Transcript Forecasting Demand for Services

Forecasting Demand for
Services
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 using
exponential smoothing with trend and
seasonal adjustments.
Forecasting Models
Subjective Models
Delphi Methods
 Causal Models
Regression Models
 Time Series Models
Moving Averages
Exponential Smoothing

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 observations
Does not consider observations older than N periods
Moving Average Example
Saturday Occupancy at a 100-room Hotel
Saturday
Aug.
1
8
15
22
29
Sept. 5
12
Period
1
2
3
4
5
6
7
Occupancy
79
84
83
81
98
100
Three-period
Moving Average
82
83
87
93
Forecast
82
83
87
93
Exponential Smoothing
Let : ST = Smoothed value at end of 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 ) +
or :
ST  ST-1   [ AT  ST 1 ]
ST   AT  (1   ) ST 1
FT 1  ST
 [ observed error ]
Exponential Smoothing
Hotel Example
Saturday Hotel Occupancy ( =0.5)
Saturday
Aug. 1
8
15
22
29
Sept. 5
Period
t
1
2
3
4
5
6
Actual
Occupancy
At
79
84
83
81
98
100
Smoothed
Value
St
79.00
81.50
82.25
81.63
89.81
94.91
Forecast
Error
|At - Ft|
Forecast
Ft
79
82
82
82
90
5
1
1
16
10
MAD = 6.6
Forecast Error (Mean Absolute Deviation) = ΣlAt – Ftl/n
Exponential Smoothing
Implied Weights Given Past Demand
Substitute for
ST  AT  (1   ) ST 1
ST 1  AT  (1   )[AT 1  (1   ) ST  2 ]
ST  AT  (1   )[AT 1  (1   ) ST  2 ]
ST  AT   (1   ) AT 1  (1   ) 2 ST  2
If continued:
ST  AT   (1   ) AT 1   (1   )2 AT 2 ..... (1   )T 1 A1  (1   )T S0
Exponential Smoothing
Weight Distribution
  0.3
Weight
0.3
 (1   )  0.21
0.2
 (1   )2  0147
.
 (1   )3  0103
.
 (1   )4  0.072
 (1   )5  0.050
0.1
0
0
1
2
3
4
5
Age of Observation (Period Old)
Relationship Between  and N

(exponential smoothing constant) : 0.05
N (periods in moving average) :
39
0.1 0.2
19 9
0.3
5.7
0.4
4
0.5
3
0.67
2
Saturday Hotel Occupancy
 =0.1 vs. =0.5)
105
100
95
90
85
80
75
Actual
Forecast
(  0.5)
Forecast
Period
6
5
4
3
2
1
(  01
.)
0
Occupancy
Effect of Alpha (
Exponential Smoothing With
Trend Adjustment
St   ( At )  (1   )( St 1  Tt 1 )
Tt   ( St  St 1 )  (1   )Tt 1
Ft 1  St  Tt
Commuter Airline Load Factor (  0.5,   0.3)
Week
t
1
2
3
4
5
6
7
8
Actual load factor
At
31
40
43
52
49
64
58
68
Smoothed value
St
Smoothed trend
Tt
31.00
35.50
39.93
47.10
49.92
58.69
60.88
66.54
0.00
1.35
2.27
3.74
3.47
5.06
4.20
4.63
Forecast Forecast error
Ft
| At - Ft|
31
37
42
51
53
64
65
9
6
10
2
11
6
3
MAD = 6.7
Exponential Smoothing with
Seasonal Adjustment
St   ( At / I t  L )  (1   ) St 1
Ft 1  ( St )( I t  L 1 )
It  
At
 (1   ) I t  L
St
Ferry Passengers taken to a Resort Island (  0.2,   0.3)
Actual
Smoothed
Index
Period
t
At
value St
It
2003
January
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
March
15
1733
2035.76
0.829
Forecast
Ft
Error
| At - Ft|
…..
…..
…..
…..
…..
…..
…..
…..
…..
…..
…..
…..
1236
1653
495
80
Topics for Discussion
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What characteristics of service organizations make
forecast accuracy important?
For each of the three forecasting methods, what are
the developmental costs and associated cost of
forecast error?
Suggest independent variables for a regression
model to predict the sales volume for a proposed
video rental store location.
Why is the N-period moving-average still in common
use if the simple exponential smoothing model is
superior?
What changes in α, β, γ would you recommend to
improve the performance of the trendline seasonal
adjustment forecast shown in Figure 11.4?
Interactive Exercise: Delphi Forecasting
Question: In what future election will a woman become president of the united states?
Year
2008
2012
2016
2020
2024
2028
2032
2036
2040
2044
2048
2052
Never
Total
1st Round
Positive Arguments
2nd Round
Negative Arguments
3rd Round