Table of Contents
Chapter 13 (Forecasting)
Some Applications of Forecasting (Section 13.1)
A Case Study: The Computer Club Warehouse Problem (Section 13.2)
Applying Time-Series Forecasting to the Case Study (Section 13.3)
Time-Series Forecasting with CB Predictor (Section 13.4)
The Time-Series Forecasting Methods in Perspective (Section 13.5)
Causal Forecasting with Linear Regression (Section 13.6)
Judgmental Forecasting Methods (Section 13.7)
Forecasting in Practice (Section 13.8)
McGraw-Hill/Irwin
13.1
13.2–13.4
13.5–13.9
13.10–13.26
13.27–13.34
13.35–13.39
13.40–13.44
13.45
13.46–13.47
© The McGraw-Hill Companies, Inc., 2003
Some Applications of Forecasting
•
Sales Forecasting
– Any company engaged in selling goods needs to forecast demand for those goods.
– Underestimating demand leads to shortages, lost sales, unhappy customers, etc.
– Overestimating demand is costly due to inventory costs, forced price reductions,
unneeded production, etc.
– Examples: Merit Brass Company (1993), Hidroeléctrica Español (1990), American
Airlines (1992).
•
Forecasting Economic Trends
– How much will the nation’s gross domestic product grow next quarter? Next year?
What is the forecast for the rate of inflation? Unemployment?
– Statistical models to forecast economic trends (econometric models) have been
developed by government agencies, universities, consulting firms, etc.
– Models can be very influential in determining govermental policies.
– Example: U.S. Department of Labor (1988).
All articles can be downloaded at www.mhhe.com/hillier2e/articles
McGraw-Hill/Irwin
13.2
© The McGraw-Hill Companies, Inc., 2003
Some Applications of Forecasting
•
Forecasting Production Yields
– The yield of a production process refers to the percentage of completed items that
meet quality standards and do not need to be discarded.
– If an expensive setup is required, or there is only one production run, an accurate
forecast is necessary to provide a good chance of fulfilling an order with acceptable
items without excessive production costs.
– Example: Albuquerque Microelectronics Operation (1994)
•
Forecasting the Need for Spare Parts
– Many companies need to maintain an inventory of spare parts to enable them to
repair either their equipment or their products leased or sold to customers.
– Example: American Airlines (1989).
•
Forecasting Staffing Needs
– For a service company, forecasting “sales” becomes forecasting demand for
services, which translates into forecasting staffing needs.
– Too few staff leads to long lines, unhappy customers, perhaps lost business. Too
many increases personnel cost.
– Examples: United Airlines (1986), Taco Bell (1998), L. L Bean (1995).
All articles can be downloaded at www.mhhe.com/hillier2e/articles
McGraw-Hill/Irwin
13.3
© The McGraw-Hill Companies, Inc., 2003
Applications of Statistical Forecasting Methods
Organization
Quantity Being Forecasted
Issue of Interfaces
Merit Brass Co.
Sales of finished goods
Jan-Feb 1993
Hidroelétrica Español
Energy demand
Jan-Feb 1990
American Airlines
Demand for different fare classes
Jan-Feb 1992
American Airlines
Need for spare parts to repair
airplanes
July-Aug 1989
Albuquerque
Microelectronics
Production yield in wafer fabrication Mar-Apr 1994
U.S. Department of Labor
Unemployment insurance payments
Mar-Apr 1988
United Airlines
Demand at reservations offices and
airports
Jan-Feb 1986
Taco Bell
Number of customer arrivals
Jan-Feb 1988
L.L. Bean
Staffing needs at call center
Nov-Dec 1995
All references available for download at www.mhhe.com/hillier2e/articles
McGraw-Hill/Irwin
13.4
© The McGraw-Hill Companies, Inc., 2003
The Computer Club Warehouse (CCW)
•
The Computer Club Warehouse (CCW) sells computer products at bargain
prices by taking telephone orders (as well as website and fax orders) directly
from customers.
•
Products include computers, peripherals, supplies, software, and computer
furniture.
