Chapter 12
Forecasting
Operations Management - 6th Edition
Roberta Russell & Bernard W. Taylor, III
Copyright 2009 John Wiley & Sons, Inc.
Beni Asllani
University of Tennessee at Chattanooga
Lecture Outline
 Strategic Role of Forecasting in Supply
Chain Management
 Components of Forecasting Demand
 Time Series Methods
 Forecast Accuracy
 Time Series Forecasting Using Excel
 Regression Methods
Copyright 2009 John Wiley & Sons, Inc.
12-2
Forecasting
 Predicting the future
 Qualitative forecast methods

subjective
 Quantitative forecast
methods

based on mathematical
formulas
Copyright 2009 John Wiley & Sons, Inc.
12-3
Forecasting and Supply Chain
Management
 Accurate forecasting determines how much
inventory a company must keep at various points
along its supply chain
 Continuous replenishment




supplier and customer share continuously updated data
typically managed by the supplier
reduces inventory for the company
speeds customer delivery
 Variations of continuous replenishment




quick response
JIT (just-in-time)
VMI (vendor-managed inventory)
stockless inventory
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12-4
Forecasting
 Quality Management

Accurately forecasting customer demand is
a key to providing good quality service
 Strategic Planning

Successful strategic planning requires
accurate forecasts of future products and
markets
Copyright 2009 John Wiley & Sons, Inc.
12-5
Forecasting when the price of
gasoline will return to $3 a gallon
: a DELPHI simulation

 Forecast when the price of gasoline will
return to $3 a gallon

Write your answer on a piece of paper
Copyright 2006 John Wiley & Sons, Inc.
11-6
Proven reserves of Oil-Worldwide
AMOUNT
(billions of barrels)
1400
1200
1000
800
AMOUNT
(billions of barrels)
600
400
200
0
1975
1980
1985
1990
1995
2000
2005
2010
Year
Copyright 2006 John Wiley & Sons, Inc.
11-7
Factors Affecting Oil Price
Factors Affecting the Price of Oil
Oil price
Proven reserves
Environmental
limitations
Terrorist Fears
Unproven reserves
Politics
Copyright 2006 John Wiley & Sons, Inc.
 Today, there
are 1.3 trillion
barrels of
reserves
worldwide—
64 years at
present rates
of usage
11-8
The fallacy of forecasts
 In 1914, U.S. Bureau of Mines predicted U.S.
oil reserves would last only ten more years
 In 1939, the U.S. Dept. of the Interior predicted
that oil would last only 13 more years, and
then in 1951, when the oil shortage never
occurred, it predicted oil would run out in just
13 more years
Copyright 2006 John Wiley & Sons, Inc.
11-9
More fallacious forecasts
 In a book published in 1972 entitled
Limits to Growth, Dennis and Donella
Meadows claimed that only 550 billion
barrels of oil remained in the earth and
that those barrels would all be consumed
by now
Copyright 2006 John Wiley & Sons, Inc.
11-10
Commentary
 Are oil, gas and coal fossil fuels or are
they of abiotic origin?
 This is not just a scientific question…
Copyright 2006 John Wiley & Sons, Inc.
11-13
Evidence for abiotic origin
 Oil and gas are being found deep within
the Earth’s crust, especially the Russians
have been successful at this—how did
decaying biomass ever get five miles
down, underneath two miles of water?
 Oil in sedimentary rock contains traces of
material from rock below—especially the
Devonian and Cambrian rock
Copyright 2006 John Wiley & Sons, Inc.
11-14
More evidence…
 Why would so much decayed biomass
exist below a desert (as in Saudi Arabia
and the rest of the Middle East)
 Why is the largest moon circling Saturn—
Titan—have an atmosphere of methane
gas—the gas most prevalent in natural
gas??
Copyright 2009 John Wiley & Sons, Inc.
12-15
Types of Forecasting Methods
 Depend on



time frame
demand behavior
causes of behavior
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12-16
Time Frame
 Indicates how far into the future is
forecast (the time horizon)

Short- to mid-range forecast
typically encompasses the immediate future
 daily up to two years


