Forecasting Supply
Chain Requirements
I hope you'll keep in mind that economic
forecasting is far from a perfect science. If recent
history's any guide, the experts have some
explaining to do about what they told us had to
happen but never did.
Ronald Reagan, 1984
Chapter 8
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8-1
CONTROLLING
Customer
service goals
• The product
• Logistics service
• Ord. proc. & info. sys.
Transport Strategy
• Transport fundamentals
• Transport decisions
PLANNING
Inventory Strategy
• Forecasting
• Inventory decisions
• Purchasing and supply
scheduling decisions
• Storage fundamentals
• Storage decisions
ORGANIZING
Forecasting in
Inventory Strategy
Location Strategy
• Location decisions
• The network planning process
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8-2
What’s Forecasted in the
Supply Chain?
•Demand, sales or requirements
•Purchase prices
•Replenishment and delivery
times
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8-3
Some Forecasting Method Choices
•Historical projection
Moving average
Exponential smoothing
•Causal or associative
Regression analysis
•Qualitative
Surveys
Expert systems or rule-based
•Collaborative
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8-4
Typical Time Series Patterns:
Random
250
Sales
200
150
Actual sales
Average sales
100
50
0
0
5
10
15
20
25
Time
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8-5
Typical Time Series Patterns:
Random with Trend
250
Sales
200
150
100
Actual sales
Average sales
50
0
0
5
10
15
20
25
Time
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8-6
Sales
Typical Time Series Patterns:
Random with Trend & Seasonal
800
700
600
500
400
300
200
100
0
Actual sales
Trend in sales
Smoothed trend and seasonal sales
0
10
20
30
40
Time
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8-7
Sales
Typical Time Series Patterns:
Lumpy
Time
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8-8
Is Time Series Pattern
Forecastable?
Whether a time series can be reasonably
forecasted often depends on the time series’
degree of variability. Forecast a regular time
series, but use other techniques for lumpy ones.
How to tell the difference:
Rule
A time series is lumpy if
X  3
where
X  mean of the series
  standard deviation of series,
regular, otherwise.
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8-9
Moving Average
Basic formula
t

MA 
Ai
n i t 1n
1
where
i = time period
t = current time period
n = length of moving average in periods
Ai = demand in period i
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8-10
Example 3-Month Moving Average Forecasting
Month, i
.
.
.
20
21
22
23
24
25
26
CR (2004) Prentice Hall, Inc.
Demand for
month, i
.
.
.
120
130
110
140
110
130
Total demand
during past 3
months
.
.
.
.
360/3
380/3
360/3
380/3
3-month
moving
average
.
.
.
.
120
126.67
120
126.67
?
8-11
n
where
w
i 1
i
1
If weights (w ) are exponential in form, then
MA  aAt  a (1  a )1 At 1
 a (1  a ) 2 At  2  a (1  a ) 3 At 3
 ...  a (1  a ) n At n
which reduces to the basic, level only,
exponential smoothing formula
MA  Ft 1  aAt  (1  a )Ft
where
a  smoothing constant usually 0.01 to 0.30
Ft 1  forecast for next period
At  actual demand in current period
Ft  forecast in current period
Weighted Moving Average
MA  w 1A1  w 2 A2  ...  w n An
8-12
Exponential Smoothing Formulas
I. Level only
IV. Forecast error
Ft+1 = a At + (1-a)Ft
MAD =
N
 |A t
t 1
N
II. Level and trend
St
= aAt + (1-a)(St-1 + Tt-1)
Tt
= ß(St - St-1) + (1-ß)Tt-1
Ft+1 = St + Tt
 Ft |
or
SF 
N
 (A t
t 1
 Ft ) 2
N
and SF @ 1.25MAD.
III. Level, trend, and seasonality
St = a(At/It-L) + (1-a)(St-1 + Tt-1)
It
= g(At/St) + (1-g)It-L
Tt
= ß(St - St-1) + (1-ß)Tt-1
Ft+1 = (St + Tt)It-L+1
where L is the time period of one full seasonal cycle.