•
The CCW call center is never closed. It is staffed by dozens of agents to take
and process customer orders.
•
A large number of telephone trunks are provided for incoming calls. If an
agent is not free when a call arrives, it is placed on hold. If all the trunks are in
use (called saturation), the call receives a busy signal.
•
An accurate forecast of the demand for agents is needed.
Question: How should the demand for agents be forecasted?
McGraw-Hill/Irwin
13.5
© The McGraw-Hill Companies, Inc., 2003
25 Percent Rule (Current Forecasting Method)
Since sales are relatively stable through the year except for a substantial increase
during the Christmas season, assume that each quarter’s call volume will be the
same as the preceding quarter, except for adding 25 percent for Quarter 4.
Forecast for Quarter 2 = Call volume for Quarter 1
Forecast for Quarter 3 = Call volume for Quarter 2
Forecast for Quarter 4 = 1.25(Call volume for Quarter 3)
Forecast for next Quarter 1 = (Call volume for Quarter 4) / 1.25
McGraw-Hill/Irwin
13.6
© The McGraw-Hill Companies, Inc., 2003
Average Daily Call Volume (3 Years of Data)
A
1
B
C
D
E
CCW's Average Daily Call Volume
2
3
Year
4
1
1
1
1
2
2
2
2
3
3
3
3
5
6
7
8
9
10
11
12
13
14
15
McGraw-Hill/Irwin
Quarter
Call Volume
1
2
3
4
1
2
3
4
1
2
3
4
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
13.7
© The McGraw-Hill Companies, Inc., 2003
Applying the 25-Percent Rule
A
1
B
C
D
E
F
G
H
I
Current Forecasting Method for CCW's Average Daily Call Volume
2
Forecasting
3
4
Year
Quarter
Data
5
1
1
6,809
6
1
2
7
1
8
9
10
11
12
13
14
15
16
17
18
19
20
Forecast
Error
6,465
6,809
344
3
6,569
6,465
104
1
4
8,266
8,211
55
2
2
2
2
3
3
3
3
4
4
4
4
1
2
3
4
1
2
3
4
1
2
3
4
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
6,613
7,257
7,064
9,730
6,979
6,992
6,822
9,936
7,720
644
193
720
1,006
13
170
1,127
286
McGraw-Hill/Irwin
Mean Absolute Deviation
MAD =
13.8
424
Mean Square Error
MSE =
317,815
© The McGraw-Hill Companies, Inc., 2003
Measuring the Forecast Error
•
The mean absolute deviation (called MAD) measures the average forecasting
error.
MAD = (Sum of forecasting errors) / (Number of forecasts)
•
The mean square error (often abbreviated MSE) measures the average of the
square of the forecasting error.
MSE = (Sum of square of forecasting errors) / (Number of forecasts).
•
The MSE increases the weight of large errors relative to the weight of small
errors.
McGraw-Hill/Irwin
13.9
© The McGraw-Hill Companies, Inc., 2003
Considering Seasonal Effects
•
When there are seasonal patterns in the data, they can be addressed by
forecasting methods that use seasonal factors.
•
The seasonal factor for any period of a year (a quarter, a month, etc.) measures
how that period compares to the overall average for an entire year.
Seasonal factor = (Average for the period) / (Overall average)
•
It is easier to analyze data and detect new trends if the data are first adjusted to
remove the seasonal patterns.
