl/n

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Exponential SmoothingImplied Weights Given Past Demand

S A S

S A A S

S A A S

S A A S

T T T

T T T T

T T T T

T T T T

( )

( )[ ( ) ]

( )[ ( ) ]

( ) ( )

1

1 1

1 1

1 1

1

1 1 2

1 2

1

2

2

Substitute for

If continued:

S A A A A S T T T T T T

( ) ( ) ..... ( ) ( )1 1 1 112

2

1

1 0

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Exponential SmoothingWeight Distribution

0

0.1

0.2

0.3

0 1 2 3 4 5

Age of Observation (Period Old)

Weight

0 3.

( ) .1 0 21

( ) .1 01472

( ) .1 0103

3

( ) .1 0 0724

( ) .1 0 0505

Relationship Between and N

(exponential smoothing constant) : 0.05 0.1 0.2 0.3 0.4 0.5 0.67

N (periods in moving average) : 39 19 9 5.7 4 3 2

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Saturday Hotel Occupancy

Effect of Alpha ( =0.1 vs. =0.5)

75

80

85

90

95

100

105

0 1 2 3 4 5 6

Period

O

ccupancy

Actual

Forecast

Forecast

( . ) 0 5

( . ) 0 1

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Exponential Smoothing WithTrend Adjustment

S A S T

T S S T

F S T

t t t t

t t t t

t t t

( ) ( )( )

( ) ( )

1

1

1 1

1 1

1

Commuter Airline Load Factor

Week Actual load factor Smoothed value Smoothed trend Forecast Forecast error

t At St Tt Ft | At - Ft|

1 31 31.00 0.002 40 35.50 1.35 31 9

3 43 39.93 2.27 37 6

4 52 47.10 3.74 42 10

5 49 49.92 3.47 51 2

6 64 58.69 5.06 53 11

7 58 60.88 4.20 64 6

8 68 66.54 4.63 65 3MAD = 6.7

( . , . ) 0 5 0 3

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Exponential Smoothing withSeasonal Adjustment

S A I S

F S I

IA

SI

t t t L t

t t t L

tt

t

t L

( / ) ( )

( )( )

( )

1

1

1

1 1

Ferry Passengers taken to a Resort Island

Actual Smoothed Index Forecast Error

Period t At value St It Ft | At - Ft|

2003January 1 1651 .. 0.837 ..

February 2 1305 .. 0.662 ..

March 3 1617 .. 0.820 ..

April 4 1721 .. 0.873 ..

May 5 2015 .. 1.022 ..

June 6 2297 .. 1.165 ..

July 7 2606 .. 1.322 ..

August 8 2687 .. 1.363 ..

September 9 2292 .. 1.162 ..October 10 1981 .. 1.005 ..

November 11 1696 .. 0.860 ..

December 12 1794 1794.00 0.910 ..

2004

January 13 1806 1866.74 0.876 - -

February 14 1731 2016.35 0.721 1236 495

March 15 1733 2035.76 0.829 1653 80

( . , . ) 0 2 0 3

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Topics for Discussion

What characteristics of service organizations makeforecast accuracy important?

For each of the three forecasting methods, what arethe developmental costs and associated cost offorecast error?

Suggest independent variables for a regressionmodel to predict the sales volume for a proposedvideo rental store location.

Why is the N-period moving-average still in commonuse if the simple exponential smoothing model issuperior?

What changes in , , would you recommend toimprove the performance of the trendline seasonal

adjustment forecast shown in Figure 11.4?

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Interactive Exercise: Delphi ForecastingQuestion: In what future election will a woman become president of the united states?

Year 1st Round Positive Arguments 2nd Round Negative Arguments 3rd Round

2008

2012

2016

2020

2024

2028

2032

2036

20402044

2048

2052

Never

Total