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8-13
Example Exponential Smoothing Forecasting
Time series data
1
Last
year
This
year
Quarter
2
3
4
1100
1200
700
900
1400
1000
?
Getting started
Assume a = 0.2. Average first 4 quarters of data
and use for previous forecast, say Fo
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8-14
Example (Cont’d)
Begin forecasting
F0  (1200 700  900 1100) / 4  975
First quarter of 2nd year
F1  0.2A0  (1 0.2)F0
 0.2(1100)  0.8(975)
 1000
Second quarter of 2nd year
F2  0.2A1  (1 0.2)F1
 0.2(1400)  0.8(1000)
 1080
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8-15
Example (Cont’d)
Third quarter of 2nd year
F3  0.2A2  (1 0.2)F0
 0.2(1000)  0.8(1080)
 1064
Summarizing
1
Last
year
This
year
Forecast
Quarter
2
3
4
1100
1200
700
900
1400
1000
?
1000
1080
1064
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Example (Cont’d)
Measuring forecast error as MAD
n
| At  Ft |
MAD  t 1 n
or RMSE (std. error of forecast)
n
SF 
(At  Ft )2
t 1
n 1
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1 degree of freedom lost
in level-only model, but 2
in level-trend and 3 in
level-trend-seasonal
models
8-17
Example (Cont’d)
Using SF and assuming n=2
2  (10001080)2
(1400

1000)
SF 
2 1
 408
Note To compute a reasonable average for
SF, n should range over at least one seasonal
cycle in most cases.
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Example (Cont’d)
Range of the forecast
If forecast errors are normally distributed andn the forecast
 At  Ft
is at the mean of the distribution, i.e., Bias  t1 n  0 ,
a forecast confidence band can be computed. The error
distribution for the level-only model results is:
Range
Bias should
be 0 or
close to it in
a model of
good fit
SF = 408
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F3=1064
8-19
Example (Cont’d)
From a normal distribution table, z@95%=1.96. The
actual time series value Y for quarter 3 is expected to
range between:
Y  F3  z(S F )
1064 1.96(408)
1064  800
or
264  Y  1864
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8-20
Correcting for Trend in ES
The trend-corrected model is
St = aAt  (1 – a)(St-1  Tt-1)
Tt = (St – St-1)  (1 – )Tt-1
Ft+1 = St  Tt
where S is the forecast without trend correction.
Assuming a = 0.2,  = 0.3, S-1 = 975, and T-1 = 0
Forecast for quarter 1 of this year
S0 = 0.2(1100)  0.8(975 + 0) = 1000
T0 = 0.3(1000 – 975)  0.7(0) = 8
F1 = 1000  8 = 1008
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8-21
Correcting for Trend in ES (Cont’d)
Forecast for quarter 2 of this year
S0
T0
S1 = 0.2(1400)  0.8(1000  8) = 1086.4
T1 = 0.3(1086.4 – 1000)  0.7(8) = 31.5
F2 = 1086.4  31.5 = 1117.9
Forecast for quarter 3 of this year
S2 = 0.2(1000)  0.8(1086.4  31.5) = 1094.3
T2 = 0.3(1094.3 – 1086.4)  0.7(31.5) = 24.4
F3 = 1094.3  24.4 = 1118.7, or 1119
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8-22
Correcting for Trend in ES (Cont’d)
Summarizing with trend correction
1
Last
year
This
year
Forecast
Quarter
2
3
4
1100
1200
700
900
1400
1000
?
1008
1118
1119
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8-23
Optimizing a for ES
Minimize average
forecast error
Forecast
error
0
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a
1
8-24
Controlling Model Fit in ES
Tracking signal monitors the fit of the model to detect
when the model no longer accurately represents the data
At  Ft
Tracking signal 
MSE
where the Mean Squared Error (MSE) is
n
(At  Ft )2
MSE  t 1 n
n is a reasonable number
of past periods depending
on the application
If tracking signal exceeds a specified value (control limit),
revise smoothing constant(s).