Seasonally adjusted data = (Actual call volume) / (Seasonal factor)
McGraw-Hill/Irwin
13.10
© The McGraw-Hill Companies, Inc., 2003
Calculation of Seasonal Factors for CCW
Quarter
Three-Year
Average
Seasonal
Factor
1
7,019
7,019 / 7,529 = 0.93
2
6,784
6,784 / 7,529 = 0.90
3
7,434
7,434 / 7,529 = 0.99
4
8,880
8,880 / 7,529 = 1.18
Total = 30,117
Average = 30,117 / 4 = 7,529
McGraw-Hill/Irwin
13.11
© The McGraw-Hill Companies, Inc., 2003
Excel Template for Calculating Seasonal Factors
A
1
B
C
D
E
F
G
Estimating Seasonal Factors for CCW
2
True
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Year
1
1
Quarter
1
2
Value
6,809
6,465
1
1
2
3
4
1
6,569
8,266
7,257
2
2
2
3
3
3
3
2
3
4
1
2
3
4
7,064
7,784
8,724
6,992
6,822
7,949
9,650
McGraw-Hill/Irwin
Type of Seasonality
Quarterly
Quarter
1
2
3
4
13.12
Estimate for
Seasonal Factor
0.9323
0.9010
0.9873
1.1794
© The McGraw-Hill Companies, Inc., 2003
Seasonally Adjusted Time Series for CCW
A
1
B
C
D
E
F
Seasonally Adjusted Time Series for CCW
2
3
Actual
Seasonally Adjusted
Factor
Call Volume
Call Volume
4
Year
5
1
1
1
2
0.93
0.90
6,809
6,465
7,322
7,183
1
1
2
2
2
2
3
3
3
3
3
4
1
2
3
4
1
2
3
4
0.99
1.18
0.93
0.90
0.99
1.18
0.93
0.90
0.99
1.18
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
6,635
7,005
7,803
7,849
7,863
7,393
7,518
7,580
8,029
8,178
6
7
8
9
10
11
12
13
14
15
16
McGraw-Hill/Irwin
Quarter
Seasonal
13.13
© The McGraw-Hill Companies, Inc., 2003
Outline for Forecasting Call Volume
1. Select a time-series forecasting method.
2. Apply this method to the seasonally adjusted time series to obtain a forecast of
the seasonally adjusted call volume for the next time period.
3. Multiply this forecast by the corresponding seasonal factor to obtain a forecast
of the actual call volume (without seasonal adjustment).
McGraw-Hill/Irwin
13.14
© The McGraw-Hill Companies, Inc., 2003
The Last-Value Forecasting Method
•
The last-value forecasting method ignores all data points in a time series
except the last one.
Forecast = Last value
•
The last-value forecasting method is sometimes called the naïve method,
because statisticians consider it naïve to use just a sample size of one when
other data are available.
•
However, when conditions are changing rapidly, it may be that the last value is
the only relevant data point.
McGraw-Hill/Irwin
13.15
© The McGraw-Hill Companies, Inc., 2003
The Last-Value Method Applied to CCW’s Problem
A
1
B
C
D
E
F
G
H
I
J
K
Last-Value Forecasting Method with Seasonality for CCW
2
3
Seasonally
Seasonally
Adjusted
Value
Adjusted
Forecast
Actual
Forecast
7,322
7,183
6,635
7,005
7,803
7,849
6,589
7,112
7,830
6,515
7,023
7,770
124
543
436
742
41
14
7,863
7,393
7,518
7,580
8,029
8,178
9,278
6,876
6,766
7,504
9,475
7,606
554
116
56
445
175
5
Year
Quarter
True
Value
6
1
1
1
1
2
2
2
1
2
3
4
1
2
3
6,809
6,465
6,569
8,266
7,257
7,064
7,784
7,322
7,183
6,635
7,005
7,803
7,849
7,863
4
1
2
3
4
1
2
3
4
1
8,724
6,992
6,822
7,949
9,650
7,393
7,518
7,580
8,029
8,178
22
2
3
3
3
3
4
4
4
4
5
23
5
2
24
25
5
5
3
4
26
6
1
4
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
McGraw-Hill/Irwin
Forecasting
Error
Type of Seasonality
Quarterly
Quarter
1
2
3
4
Seasonal Factor
0.93
0.90
0.99
1.18
Mean Absolute Deviation
MAD =
295
Mean Square Error
MSE =
13.16
145,909
© The McGraw-Hill Companies, Inc., 2003
The Averaging Forecasting Method
•
The averaging forecasting method uses all the data points in the time series
and simply averages these points.
Forecast = Average of all data to date
•
The averaging forecasting method is a good one to use when conditions are
very stable.
•
However, the averaging method is very slow to respond to changing
conditions. It places the same weight on all the data, even though the older
values may be less representative of current conditions than the last value
observed.
