Supply Chain Management
Lecture 13
Outline
• Today
– Chapter 7
• Thursday
– Network design simulation assignment
– Chapter 8
• Friday
– Homework 3 due before 5:00pm
Outline
• February 23 (Today)
– Chapter 7
• February 25
– Network design simulation description
– Chapter 8
– Homework 4 (short)
• March 2
– Chapter 8, 9
– Network design simulation due before 5:00pm
• March 4
– Simulation results
– Midterm overview
– Homework 4 due
• March 9
– Midterm
Summary: Static Forecasting Method
1. Estimate level and trend
•
•
•
Deseasonalize the demand data
Estimate level L and trend T using linear regression
Obtain deasonalized demand Dt
2. Estimate seasonal factors
•
•
Estimate seasonal factors for each period St = Dt /Dt
Obtain seasonal factors Si = AVG(St) such that t is the same
season as i
Forecast
Ft+n = (L + nT)St+n
3. Forecast
3000
Forecast for future periods is
•
Ft+n = (L + nT)*St+n
2500
Demand
•
3500
2000
1500
1000
500
0
1
2
3
4
5
6
7
8
9
Quarter
10 11 12 13 14 15 16
Ethical Dilemma?
In 2009, the board of regents for all public higher education in a
large Midwestern state hired a consultant to develop a series of
enrollment forecasting models, one for each college. These models
used historical data and exponential smoothing to forecast the
following year’s enrollments. Each college’s budget was set by the
board based on the model, which included a smoothing constant
() for each school. The head of the board personally selected
each smoothing constant based on “gut reactions and political
acumen.”
How can this model be abused?
What can be done to remove any biases?
Can a regression model be used to bias results?
Time Series Forecasting
Observed demand =
Systematic component + Random component
L
T
S
Forecast
Level (current deseasonalized demand)
Trend (growth or decline in demand)
Seasonality (predictable seasonal fluctuation)
Forecast error
The goal of any forecasting method is to predict the systematic
component (Forecast) of demand and measure the size and
variability of the random component (Forecast error)
1) Characteristics of Forecasts
• Forecasts are always wrong!
– Forecasts should include an expected value and a
measure of error (or demand uncertainty)
• Forecast 1: sales are expected to range between 100 and
1,900 units
• Forecast 2: sales are expected to range between 900 and
1,100 units
Examples
10000
1000000
Demand
Demand
Forecast
Forecast
900000
9000
800000
8000
1
2
3
4
5
6
7
8
9
10
11
Demand
50000
1
12
2
3
4
5
6
7
8
9
10
11
12
4
5
6
7
8
9
10
11
12
Demand
40000
Forecast
Forecast
40000
30000
30000
20000
20000
10000
10000
0
0
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
Measures of Forecast Error
Measure
Description
Error
Absolute Error
Mean Squared Error (MSE)
Forecast – Actual Demand
Absolute deviation
Squared deviation of forecast
from demand
Absolute deviation of forecast
from demand
Absolute deviation of forecast
from demand as a percentage
of the demand
Ratio of bias and MAD
Mean Absolute Deviation
(MAD)
Mean Absolute Percentage
Error (MAPE)
Tracking signal (TS)
Forecast Error
• Error (E)
Et = Ft – Dt
• Measures the difference between the forecast
and the actual demand in period t
• Want error to be relatively small
Forecast Error
100000
500
Et
75000
Et
400
300
50000
200
25000
100
0
0
1
-25000
2
3
4
5
6
7
8
9
10
11
12
-100
1
2
3
4
5
6
7
8
9
10
11
12
5
6
7
8
9
10
11
12
-200
-50000
-300
-75000
-400
-100000
-500
5000
5000
Et
4000
3000
3000
2000
2000
1000
1000
0
0
-1000
Et
4000
1
2
3
4
5
6
7
8
9
10
11
12
-1000
-2000
-2000
-3000
-3000
-4000
-4000
-5000
-5000
1
2
3
4
Forecast Error
• Bias
biast = ∑nt=1 Et
• Measures the bias in the forecast error
• Want bias to be as close to zero as possible
– A large positive (negative) bias means that the
forecast is overshooting (undershooting) the actual
observations
– Zero bias does not imply that the forecast is perfect
(no error) -- only that the mean of the forecast is “on
target”
Forecast Error
Bias
-19000
12000
73000
14000
-15000
-4000
67000
-2000
-51000
-10000
11000
-78000
Bias
1000000
Demand
Forecast
900000
800000
1
Bias
-300
-900
-1800
-3000
-4500
-6300
-8400
-10800
-13500
-16500
-19800
-23400
2
3
4
5
6
7
8
9
10
11
12
Demand