Long-range forecast

usually encompasses a period of time longer
than two years
Copyright 2009 John Wiley & Sons, Inc.
12-17
Demand Behavior
 Trend

a gradual, long-term up or down movement of
demand
 Random variations

movements in demand that do not follow a pattern
 Cycle

an up-and-down repetitive movement in demand
 Seasonal pattern

an up-and-down repetitive movement in demand
occurring periodically
Copyright 2009 John Wiley & Sons, Inc.
12-18
Demand
Demand
Forms of Forecast Movement
Random
movement
Time
(b) Cycle
Demand
Demand
Time
(a) Trend
Time
(c) Seasonal pattern
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Time
(d) Trend with seasonal pattern
12-19
Forecasting Methods
 Time series

statistical techniques that use historical demand data
to predict future demand
 Regression methods

attempt to develop a mathematical relationship
between demand and factors that cause its behavior
 Qualitative

use management judgment, expertise, and opinion to
predict future demand
Copyright 2009 John Wiley & Sons, Inc.
12-20
Qualitative Methods
 Management, marketing, purchasing,
and engineering are sources for internal
qualitative forecasts
 Delphi method

involves soliciting forecasts about
technological advances from experts
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12-21
Forecasting Process
1. Identify the
purpose of forecast
2. Collect historical
data
3. Plot data and identify
patterns
6. Check forecast
accuracy with one or
more measures
5. Develop/compute
forecast for period of
historical data
4. Select a forecast
model that seems
appropriate for data
7.
Is accuracy of
forecast
acceptable?
No
8b. Select new
forecast model or
adjust parameters of
existing model
Yes
8a. Forecast over
planning horizon
9. Adjust forecast based
on additional qualitative
information and insight
Copyright 2009 John Wiley & Sons, Inc.
10. Monitor results
and measure forecast
accuracy
12-22
Time Series
 Assume that what has occurred in the past will
continue to occur in the future
 Relate the forecast to only one factor - time
 Include



moving average
exponential smoothing
linear trend line
Copyright 2009 John Wiley & Sons, Inc.
12-23
Moving Average
 Naive forecast

demand in current period is used as next period’s
forecast
 Simple moving average


uses average demand for a fixed sequence of
periods
stable demand with no pronounced behavioral
patterns
 Weighted moving average

weights are assigned to most recent data
Copyright 2009 John Wiley & Sons, Inc.
12-24
Moving Average:
Naïve Approach
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
120
90
100
75
110
50
75
130
110
90
-
Copyright 2009 John Wiley & Sons, Inc.
FORECAST
120
90
100
75
110
50
75
130
110
90
12-25
Simple Moving Average
n
Di

i=1
MAn =
n
where
n = number of periods in
the moving average
Di = demand in period i
Copyright 2009 John Wiley & Sons, Inc.
12-26
3-month Simple Moving Average
3
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
Di

i=1
MOVING
AVERAGE
120
90
100
75
110
50
75
130
110
90
-
Copyright 2009 John Wiley & Sons, Inc.
–
–
–
103.3
88.3
95.0
78.3
78.3
85.0
105.0
110.0
MA3 =
=
3
90 + 110 + 130
3
= 110 orders
for Nov
12-27
5-month Simple Moving Average
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
MOVING
AVERAGE
120
90
100
75
110
50
75
130
110
90
-
Copyright 2009 John Wiley & Sons, Inc.
–
–
–
–
–
99.0
85.0
82.0
88.0
95.0
91.0
5
Di

i=1
MA5 =
=
5
90 + 110 + 130+75+50
5
= 91 orders
for Nov
12-28
Smoothing Effects
150 –
5-month
125 –
Orders
100 –
75 –
50 –
3-month
Actual
25 –
0–
|
Jan
|
Feb
|
Mar
|
|
Apr May
|
|
June July
|
|
Aug Sept
|
Oct
|
Nov
Month
Copyright 2009 John Wiley & Sons, Inc.
12-29
Weighted Moving Average
n
 Adjusts
moving
average
method to
more closely
reflect data
fluctuations
WMAn =
 Wi Di
i=1
where
Copyright 2009 John Wiley & Sons, Inc.
Wi = the weight for period i,
between 0 and 100
percent
 Wi = 1.00
12-30
Weighted Moving Average Example
MONTH
WEIGHT
DATA
17%
33%
50%
130
110
90
August
September
October
3
November Forecast
WMA3 =
Wi Di

i=1
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= 103.4 orders
Copyright 2009 John Wiley & Sons, Inc.
12-31
Exponential Smoothing