McGraw-Hill/Irwin
13.17
© The McGraw-Hill Companies, Inc., 2003
The Averaging Method Applied to CCW’s Problem
A
1
B
C
D
E
F
G
H
I
J
K
Averaging Forecasting Method with Seasonality for CCW
2
3
Seasonally
Seasonally
Year
1
Quarter
1
True
Value
6,809
Adjusted
Value
7,322
Adjusted
Forecast
Actual
Forecast
1
1
1
2
2
2
2
3
4
1
2
3
6,465
6,569
8,266
7,257
7,064
7,784
7,183
6,635
7,005
7,803
7,849
7,863
7,322
7,252
7,047
7,036
7,190
7,300
6,589
7,180
8,315
6,544
6,471
7,227
124
611
49
713
593
557
4
1
2
3
4
1
2
3
4
1
8,724
6,992
6,822
7,949
9,650
7,393
7,518
7,580
8,029
8,178
7,380
7,382
7,397
7,415
7,471
7,530
8,708
6,865
6,657
7,341
8,816
7,003
16
127
165
608
834
22
2
3
3
3
3
4
4
4
4
5
23
5
2
24
25
5
5
3
4
26
6
1
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
McGraw-Hill/Irwin
Forecasting
Error
Type of Seasonality
Quarterly
Quarter
1
2
3
4
Seasonal Factor
0.93
0.90
0.99
1.18
Mean Absolute Deviation
MAD =
400
Mean Square Error
MSE =
13.18
242,876
© The McGraw-Hill Companies, Inc., 2003
The Moving-Average Forecasting Method
•
The moving-average forecasting method averages the data for only the most
recent time periods.
n = Number of recent periods to consider as relevant for forecasting
Forecast = Average of last n values
•
The moving-average forecasting method is a good one to use when conditions
don’t change much over the number of time periods included in the average.
•
However, the moving-average method is slow to respond to changing
conditions. It places the same weight on each of the last n values even though
the older values may be less representative of current conditions than the last
value observed.
McGraw-Hill/Irwin
13.19
© The McGraw-Hill Companies, Inc., 2003
The Moving-Average Method Applied to CCW
A
1
B
C
D
E
F
G
H
I
J
K
Moving Average Forecasting Method with Seasonality for CCW
2
3
Seasonally
Seasonally
Adjusted
Value
Adjusted
Forecast
5
Year
Quarter
True
Value
6
1
1
1
1
2
2
2
2
1
2
3
4
1
2
3
4
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
7,322
7,183
6,635
7,005
7,803
7,849
7,863
7,393
1
2
3
4
1
2
3
4
1
2
3
4
6,992
6,822
7,949
9,650
7,518
7,580
8,029
8,178
25
3
3
3
3
4
4
4
4
5
5
5
5
26
6
1
27
28
6
6
2
3
29
6
4
4
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
McGraw-Hill/Irwin
Actual
Forecast
Forecasting
Error
Number of previous
periods to consider
n=
4
Type of Seasonality
Quarterly
7,036
7,157
7,323
7,630
6,544
6,441
7,250
9,003
713
623
534
279
7,727
7,656
7,589
7,630
7,826
7,186
6,890
7,513
9,004
7,279
194
68
436
646
Quarter
1
2
Seasonal Factor
0.93
0.90
3
4
0.99
1.18
Mean Absolute Deviation
MAD =
437
Mean Square Error
MSE =
13.20
238,816
© The McGraw-Hill Companies, Inc., 2003
The Exponential Smoothing Forecasting Method
•
The exponential smoothing forecasting method places the greatest weight on
the last value in the time series and then progressively smaller weights on the
older values.
Forecast = a (Last value) + (1 – a) (Last forecast)
a is the smoothing constant between 0 and 1.
•
This method places a weight of a on the last value, a(1–a) on the next-to-last
value, a(1–a)2 on the next prior value, etc.
– For example, when a = 0.5, the method places a weight of 0.5 on the last value,
0.25 on the next-to-last, 0.125 on the next prior, etc.
