3-1
Forecasting
Chapter 3
Forecasting
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-2
Forecasting
FORECAST:
• A statement about the future
• Used to help managers
– Plan the system
– Plan the use of the system
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-3
Forecasting
Forecast Uses
• Plan the system
– Generally involves long-range plans related to:
• Types of products and services to offer
• Facility and equipment levels
• Facility location
• Plan the use of the system
– Generally involves short- and medium-range plans related to:
• Inventory management
• Workforce levels
• Purchasing
• Budgeting
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-4
Forecasting
Common Features
• Assumes causal system
past ==> future
• Forecasts rarely perfect because of
randomness
I see that you will
• Forecasts more accurate for
get an A this quarter.
groups vs. individuals
• Forecast accuracy decreases
as time horizon increases
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-5
Forecasting
Elements of a Good Forecast
Timely
Reliable
Accurate
Written
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-6
Forecasting
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Make the forecast
Step 4 Gather and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-7
Forecasting
Types of Forecasts
• Judgmental - uses subjective inputs (qualitative)
• Time series - uses historical data assuming the
future will be like the past (quantitative)
• Associative models - uses explanatory variables
to predict the future
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-8
Forecasting
Judgmental Forecasts
(Qualitative)
• Consumer surveys
• Delphi method
• Executive opinions
– Opinions of managers and staff
• Sales force.
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-9
Forecasting
Time Series Forecasts
(Quantitative)
• Trend - long-term movement in data
• Seasonality - short-term regular variations in
data
• Irregular variations - caused by unusual
circumstances
• Random variations - caused by chance
• CYCLE- wave like variations lasting more
than one year
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-10
Forecasting
Forecast Variations
Figure 3-1
Irregular
variation
Trend
cycle
Cycles
90
89
88
Seasonal variations
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-11
Forecasting
The Forecast of Forecasts
•
•
•
•
•
Naïve
Simple Moving Average
Weighted Moving Average
Exponential Smoothing
ES with Trend and Seasonality
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-12
Forecasting
Naïve Forecast
•
•
•
•
•
Simple to use
Virtually no cost
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-13
Forecasting
NAÏVE METHOD
• No smoothing of data
Period
Demand
Forecast
change
McGraw-Hill/Irwin
1
74
2
86
12
3
88
98
2
4
5
6
7
8 Average
90
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-14
Forecasting
Techniques for Averaging
• Moving average
• Weighted moving average
• Exponential smoothing
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-15
Forecasting
Simple Moving Average
• Smoothes out randomness by averaging positive and
negative random elements over several periods
• n - number of periods (this example uses 4)
Period
Demand
Forecast
McGraw-Hill/Irwin
1
74
2
90
3
100
4
60
5
80
81
6
90
82.5
7
82.5
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-16
Forecasting
Points to Know on Moving Averages
• Pro: Easy to compute and understand
• Con: All data points were created equal….
…. Weighted
McGraw-Hill/Irwin
Moving Average
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-17
Forecasting
Weighted Moving Average
• Similar to a moving average methods except that it
assigns more weight to the most recent values in a time
series.
• n -- number of periods
ai – weight applied to period t-i+1
Ft 1 
Period
Demand
Forecast
McGraw-Hill/Irwin
t
 a t  i 1 A i
1
i  t  n 1
1
46
Alpha
2
48
3
47
4
23
5
40
32.70
2
0.6
0.3
6
7
3
0.1
8 Average
35.60
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-18
Forecasting
Exponential Smoothing
• Simpler equation, equivalent to WMA
a – exponential smoothing parameter (0< a<1)
•
Ft  Ft 1  a ( At 1  Ft 1 )
a
Period
Demand
Forecast
McGraw-Hill/Irwin
1
74
72
2
90
72.2
3
100
73.98
4
60
5
6
0.1
7
8 Average
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-19
Forecasting
Exponential Smoothing (α=0.30)
Ft  Ft 1  a ( At 1  Ft 1 )
PERIOD
MONTH
1
2
3
4
5
6
7
8
9
10
11
12
McGraw-Hill/Irwin
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
DEMAND
37
40
41
37
45
50
43
47
56
52
55
54
F2
=
37 + (0.30)(37-37)
= 37
F3 =37+ (0.30)(40-37)
= 37.9
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-20
Forecasting
Exponential Smoothing (cont.)
PERIOD
MONTH
DEMAND
1
2
3
4
5
6
7
8
9
10
11
12
13
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
37
40
41
37
45
50
43
47
56
52
55
54
–
McGraw-Hill/Irwin
FORECAST, Ft + 1
(a = 0.3)
(a = 0.5)
–
37.00
37.90
38.83
38.28
40.29
43.20
43.14
44.30
47.81
49.06
50.84
51.79
–
37.00
38.50
39.75
38.37
41.68
45.84
44.42
45.71
50.85
51.42
53.21
53.61
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-21
Forecasting
Adjusted Exponential Smoothing
AFt +1 = Ft +1 + Tt +1
where
T = an exponentially smoothed trend factor
Tt +1 = (Ft +1 - Ft) + (1 - ) Tt
where
Tt = the last period trend factor
= a smoothing constant for trend
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-22
Forecasting
Adjusted Exponential Smoothing
(β=0.30)
PERIOD
MONTH
DEMAND
1
2
3
4
5
6
7
8
9
10
11
12
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
37
40
41
37
45
50
43
47
56
52
55
54
McGraw-Hill/Irwin
T3
= (F3 - F2) + (1 - ) T2
= (0.30)(38.5 - 37.0) + (0.70)(0)
= 0.45
AF3 = F3 + T3 = 38.5 + 0.45
= 38.95
T13 = (F13 - F12) + (1 - ) T12
= (0.30)(53.61 - 53.21) + (0.70)(1.77)
= 1.36
AF13 = F13 + T13 = 53.61 + 1.36 = 54.96
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-23
Forecasting
Adjusted Exponential Smoothing:
Example
PERIOD
MONTH
DEMAND
FORECAST
Ft +1
1
2
3
4
5
6
7
8
9
10
11
12
13
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
37
40
41
37
45
50
43
47
56
52
55
54
–
37.00
37.00
38.50
39.75
38.37
38.37
45.84
44.42
45.71
50.85
51.42
53.21
53.61
McGraw-Hill/Irwin
TREND
Tt +1
ADJUSTED
FORECAST AFt +1
–
0.00
0.45
0.69
0.07
0.07
1.97
0.95
1.05
2.28
1.76
1.77
1.36
–
37.00
38.95
40.44
38.44
38.44
47.82
45.37
46.76
58.13
53.19
54.98
54.96
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-24
Forecasting
Linear Trend Equation
Y
Yt = a + bt
a
0 1 2 3 4 5
t
• b is the line slope.