Averaging method
Weights most recent data more strongly
Reacts more to recent changes
Widely used, accurate method
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12-32
Exponential Smoothing (cont.)
Ft +1 = Dt + (1 - )Ft
where:
Ft +1 = forecast for next period
Dt = actual demand for present period
Ft = previously determined forecast for
present period
=
weighting factor, smoothing constant
Copyright 2009 John Wiley & Sons, Inc.
12-33
Effect of Smoothing Constant
0.0  1.0
If = 0.20, then Ft +1 = 0.20 Dt + 0.80 Ft
If = 0, then Ft +1 = 0 Dt + 1 Ft = Ft
Forecast does not reflect recent data
If = 1, then Ft +1 = 1 Dt + 0 Ft = Dt
Forecast based only on most recent data
Copyright 2009 John Wiley & Sons, Inc.
12-34
Exponential Smoothing (α=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
Copyright 2009 John Wiley & Sons, Inc.
F2 = D1 + (1 - )F1
= (0.30)(37) + (0.70)(37)
= 37
F3 = D2 + (1 - )F2
= (0.30)(40) + (0.70)(37)
= 37.9
F13 = D12 + (1 - )F12
= (0.30)(54) + (0.70)(50.84)
= 51.79
12-35
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
–
Copyright 2009 John Wiley & Sons, Inc.
FORECAST, Ft + 1
( = 0.3)
( = 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
12-36
Exponential Smoothing (cont.)
70 –
60 –
 = 0.50
Actual
Orders
50 –
40 –
 = 0.30
30 –
20 –
10 –
0–
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
Month
Copyright 2009 John Wiley & Sons, Inc.
12-37
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
Copyright 2009 John Wiley & Sons, Inc.
12-38
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
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 = 54.97
Copyright 2009 John Wiley & Sons, Inc.
12-39
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
Copyright 2009 John Wiley & Sons, Inc.
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
12-40
Adjusted Exponential Smoothing
Forecasts
70 –
Adjusted forecast ( = 0.30)
60 –
Actual
Demand
50 –
40 –
Forecast ( = 0.50)
30 –
20 –
10 –
0–
|
1
|
2
|
3
|
4
|
5
Copyright 2009 John Wiley & Sons, Inc.
|
|
6
7
Period
|
8
|
9
|
10
|
11
|
12
|
13
12-41
Linear Trend Line
y = a + bx
where
a = intercept
b = slope of the line
x = time period
y = forecast for
demand for period x
xy - nxy
b =
x2 - nx2
a = y-bx
where
n = number of periods
x
x =
= mean of the x values
n
y
y = n = mean of the y values
Copyright 2009 John Wiley & Sons, Inc.
12-42
Least Squares Example
x(PERIOD)
y(DEMAND)
xy
x2
1
2
3
4
5
6
7
8
9
10
11
12
73
40
41
37
45
50
43
47
56
52
55
54
37
80
123
148
225
300
301
376
504
520
605
648
1
4
9
16
25
36
49
64
81
100
121
144
78
557
3867
650
Copyright 2009 John Wiley & Sons, Inc.
12-43
Least Squares Example
(cont.)
78
x =
= 6.5
12
557
y =
= 46.42
12
xy - nxy
b =
=
2
2
x - nx
3867 - (12)(6.5)(46.42)
=1.72
2
650 - 12(6.5)
a = y - bx
= 46.42 - (1.72)(6.5) = 35.2
Copyright 2009 John Wiley & Sons, Inc.
12-44
Linear trend line y = 35.2 + 1.72x
Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units
70 –
60 –
Actual
Demand
50 –
40 –
Linear trend line
30 –
20 –
10 –
|
1
|
2
|
3
|
4
|
5
0–
Copyright 2009 John Wiley & Sons, Inc.
|
|
6
7
Period
|
8
|
9
|
10
|
11
|
12
|
13
12-45
Seasonal Adjustments
 Repetitive increase/ decrease in demand
 Use seasonal factor to adjust forecast
Seasonal factor = Si =
Copyright 2009 John Wiley & Sons, Inc.
Di
D
12-46
Seasonal Adjustment (cont.)
YEAR
2002
2003
2004
Total
DEMAND (1000’S PER QUARTER)
1
2
3
4
Total
12.6
14.1
15.3
42.0
8.6
10.3
10.6
29.5
6.3
7.5
8.1
21.9
17.5
18.2
19.6
55.3
45.0
50.1
53.6
148.7
D1
42.0
S1 =
=
= 0.28
D 148.7
D3
21.9
S3 =
=
= 0.15
D 148.7
D2
29.5
S2 =
=
= 0.20
D 148.7
D4
55.3
S4 =
=
= 0.37
D 148.7
Copyright 2009 John Wiley & Sons, Inc.
12-47
Seasonal Adjustment (cont.)
For 2005
y = 40.97 + 4.30x = 40.97 + 4.30(4) = 58.17
SF1 = (S1) (F5) = (0.28)(58.17) = 16.28
SF2 = (S2) (F5) = (0.20)(58.17) = 11.63
SF3 = (S3) (F5) = (0.15)(58.17) = 8.73
SF4 = (S4) (F5) = (0.37)(58.17) = 21.53
Copyright 2009 John Wiley & Sons, Inc.
12-48
Forecast Accuracy
 Forecast error