– A larger value of a places more emphasis on the more recent values, a smaller
value places more emphasis on the older values.
•
The choice of the value of the smoothing constant a has a substantial effect on
the forecast.
– A small value (say, a = 0.1) is appropriate if conditions are relatively stable.
– A larger value (say, a = 0.5) is appropriate if significant changes occur frequently.
McGraw-Hill/Irwin
13.21
© The McGraw-Hill Companies, Inc., 2003
The Exponential Smoothing Method Applied to CCW
A
1
B
C
D
E
F
G
H
I
J
K
Exponential-Smoothing Forecasting Method with Seasonality for CCW
2
Seasonally
Seasonally
True
Value
Adjusted
Value
Adjusted
Forecast
Actual
Forecast
3
4
Year
6
1
1
1
1
2
2
2
2
3
1
2
3
4
1
2
3
4
1
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
7,322
7,183
6,635
7,005
7,803
7,849
7,863
7,393
7,518
7,500
7,411
7,297
6,966
6,986
7,394
7,622
7,742
7,568
6,975
6,670
7,224
8,220
6,497
6,655
7,545
9,136
7,038
166
205
655
46
760
409
239
412
46
2
3
4
1
2
3
4
1
2
3
4
1
2
6,822
7,949
9,650
7,580
8,029
8,178
7,543
7,561
7,795
7,987
6,789
7,486
9,199
7,428
33
463
451
27
3
3
3
4
4
4
4
5
5
5
5
6
6
28
6
3
29
6
7
4
1
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
30
Quarter
Forecasting
Error
5
Initial Estimate
Average =
0.5
7,500
Type of Seasonality
Quarterly
Quarter
1
Seasonal Factor
0.93
2
3
4
0.90
0.99
1.18
Mean Absolute Deviation
MAD =
324
Mean Square Error
MSE =
31
McGraw-Hill/Irwin
Smoothing Constant
a
13.22
157,836
© The McGraw-Hill Companies, Inc., 2003
A Time Series with Trend
(Population of a State over Time)
Population
(Millions)
5.4
5.2
5.0
Trend
line
4.8
1995
McGraw-Hill/Irwin
2000
13.23
2005
Year
© The McGraw-Hill Companies, Inc., 2003
Exponential Smoothing with Trend Forecasting Method
•
The exponential smoothing with trend forecasting method uses the recent
values in the time series to estimate any current upward or downward trend in
these values.
Trend = Average change from one time-series value to the next
•
The formula for forecasting the next value in the time series adds the estimated
trend.
Forecast = a (Last value) + (1 – a) (Last forecast) + Estimated trend
a is the smoothing constant between 0 and 1.
•
Exponential smoothing also is used to obtain and update the estimated trend.
Estimated trend = b (Latest trend) + (1 – b) (Last estimate of trend)
b is the trend smoothing constant.
•
The formula for forecasting n periods from now is
Forecast = a (Last value) + (1 – a) (Last forecast) + n (Estimated trend)
McGraw-Hill/Irwin
13.24
© The McGraw-Hill Companies, Inc., 2003
Exponential Smoothing with Trend Applied to CCW
A
1
B
C
D
E
F
G
H
I
J
K
L
M
Exponential-Smoothing with Trend Forecasting Method with Seasonality for CCW
2
Seasonally
3
4
Adjusted
Value
5
Year
6
1
1
1
1
2
2
2
2
3
3
3
1
2
3
4
1
2
3
4
1
2
3
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
7,322
7,183
6,635
7,005
7,803
7,849
7,863
7,393
7,518
7,580
8,029
4
1
2
3
4
1
2
3
4
1
2
3
4
9,650
8,178
29
3
4
4
4
4
5
5
5
5
6
6
6
6
30
7
1
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Quarter
True
Value
Seasonally
Latest
Trend
Estimated
Trend
Adjusted
Forecast
Actual
Forecast
Forecasting
Error
-54
-90
-243
-102
167
187
179
13
32
34
0
-16
-38
-100
-100
-20
42
83
62
53
47
7,500
7,430
7,318
7,013
6,910
7,158
7,407
7,627
7,619
7,642
7,670
6,975
6,687
7,245
8,276
6,427
6,442
7,333
9,000
7,085
6,877
