Forecasting
The future is made of the same stuff as the present.
– Simone Weil
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
1
MRP II Planning Hierarchy
Demand
Forecast
Resource
Planning
Aggregate Production
Planning
Rough-cut Capacity
Planning
Master Production
Scheduling
Bills of
Material
Inventory
Status
Material Requirements
Planning
Job
Pool
Capacity Requirements
Planning
Job
Release
Routing
Data
Job
Dispatching
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
2
Forecasting
Basic Problem: predict demand for planning purposes.
Laws of Forecasting:
1. Forecasts are always wrong!
2. Forecasts always change!
3. The further into the future, the less reliable the forecast will be!
Forecasting Tools:
• Qualitative:
– Delphi
– Analogies
– Many others
• Quantitative:
– Causal models (e.g., regression models)
– Time series models
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
3
Forecasting “Laws”
1) Forecasts are always wrong!
2) Forecasts always change!
3) The further into the future, the less reliable the forecast!
40%
Trumpet of Doom
20%
+10%
-10%
Start of
season
16 weeks
26 weeks
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
4
Quantitative Forecasting
Goals:
• Predict future from past
• Smooth out “noise”
• Standardize forecasting procedure
Methodologies:
• Causal Forecasting:
– regression analysis
– other approaches
• Time Series Forecasting:
–
–
–
–
–
moving average
exponential smoothing
regression analysis
seasonal models
many others
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
5
Time Series Forecasting
Historical Data
A(i), i = 1, … , t
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Forecast
Time series model
http://factory-physics.com
f(t+t), t = 1, 2, …
6
Time Series Approach
Notation:
A(i )  observatio n in period i
t  current period
f (t  t )  forecast for period t  t
F (t )  smoothed estimate as of period t
T (t )  smoothed trend as of period t
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
7
Time Series Approach (cont.)
Procedure:
1. Select model that computes f(t+t) from A(i), i = 1, … , t
2. Forecast existing data and evaluate quality of fit by using:
MAD 
MSD 
BIAS 
n
 f (t )  A(t )
n
t 1
n
 ( f (t )  A(t )) 2
n
t 1
n
 ( f (t )  A(t ))
n
t 1
3. Stop if fit is acceptable. Otherwise, adjust model constants and go
to (2) or reject model and go to (1).
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
8
Moving Average
Assumptions:
• No trend
• Equal weight to last m observations
Model:

F (t ) 
t
i t  m 1
f (t  t )  F (t ),
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
A(i )
m
t  1, 2, ...
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9
Moving Average (cont.)
Example: Moving Average with m = 3 and m = 5.
Month
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Demand
A (t )
10
12
12
11
15
14
18
22
18
28
33
31
31
37
40
33
50
45
55
60
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Forecast (m =3)
f (t )
11.33
11.67
12.67
13.33
15.67
18.00
19.33
22.67
26.33
30.67
31.67
33.00
36.00
36.67
41.00
42.67
50.00
Forecast (m =5)
f (t )
12.0
12.8
14.0
16.0
17.4
20.0
23.8
26.4
28.2
32.0
34.4
34.4
38.2
41.0
44.6
http://factory-physics.com
Note: bigger
m makes forecast
more stable, but
less responsive.
F (t ) 