difference between forecast and actual demand
MAD


MAPD



mean absolute deviation
mean absolute percent deviation
Cumulative error
Average error or bias
Copyright 2009 John Wiley & Sons, Inc.
12-49
Mean Absolute Deviation
(MAD)
 Dt - Ft 
MAD =
n
where
t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value
Copyright 2009 John Wiley & Sons, Inc.
12-50
MAD Example
PERIOD
1
2
3
4
5
6
7
8
9
10
11
12
DEMAND, Dt
37
40
41
37
MAD
45
50
43
47
56
52
55
54
=
=
=
Ft ( =0.3)
(Dt - Ft)
|Dt - Ft|
37.00
–
37.00
3.00
37.90
3.10
 D
t - Ft  -1.83
38.83
n
38.28
6.72
40.29
9.69
53.39
43.20
-0.20
43.14
3.86
11
44.30
11.70
4.19
4.8547.81
49.06
5.94
50.84
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
557
Copyright 2009 John Wiley & Sons, Inc.
12-51
Other Accuracy Measures
Mean absolute percent deviation (MAPD)
|Dt - Ft|
MAPD =
Dt
Cumulative error
E = e t
Average error
et
E= n
Copyright 2009 John Wiley & Sons, Inc.
12-52
Comparison of Forecasts
FORECAST
MAD
MAPD
E
(E)
Exponential smoothing (= 0.30)
Exponential smoothing (= 0.50)
Adjusted exponential smoothing
(= 0.50, = 0.30)
Linear trend line
4.85
4.04
3.81
9.6%
8.5%
7.5%
49.31
33.21
21.14
4.48
3.02
1.92
2.29
4.9%
–
–
Copyright 2009 John Wiley & Sons, Inc.
12-53
Forecast Control
 Tracking signal

monitors the forecast to see if it is biased
high or low
Tracking signal =


(Dt - Ft)
E
=
MAD
MAD
1 MAD ≈ 0.8 б
Control limits of 2 to 5 MADs are used most
frequently
Copyright 2009 John Wiley & Sons, Inc.
12-54
Tracking Signal Values
PERIOD
DEMAND
Dt
1
2
3
4
5
6
7
8
9
10
11
12
37
40
41
37
45
50
43
47
56
52
55
54
FORECAST,
Ft
ERROR
Dt - Ft
E =
(Dt - Ft)
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
43.14
TS3 = 3.86 =24.34
2.00
3.05
44.30
11.70
36.04
47.81
4.19
40.23
49.06
5.94
46.17
50.84
3.15
49.32
Copyright 2009 John Wiley & Sons, Inc.
MAD
–
3.00
3.05
2.64
3.66
4.87
4.09
4.06
5.01
4.92
5.02
4.85
TRACKING
SIGNAL
–
1.00
2.00
1.62
3.00
4.25
5.01
6.00
7.19
8.18
9.20
10.17
12-55
Tracking Signal Plot
Tracking signal (MAD)
3 –
2 –
Exponential smoothing ( = 0.30)
1 –
0 –
-1 –
-2 –
Linear trend line
-3 –
|
0
|
1
|
2
|
3
|
4
|
5
Copyright 2009 John Wiley & Sons, Inc.
|
6
Period
|
7
|
8
|
9
|
10
|
11
|
12
12-56
Statistical Control Charts
=
(Dt - Ft)2
n-1
 Using  we can calculate statistical
control limits for the forecast error
 Control limits are typically set at  3
Copyright 2009 John Wiley & Sons, Inc.
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Statistical Control Charts
18.39 –
UCL = +3
12.24 –
Errors
6.12 –
0–
-6.12 –
-12.24 –
-18.39 –
|
0
LCL = -3
|
1
|
2
|
3
|
4
|
5
Copyright 2009 John Wiley & Sons, Inc.
|
6
Period
|
7
|
8
|
9
|
10
|
11
|
12
12-58
Computing a Forecast with
Seasonal Adjustment
Copyright 2009 John Wiley & Sons, Inc.
12-63
OM Tools
Copyright 2009 John Wiley & Sons, Inc.
12-64
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All rights reserved. Reproduction or translation of this work beyond that
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Copyright 2009 John Wiley & Sons, Inc.
12-77