7,594
166
222
676
10
830
622
451
276
93
55
355
155
176
80
108
7,858
8,062
9,272
7,498
378
Smoothing Constant
a
0.3
b
0.3
Initial Estimate
Average =
Trend =
7,500
0
Type of Seasonality
Quarterly
Quarter
1
Seasonal Factor
0.93
2
3
4
0.90
0.99
1.18
Mean Absolute Deviation
MAD =
345
31
Mean Square Error
32
MSE =
33
McGraw-Hill/Irwin
13.25
180,796
© The McGraw-Hill Companies, Inc., 2003
MAD and MSE for the Various Forecasting Method
Forecasting Method
MAD
MSE
CCW’s 25 percent rule
424
317,815
Last-value method
295
145,909
Averaging method
400
242,876
Moving-average method
437
238,816
Exponential smoothing
324
157,836
Exponential smoothing with trend
345
180,796
McGraw-Hill/Irwin
13.26
© The McGraw-Hill Companies, Inc., 2003
Using CB Predictor: Enter the Data on a Spreadsheet
A
1
B
C
D
Crystal Ball Predictor for CCW
2
3
4
5
6
7
8
9
10
11
12
13
14
15
McGraw-Hill/Irwin
Year
1
1
1
1
2
2
2
2
3
3
3
3
Quarter
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
13.27
Call Volume
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
© The McGraw-Hill Companies, Inc., 2003
Using CB Predictor: Input Data Pane
McGraw-Hill/Irwin
13.28
© The McGraw-Hill Companies, Inc., 2003
Using CB Predictor: Data Attributes Pane
McGraw-Hill/Irwin
13.29
© The McGraw-Hill Companies, Inc., 2003
Using CB Predictor: Method Gallery Pane
McGraw-Hill/Irwin
13.30
© The McGraw-Hill Companies, Inc., 2003
Using CB Predictor: Results Pane
McGraw-Hill/Irwin
13.31
© The McGraw-Hill Companies, Inc., 2003
CB Predictor Preview Graph
McGraw-Hill/Irwin
13.32
© The McGraw-Hill Companies, Inc., 2003
CB Predictor Results
A
1
B
C
D
Crystal Ball Predictor for CCW
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
McGraw-Hill/Irwin
Year
1
1
1
1
2
2
2
2
3
3
3
3
Quarter
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Call Volume
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
4
4
4
4
Q1
Q2
Q3
Q4
7,791
7,515
8,203
9,799
13.33
© The McGraw-Hill Companies, Inc., 2003
Relationship Between CB Predictor Techniques and the
Forecasting Techniques in the Textbook
CB Predictor Technique
Related Technique in Section 13.3
Single moving average
Moving average
Double moving average
Not covered
Single exponential smoothing
Exponential smoothing
Double exponential smoothing
Exponential smoothing with trend
Seasonal additive
Not covered
Holt-Winters additive
Not covered
Seasonal multiplicative
Exponential smoothing with seasonality
Holt-Winters multiplicative
Exponential smoothing with seasonality and trend
McGraw-Hill/Irwin
13.34
© The McGraw-Hill Companies, Inc., 2003
Typical Probability Distribution of Call Volume
(Assumes Mean = 7,500)
7,250
7,500
7,750
Mean
McGraw-Hill/Irwin
13.35
© The McGraw-Hill Companies, Inc., 2003
Typically Probability Distributions of Call Volume
in the Four Quarters (Assumes Annual Mean = 7,500)
Quarter 2
6,500
Quarter 1
7,000
McGraw-Hill/Irwin
Quarter 3
7,500
Quarter 4
8,000
13.36
8,500
9,000
© The McGraw-Hill Companies, Inc., 2003
Comparison of Typical Probability Distributions
of Seasonally-Adjusted Call Volumes in Years 1 and 2
Year 1
6,500
McGraw-Hill/Irwin
7,000
7,500
13.37
Year 2
8,000
© The McGraw-Hill Companies, Inc., 2003
Comparison of the Forecasting Methods
•
Last value method: Suitable for a time series that is so unstable that even the
next-to-last value is not considered relevant for forecasting the next value.