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8-25
Classic Time Series
Decomposition Model
Basic formulation
F=TSCR
where
F = forecast
T = trend
S = seasonal index
C = cyclical index (usually 1)
R = residual index (usually 1)
Some time series data
Last year
This year
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1
1200
1400
Quarter
2
3
700
900
1000
?
4
1100
8-26
Classic Time Series
Decomposition Model (Cont’d)
Trend estimation
Use simple regression analysis to find the trend
equation of the form T = a  bt. Recall the basic
formulas:
Yt  nY t
b
2
2
 t  nt
and
a  Y  bt
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8-27
Classic Time Series
Decomposition Model (Cont’d)
Redisplaying the data for ease of computation.
2
t
Y
Yt
t
1
1200
1200
1
2
700
1400
4
3
900
2700
9
4
1100
4400
16
5
1400
7000
25
6
1000
6000
36
2
t=21 Y=6300 Yt=22700 t =91
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Classic Time Series
Decomposition Model (Cont’d)
Hence,
00/6)
b  22700 6(21/6)(63
91 6(21/6)2
and
a  6300  37.14(21/6)  920.01
6
then
T = 920.01  27.14t
Forecast for 3rd quarter of this year is:
T = 920.01  37.14(7) = 1179.99
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8-29
Classic Time Series
Decomposition Model (Cont’d)
Compute seasonal indices
The procedure is to form a ratio of actual demand to the
estimated demand for a full seasonal cycle (4 quarters).
One way is as follows.
Seasonal
t
Y
T
Index, St
1
1200
957.15*
1.25**
2
700
994.29
0.70
3
900
1031.43
0.87
4
1100
1068.57
1.03
*T=920.01  37.14(1)=957.15
**St=1200/957.15=1.25
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8-30
Classic Time Series
Decomposition Model (Cont’d)
Compute seasonal indices
Since C and R index values are usually 1, the
adjusted seasonal forecast for the 3rd quarter of this
year would be:
F7 = 1179.99 x 0.87 = 1026.59
Forecast range
The standard error of the forecast is:
n
SF 
2
 (Yt  Ft )
t 1
n2
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A degree of freedom is lost for the a and
b values in forecast equation
8-31
Classic Time Series
Decomposition Model (Cont’d)
Tabled computations
Qtr
1
2
3
4
1
2
3
t
1
2
3
4
5
6
7
Yt
1200
700
900
1100
1400
1000
Tt
957.15
994.29
1031.43
1068.57
1105.71
1142.85
1179.99
St
Ft
1.25
0.70
0.87
1.03
1.27 1404.25*
0.88 1005.71**
1026.59
*1105.71x1.27=1404.25
**1142.85x0.88=1005.71
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Classic Time Series
Decomposition Model (Cont’d)
There is inadequate data to make a meaningful estimate
of SF. However, we would proceed as follows:
(1400  1404.25)2  (1000  1005.71)2
SF 
22
 infinity
Normally, a larger sample
Then,
size would be used giving a
positive value for SF
Ft  z(SF)  Y  Ft  z(SF)
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8-33
Regression Analysis
Basic formulation
F = o  1X1  2X2  …  nXn
Example
Bobbie Brooks, a manufacturer of teenage women’s
clothes, was able to forecast seasonal sales from the
following relationship
F = constant  1(no. nonvendor accounts)
 2(consumer debt ratio)
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8-34
Regression Forecasting Using Bobbie Brooks Sales Data
(1)
(2)
Summer
Trans-season
Fall
Holiday
Spring
Time
period, t
1
2
3
4
5
Sales (Dt )
($000s)
$9,458
11,542
14,489
15,754
17,269
Dt  t
9,458
23,084
43,467
63,016
86,345
1
4
9
16
25
Trend value
(Tt )
$12,053
12,539
13,025
13,512
13,998
Summer
Trans-season
Fall
Holiday
Spring
6
7
8
9
10
11,514
12,623
16,086
18,098
21,030
69,084
88,361
128,688
162,882
210,300
36
49
64
81
100
14,484
14,970
15,456
15,942
16,428
0.79
0.84
1.04
1.14
1.28
Summer
Trans-season
Fall
Holiday
Totals
11
12
13
14
78
12,788
16,072
?