t
i t  m 1
f (t  t )  F (t ),
A(i )
m
t  1, 2, ...
10
Exponential Smoothing
Assumptions:
• No trend
• Exponentially declining weight given to past observations
Model:
F (t )  A(t )  (1   ) F (t  1)
f (t  t )  F (t ),
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
t  1, 2, ...
http://factory-physics.com
11
Exponential Smoothing (cont.)
Example: Exponential Smoothing with  = 0.2 and  = 0.6.
Month
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Demand
A (t )
10
12
12
11
15
14
18
22
18
28
33
31
31
37
40
33
50
45
55
60
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Forecast (a =0.2)
f (t )
10.00
10.40
10.72
10.78
11.62
12.10
13.28
15.02
15.62
18.09
21.08
23.06
24.65
27.12
29.69
30.36
34.28
36.43
40.14
Forecast (a =0.6)
f (t )
10.00
11.20
11.68
11.27
13.51
13.80
16.32
19.73
18.69
24.28
29.51
30.40
30.76
34.50
37.80
34.92
43.97
44.59
50.83
http://factory-physics.com
Note: we are
still lagging
behind actual
values.
F (t )  A(t )  (1   ) F (t  1)
f (t  t )  F (t ),
t  1, 2, ...
12
Exponential Smoothing with a Trend
Assumptions:
• Linear trend
• Exponentially declining weights to past observations/trends
Model:
F (t )  A(t )  (1   )( F (t  1)  T (t  1))
T (t )   ( F (t )  F (t  1))  (1   )T (t  1)
f (t  t )  F (t )  tT (t )
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Note: these calculations are
easy, but there is some “art”
in choosing F(0) and T(0) to
start the time series.
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13
Exponential Smoothing with a Trend (cont.)
Example: Exponential Smoothing with Trend,  = 0.2,  = 0.5.
Note: we start with
trend equal to
difference between
first two demands.
F (t )  A(t )  (1   )( F (t  1)  T (t  1))
T (t )   ( F (t )  F (t  1))  (1   )T (t  1)
f (t  t )  F (t )  tT (t )
Month
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Demand
A (t )
10
12
12
11
15
14
18
22
18
28
33
31
31
37
40
33
50
45
55
60
Smoothed Estimate
F (t )
10.40
12.32
13.62
15.20
16.25
17.66
19.62
20.63
23.17
26.69
29.73
32.30
35.42
38.67
40.01
43.78
46.41
50.38
55.02
http://factory-physics.com
Smoothed Trend
T (t )
2.00
1.96
1.63
1.61
1.33
1.37
1.67
1.34
1.94
2.73
2.89
2.72
2.92
3.09
2.21
2.99
2.81
3.39
4.01
Forecast
f (t )
12.40
14.28
15.26
16.81
17.57
19.03
21.29
21.97
25.11
29.42
32.62
35.02
38.34
41.76
42.22
46.77
49.23
53.77
14
Exponential Smoothing with a Trend (cont.)
Example: Exponential Smoothing with Trend,  = 0.2,  = 0.5.
Note: we start with
trend equal to
zero.
F (t )  A(t )  (1   )( F (t  1)  T (t  1))
T (t )   ( F (t )  F (t  1))  (1   )T (t  1)
f (t  t )  F (t )  tT (t )
Month
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Demand
A (t )
10
12
12
11
15
14
18
22
18
28
33
31
31
37
40
33
50
45
55
60
Smoothed Estimate
F (t )
10.00
10.40
10.88
11.18
12.20
13.09
14.70
17.11
18.74
21.96
26.14
29.77
32.80
36.25
39.67
41.05
44.75
47.23
50.99
55.40
http://factory-physics.com
Smoothed Trend
T (t )
0.00
0.20
0.34
0.32
0.67
0.78
1.19
1.81
1.71
2.47
3.33
3.48
3.25
3.35
3.39
2.38
3.04
2.76
3.26
3.84
Forecast
f (t )
10.60
11.22
11.49
12.86
13.87
15.89
18.92
20.45
24.43
29.47
33.25
36.06
39.59
43.06
43.43
47.79
49.99
54.25
15
Effects of Altering Smoothing Constants
Exponential Smoothing with Trend: various values of  and 
Note: these assume
we start with trend
equal diff between
first two demands.
n
MAD   f (t )  A(t ) n
t 1
n
MSD   ( f (t )  A(t )) 2 n
t 1
n
BIAS   ( f (t )  A(t )) n
t 1
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000


0.1
0.1
0.1
0.1
0.1
0.4
0.4
0.4
0.4
0.4
0.7
0.7
0.7
0.7
0.7
1.0
1.0
1.0
1.0
1.0
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
0.2
0.4
0.6
8.0
1.0
MAD
4.11
3.98
3.76
3.63
3.54
3.75
3.83
3.93
4.01
4.08
4.34
4.53
4.74
4.99
5.27
4.94
5.25
5.83
6.66
7.72
http://factory-physics.com
MSD
27.56
24.82
21.98
20.07
19.26
21.82
22.52
23.87
24.82
25.44
27.18
30.00
33.65
38.39
44.59
39.82
48.75
61.27
78.86
104.06
BIAS
-2.00
-1.94
-1.73
-1.47
-1.20
-1.07
-0.85
-0.78
-0.74
-0.67
-0.75
-0.60
-0.50
-0.41
-0.34
-0.56
-0.42
-0.32
-0.25
-0.17
16
Effects of Altering Smoothing Constants
Exponential Smoothing with Trend: various values of  and 

Note: these
assume we
start with
trend equal
to zero.