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-25
Forecasting
Calculating a and b
n  (ty) -  t  y
b =
n t 2 - (  t) 2
 y - b t
a =
n
Yes… Linear Regression!!
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-26
Forecasting
Linear Trend Equation Example
t
y
Week
t2
Sales
ty
1
1
150
150
2
4
157
314
3
9
162
486
4
16
166
664
5
25
177
885
 t = 15
t2 = 55
 y = 812
 ty = 2499
(t)2 = 225
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-27
Forecasting
Linear Trend Calculation
b =
5 (2499) - 15(812)
5(55) - 225
=
12495-12180
275 -225
= 6.3
812 - 6.3(15)
a =
= 143.5
5
y = 143.5 + 6.3t
McGraw-Hill/Irwin
Look on page 85
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-28
Forecasting
Disadvantage of simple linear regression
1-apply only to linear relationship with an
independent variable.
2-one needs a considerable amount of data to
establish the relationship ( at least 20).
3-all observations are weighted equally
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-29
Forecasting
Forecast Accuracy
• Forecast error
– difference between forecast and actual demand
– MAD
• mean absolute deviation
– MAPD
• mean absolute percent deviation
– Cumulative error
– Average error or bias
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-30
Forecasting
Mean Absolute Deviation (MAD)
 At - Ft 
MAD =
n
where
t = period number
At = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-31
Forecasting
MAD Example
PERIOD
1
2
3
4
5
6
7
8
9
10
11
12
DEMAND, At
37
40
41
37
MAD
45 =
50
43
=
47
56
52 =
55
54
557
McGraw-Hill/Irwin
Ft (a =0.3)
37.00
37.00
37.90
 At38.83
- Ft 
n38.28
40.29
53.39
43.20
1143.14
44.30
4.85 47.81
49.06
50.84
(At - Ft)
|At - Ft|
–
3.00
3.10
-1.83
6.72
9.69
-0.20
3.86
11.70
4.19
5.94
3.15
–
3.00
3.10
1.83
6.72
9.69
0.20
3.86
11.70
4.19
5.94
3.15
49.31
53.39
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-32
Forecasting
Other Accuracy Measures
Mean absolute percent deviation (MAPD)
|At - Ft|
MAPD =
At
Cumulative error
E = et
Average error
et
(E )= n
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-33
Forecasting
Comparison of Forecasts
FORECAST
Exponential smoothing (a= 0.30)
Exponential smoothing (a= 0.50)
Adjusted exponential smoothing
(a= 0.50, = 0.30)
McGraw-Hill/Irwin
MAD
MAPD
E
(E)
4.85
4.04
3.81
9.6%
8.5%
7.5%
49.31
33.21
21.14
4.48
3.02
1.92
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-34
Forecasting
Forecast Control
• Tracking signal
– monitors the forecast to see if it is biased high
or low
(At - Ft)
E
Tracking signal =
=
MAD
MAD
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-35
Forecasting
Tracking Signal Values
PERIOD
DEMAND
At
1
2
3
4
5
6
7
8
9
10
11
12
37
40
41
37
45
50
43
47
56
52
55
54
McGraw-Hill/Irwin
E =
(At - Ft)
MAD
37.00
–
–
37.00
3.00
3.00
37.90
3.10
6.10
38.83
-1.83
4.27
38.28
6.72 for period
10.99 3
Tracking
signal
40.29
9.69
20.68
43.20
-0.20
6.10 20.48
43.14TS = 3.86
= 24.34
2.00
3
3.05 36.04
44.30
11.70
47.81
4.19
40.23
49.06
5.94
46.17
50.84
3.15
49.32
–
3.00
3.05
2.64
3.66
4.87
4.09
4.06
5.01
4.92
5.02
4.85
FORECAST,
Ft
ERROR
At - Ft
TRACKING
SIGNAL
–
1.00
2.00
1.62
3.00
4.25
5.01
6.00
7.19
8.18
9.20
10.17
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-36
Forecasting
Sources of forecast errors
• The model may be inadequate.
• Irregular variation may be occur.
• The forecasting technique may be used
incorrectly or the results misinterpreted.
• There are always random variation in the
data.
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
3-37
Forecasting
End Notes
• The two most important factors in choosing
a forecasting technique:
– Cost
– Accuracy
• Keep it SIMPLE!
• =FORECAST(70,{23,34,12},{67,76,56})
(if you can…let the computer do it)
McGraw-Hill/Irwin
Operations Management, Seventh Edition, by William J. Stevenson
Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.