?
176,723
140,668
192,864
121
144
16,915
17,401
17,887 *
18,373 *
0.76
0.92
Sales period
(3)
1,218,217
(4)
t2
(5)
(6)=
(2)/(5)
Seasonal Forecast
index
($000s)
0.78
0.92
1.11
1.17
1.23
$18,602
20,945
650
N = 12  Dt  t = 1,218,217  t2 = 650 D = (176 ,723 / 12 ) = 14 ,726 .92
Regression equation is: Tt = 11,567.08 + 486.13t
t = 78 / 12 = 6 .5
*Forecasted values
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8-35
Combined Model Forecasting
Combines the results of several models to improve overall
accuracy. Consider the seasonal forecasting problem of Bobbie
Brooks. Four models were used. Three of them were two forms
of exponential smoothing and a regression model. The fourth
was managerial judgement used by a vice president of marketing
using experience. Each forecast is then weighted according to its
respective error as shown below.
Calculation of forecast weights
(1)
(3)=
(4)=
1.0/(2)
(3)/48.09
Percent Inverse of
Model Forecast of total
error
Model
type
error
error proportion weights
MJ
R
ES1
ES2
Total
9.0
0.7
1.2
8.4
19.3
CR (2004) Prentice Hall, Inc.
(2)
0.466
0.036
0.063
0.435
1.000
2.15
27.77
15.87
2.30
48.09
0.04
0.58
0.33
0.05
1.00
8-36
Forecast
type
(1)
(2)
Model
forecast
Weighting
factor
Regression
model (R)
$20,367,000
0.58
Exponential
Smoothing
ES1
20,400,000
0.33
Combined
exponential
smoothing-regression
model
17,660,000
0.05
(ES2)
Managerial
judgment
(MJ)
19,500,000
0.04
Weighted average forecast
CR (2004) Prentice Hall, Inc.
(3)=
(1)  (2)
Weighted
proportion
$11,813,000
6,732,000
883,000
780,000
$20,208,000
Weighted Average Fall Season Forecast
Using Multiple Forecasting Techniques
Combined Model Forecasting (Cont’d)
8-37
Multiple Model Errors
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8-38
Actions When Forecasting is
Not Appropriate
 Seek information directly from customers
Collaborate with other channel members
 Apply forecasting methods with caution (may work
where forecast accuracy is not critical)
 Delay supply response until demand
becomes clear
 Shift demand to other periods for better
supply response
 Develop quick response and flexible supply
systems
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8-39
Collaborative Forecasting
• Demand is lumpy or highly uncertain
• Involves multiple participants each with
•
•
a unique perspective—“two heads are
better than one”
Goal is to reduce forecast error
The forecasting process is inherently
unstable
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8-40
Collaborative Forecasting:
Key Steps
• Establish a process champion
• Identify the needed Information and collection processes
• Establish methods for processing information from multiple
sources and the weights assigned to multiple forecasts
• Create methods for translating forecast into form needed by
each party
• Establish process for revising and updating forecast in real
time
• Create methods for appraising the forecast
• Show that the benefits of collaborative forecasting are obvious
and real
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Managing Highly
Uncertain Demand
Delay forecasting as long as possible
Prioritize supply by product’s degree of uncertainty
(supply to the more certain products first)
Apply the principle of postponement to the most
uncertain products (delay committing to a final product
form until an order is received)
Create flexible supply to changing demand (alter
capacity and output rates through subcontracting,
computer technology, multi-purpose processes, etc.)
Be able to respond quickly to uncertain demand levels
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