0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.3
0.1
0.2
0.3
0.4
0.5
0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.1
0.2
0.3
0.4
0.5
0.6
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
MAD
10.23
8.27
6.83
5.83
5.16
4.69
6.48
5.04
4.26
3.9
3.73
3.65
4.98
4.11
3.82
3.66
3.65
3.68
MSD
146.94
95.31
64.91
47.17
36.88
30.91
60.55
37.04
27.56
23.75
22.32
21.94
37.81
26.3
22.74
21.81
21.78
22.06
BIAS
-10.23
-8.27
-6.69
-5.43
-4.42
-3.62
-6.29
-4.49
-3.29
-2.51
-2.02
-1.71
-4.45
-3.03
-2.23
-1.77
-1.52
-1.38

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
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.6
0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.1
0.2
0.3
0.4
0.5
0.6
MAD
4.3
3.89
3.77
3.75
3.76
3.79
4.13
3.91
3.88
3.9
3.94
3.97
4.12
4.03
4.04
4.09
4.14
4.21
MSD
30.14
23.78
22.25
22.11
22.36
22.67
27.4
23.61
23.02
23.26
23.73
24.27
26.85
24.63
24.69
25.35
26.25
27.29
BIAS
-3.45
-2.34
-1.77
-1.46
-1.29
-1.18
-2.84
-1.94
-1.49
-1.25
-1.1
-1
-2.42
-1.66
-1.29
-1.08
-0.95
-0.84
17
Effects of Altering Smoothing Constants (cont.)
Observations: assuming we start with zero trend
•  = 0.3,  = 0.5 work well for MAD and MSD
•  = 0.6,  = 0.6 work better for BIAS
• Our original choice of  = 0.2,  = 0.5 had
MAD = 3.73, MSD = 22.32, BIAS = -2.02,
which is pretty good,
• although  = 0.3,  = 0.6, with
MAD = 3.65, MSD=21.78, BIAS = -1.52
is better.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
18
Winters Method for Seasonal Series
Seasonal series: a series that has a pattern that repeats every N periods
for some value of N (which is at least 3).
Seasonal factors: a set of multipliers ct , representing the average
amount that the demand in the tth period of the season is above or
below the overall average.
Winter’s Method:
• The series:
• The trend:
F (t )  A(t ) / c(t  N )  (1   )F (t 1)  T (t 1)
T (t )   F (t )  F (t 1)  (1   )T (t 1)
• The seasonal factors:
c(t )  A(t ) / F (t )  (1   )c(t  N )
• The forecast:
f (t  t )  F (t )  tT (t )c(t  t  N )
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
19
Winters Method Example
Smoothed
Time
Actual
Estimate
Period t Demand A(t)
F(t)
1
4
2
2
3
5
4
8
5
11
6
13
7
18
8
15
9
9
10
6
11
5
12
4
8.33
13
5
8.54
14
4
9.37
15
7
9.69
16
7
9.57
17
15
9.83
18
17
10.04
19
24
10.26
20
18
10.36
21
12
10.55
22
7
10.59
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
Smoothed
Trend
T(t)
0.00
0.02
0.10
0.12
0.10
0.12
0.13
0.13
0.13
0.14
0.13
Seasonal
Factor
c(t)
0.480
0.240
0.600
0.960
1.320
1.560
2.160
1.800
1.080
0.720
0.600
0.480
0.491
0.259
0.612
0.937
1.341
1.573
2.178
1.794
1.086
0.714
Forecast
f(t)
http://factory-physics.com
alpha
beta
gamma
4.00
2.06
5.68
9.43
12.76
15.52
21.97
18.72
11.33
7.69
0.1
0.1
0.1
20
Winters Method - Sample Calculations
12
F (12 ) 
c(1) 
 A(t )
t 1
12

4  2  4
 8.33
12
A(1)
4

 0.480
F (12 ) 8.33
Initially we set:
• smoothed estimate = first season average
• smoothed trend = zero (T(N)=T(12) = 0)
• seasonality factor = ratio of actual to
average demand
F (13)   ( A(13) / c(13  12 )  (1   )( F (12 )  T (12 ))
 0.1(5 / 0.480 )  (1  0.1)(8.33  0)  8.54
From period 13 on we can use
initial values and standard
formulas...
T (13)   ( F (13)  F (12 ))  (1   )T (12 )
 0.1(8.54  8.33)  (1  0.1)(0)  0.02
c(13)   ( A(13) / F (13))  (1   )c(1)
 0.1((5 / 8.54 )  (1  0.1)(0.48)  0.491
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
21
Conclusions
Sensitivity: Lower values of m or higher values of  will make moving
average and exponential smoothing models (without trend) more sensitive to
data changes (and hence less stable).
Trends: Models without a trend will underestimate observations in time series
with an increasing trend and overestimate observations in time series with a
decreasing trend.
Smoothing Constants: Choosing smoothing constants is an art; the best
we can do is choose constants that fit past data reasonably well.
Seasonality: Methods exist for fitting time series with seasonal behavior
(e.g., Winters method), but require more past data to fit than the simpler
models.
Judgement: No time series model can anticipate structural changes not
signaled by past observations; these require judicious overriding of the model
by the user.
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
http://factory-physics.com
22