•
Averaging method: Suitable for a very stable time series where even its first
few values are considered relevant for forecasting the next value.
•
Moving-average method: Suitable for a moderately stable time series where
the last few values are considered relevant for forecasting the next value.
•
Exponential smoothing method: Suitable for a time series in the range from
somewhat unstable to rather stable, where the value of the smoothing constant
needs to be adjusted to fit the anticipated degree of stability.
•
Exponential smoothing with trend: Suitable for a time series where the mean
of the distribution tends to follow a trend either up or down, provided that
changes in the trend occur only occasionally and gradually.
McGraw-Hill/Irwin
13.38
© The McGraw-Hill Companies, Inc., 2003
The Consultant’s Recommendations
1. Forecasting should be done monthly rather than quarterly.
2. Hiring and training of new agents also should be done monthly.
3. Recently retired agents should be offered the opportunity to work part time on an on-call
basis.
4. Since sales drive call volume, the forecasting process should begin by forecasting sales.
5. For forecasting purposes, total sales should be broken down into the major components:
a) The relatively stable market base of numerous small-niche products.
b) Each of the few (perhaps three or four) major new products.
6. Exponential smoothing with a relatively small smoothing constant is suggested for
forecasting sales of the marketing base of numerous small-niche products.
7. Exponential smoothing with trend, with relatively large smoothing constants, is
suggested for forecasting sales of each major new product.
8. Seasonally adjusted time series should be used for each application of the methods.
9. The forecasts in recommendation 5 should be summed to obtain a forecast of total sales.
10. Causal forecasting with linear regression should be used to obtain a forecast of call
volume from this forecast of total sales.
McGraw-Hill/Irwin
13.39
© The McGraw-Hill Companies, Inc., 2003
Causal Forecasting
Causal forecasting obtains a forecast of the quantity of interest (the dependent
variable) by relating it directly to one or more other quantities (the independent
variables) that drive the quantity of interest.
Type of Forecasting
Possible Dependent
Variable
Possible Independent
Variable
Sales
Sales of a product
Amount of advertising
Spare parts
Demand for spare parts
Usage of equipment
Economic trends
Gross domestic product
Various economic factors
CCW call volume
Call volume
Total sales
Any quantity
This same quantity
Time
McGraw-Hill/Irwin
13.40
© The McGraw-Hill Companies, Inc., 2003
Sales and Call Volume Data for CCW
A
1
B
C
D
E
CCW's Average Daily Sales and Call Volume
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
McGraw-Hill/Irwin
Year
1
1
1
1
2
2
2
2
3
3
3
3
Quarter
1
2
3
4
1
2
3
4
1
2
3
4
Sales
($thousands)
4,894
4,703
4,748
5,844
5,192
5,086
5,511
6,107
5,052
4,985
5,576
6,647
13.41
Call
Volume
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
© The McGraw-Hill Companies, Inc., 2003
Adding a Trendline to the Graph
A
1
B
C
D
E
CCW's Average Daily Sales and Call Volume
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
McGraw-Hill/Irwin
Year
1
1
1
1
2
2
2
2
3
3
3
3
Quarter
1
2
3
4
1
2
3
4
1
2
3
4
Sales
($thousands)
4,894
4,703
4,748
5,844
5,192
5,086
5,511
6,107
5,052
4,985
5,576
6,647
13.42
Call
Volume
6,809
6,465
6,569
8,266
7,257
7,064
7,784
8,724
6,992
6,822
7,949
9,650
© The McGraw-Hill Companies, Inc., 2003
Linear Regression
•
When doing causal forecasting with a single independent variable, linear
regression involves approximating the relationship between the dependent
variable (call volume for CCW) and the independent variable (sales for CCW)
by a straight line.
•
This linear regression line is drawn on a graph with the independent variable
on the horizontal axis and the dependent variable on the vertical axis. The line
is constructed after plotting a number of points showing each observed value
of the independent variable and the corresponding value for the dependent
variable.
•
The linear regression line has the form
y = a + bx
where
y = Estimated value of the dependent variable
a = Intercept of the linear regression line with the y-axis
b = Slope of the linear regression line
x = Value of the independent variable
McGraw-Hill/Irwin
13.43
© The McGraw-Hill Companies, Inc., 2003
Excel Template for Linear Regression
A
1
B
C
D
E
F
G
H
I
J
Linear Regression of Call Volume vs. Sales Volume for CCW
2
3
Time
Independent
Dependent
4
Period
Variable
Variable
5
1
2
4,894
4,703
6,809
6,465
11
3
4
5
6
7
4,748
5,844
5,192
5,086
5,511
12
8
13
9
10
11
12
6
7
8
9
10
14
15
16
Estimation
Square
Linear Regression Line
Estimate
Error
of Error
y = a + bx
6,765
6,453
43.85
11.64
1,923
136
6,569
8,266
7,257
7,064
7,784
6,527
8,316
7,252
7,079
7,772
42.18
49.93
5.40
14.57
11.66
1,780
2,493
29
212
136
6,107
8,724
8,745
21.26
452
5,052
4,985
5,576
6,647
6,992
6,822
7,949
9,650
7,023
6,914
7,878
9,627
31.07
91.70
70.55
23.24
965
8,408
4,977
540
McGraw-Hill/Irwin
13.44
a=
b=
-1,223.86
1.63
Estimator
If x =
5,000
then y=
6,938.18
© The McGraw-Hill Companies, Inc., 2003
Judgmental Forecasting Methods
•
Manager’s Opinion: A single manager uses his or her best judgment.
•
Jury of Executive Opinion: A small group of high-level managers pool their
best judgment to collectively make the forecast.
•
Salesforce Composite: A bottom-up approach where each salesperson
provides an estimate of what sales will be in his or her region. These estimates
are then aggregated into a corporate sales forecast.
•
Consumer Market Survey: A grass-roots approach that surveys customers
and potential customers regarding their future purchasing plans and how they
would respond to various new features in products.
•
Delphi Method: A panel of experts in different locations who independently
fill out a series of questionnaires. The results from each questionnaire are
provided with the next one, so each expert can evaluate the group information
in adjusting his or her responses next time.
McGraw-Hill/Irwin
13.45
© The McGraw-Hill Companies, Inc., 2003
Forecasting in Practice
•
A survey of forecasting practices at 500 U.S. corporations indicates that
judgmental forecasting methods are somewhat more widely used than
statistical methods.
•
Among judgmental methods, the most popular is a jury of executive opinion.
When forecasting sales, manager’s opinion is a close second.
•
Statistical forecasting methods also are fairly widely used, especially in
companies with high sales.
•
Among statistical methods, the moving-average method and linear regression
are the most widely used. Both exponential smoothing and the last-value
method also receive considerable use.
McGraw-Hill/Irwin
13.46
© The McGraw-Hill Companies, Inc., 2003
The Forecasting Method Used in Actual Applications
Organization
Quantity Being Forecasted
Forecasting Method
Merit Brass Co.
Sales of finished goods
Exponential smoothing
Hidroelétrica Español
Energy demand
ARIMA (Box-Jenkins), etc.
American Airlines
Demand for different fare
classes
Exponential smoothing
American Airlines
Need for spare parts to repair
airplanes
Causal forecasting with
linear regression
Albuquerque
Microelectronics
Production yield in wafer
fabrication
Exponential smoothing with
trend
U.S. Department of Labor
Unemployment insurance
payments
Causal forecasting with
linear regression
United Airlines
Demand at reservations
offices and airports
ARIMA (Box-Jenkins)
Taco Bell
Number of customer arrivals
Moving average
L.L. Bean
Staffing needs at call center
ARIMA (Box-Jenkins)
All references available for download at www.mhhe.com/hillier2e/articles
McGraw-Hill/Irwin
13.47
© The McGraw-Hill Companies, Inc., 2003