50000
Forecast
40000
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
Undershooting
10
11
12
-200
-500
-200
-500
-300
-100
0
100
-100
-400
-90
-390
Bias
912.61
1091.15
1350.81
1386.80
1109.80
-2332.49
648.46
435.64
-754.75
2789.40
-1361.73
-920.13
10000
Demand
Forecast
9000
8000
1
2
3
4
5
6
7
8
9
10
11
12
Forecast mean “on
target” but not perfect
Demand
40000
Forecast
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
10
11
12
Forecast Error
• Absolute deviation (A)
At = |Et|
• Measures the absolute value of error in period t
• Want absolute deviation to be relatively small
Forecast Error
• Mean absolute deviation (MAD)
n A
MADn = 1 ∑t=1
t
n
• Measures absolute error
• Positive and negative errors do not cancel out (as
with bias)
• Want MAD to be as small as possible
– No way to know if MAD error is large or small in
relation to the actual data
 = 1.25*MAD
Forecast Error
MAD
19000
25000
37000
42500
39800
35000
40143
43750
44333
44000
41909
45833
MAD
1000000
Demand
Forecast
900000
800000
1
2
3
4
5
6
7
8
9
10
11
12
Not all that large
relative to data
MAD
200
250
267
275
260
250
229
213
211
220
228
234
10000
913
546
450
347
333
851
1155
1037
1054
1303
1562
1469
40000
Demand
Forecast
9000
8000
1
2
3
4
5
6
7
8
9
10
11
12
4
5
6
7
8
9
10
11
12
MAD
300
450
600
750
900
1050
1200
1350
1500
1650
1800
1950
Demand
50000
Forecast
40000
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
10
11
12
Demand
Forecast
30000
20000
10000
0
1
2
3
Forecast Error
• Tracking signal (TS)
TSt = biast / MADt
• Want tracking signal to stay within (–6, +6)
– If at any period the tracking signal is outside the
range (–6, 6) then the forecast is biased
Forecast Error
TS
TS
-1.00
0.48
1.97
0.33
-0.38
-0.11
1.67
-0.05
-1.15
-0.23
0.26
-1.70
TS
Tracking Signal
4.00
2.00
0.00
1
2
3
4
5
6
7
8
9
10
11
12
-2.00
-4.00
-6.00
TS
15.00
-1.00
-2.00
-3.00
-4.00
-5.00
-6.00
-7.00
-8.00
-9.00
-10.00
-11.00
-12.00
-1.00
-2.00
-0.75
-1.82
-1.15
-0.40
0.00
0.47
-0.47
-1.82
-0.39
-1.67
6.00
Tracking Signal
10.00
5.00
0.00
1
2
3
4
5
6
7
8
9
10
-5.00
-10.00
-15.00
Biased
(underforecasting)
11
12
6.00
Tracking Signal
4.00
2.00
0.00
1
2
3
4
5
6
7
8
9
10
11
12
5
6
7
8
9
10
11
12
-2.00
-4.00
-6.00
6.00
1.00
2.00
3.00
4.00
3.34
-2.74
0.56
0.42
-0.72
2.14
-0.87
-0.63
Tracking Signal
4.00
40000
2.00
0.00
30000
-2.00
-4.00
-6.00
20000
10000
1
2
3
4
Forecast Error
• Mean absolute percentage error (MAPE)
MAPEn =
∑nt=1
Et
100
Dt
n
• Same as MAD, except ...
• Measures absolute deviation as a percentage of
actual demand
• Want MAPE to be less than 10 (though values
under 30 are common)
Forecast Error
MAPE
2.11
2.88
4.40
4.87
4.53
3.99
4.67
4.99
5.02
5.01
4.78
5.14
MAPE
3.75
5.21
6.47
7.58
8.57
9.45
10.24
10.96
11.62
12.22
12.78
13.29
1000000
Demand
Forecast
900000
800000
1
2
3
4
5
6
7
8
9
10
11
12
Demand
50000
Forecast
40000
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
10
11
12
MAPE < 10 is
considered very good
MAPE
2.22
2.88
3.14
3.15
2.96
2.85
2.62
2.42
2.39
2.51
2.61
2.65
MAPE
11.41
6.39
4.64
3.50
3.36
5.98
6.98
6.18
6.59
8.66
9.05
8.39
10000
Demand
Forecast
9000
8000
1
2
3
4
5
6
7
8
9
10
11
12
Smallest absolute
deviation relative to
demand
Demand
40000
Forecast
30000
20000
10000
0
1
2
3
4
5
6
7
8
9
10
11
12
Forecast Error
• Mean squared error (MSE)
n E2
MSEn = 1 ∑t=1
t
n
• Measures squared forecast error
• Recognizes that large errors are
disproportionately more “expensive” than small
errors
• Not as easily interpreted as MAD, MAPE -- not
as intuitive
VAR = MSE
Measures of Forecast Error
Measure
Description
Error
Absolute Error
Mean Squared Error (MSE)
Mean Absolute Percentage
Error (MAPE)
Et = Ft – Dt
At = |Et|
n E2
MSEn = 1 ∑t=1
t
n
n A
MADn = 1 ∑t=1
t
n
Et
n
∑t=1
100
Dt
MAPEn =
n
Tracking signal (TS)
TSt = biast / MADt
Mean Absolute Deviation
(MAD)
Summary
1. What information does the bias and TS provide to a
manager?
•
The bias and TS are used to estimate if the forecast
consistently over- or underforecasts
2. What information does the MSE and MAD provide to a
manager?
•
MSE estimates the variance of the forecast error
•
•
VAR(Forecast Error) = MSEn
MAD estimates the standard deviation of the forecast error
•
STDEV(Forecast Error) = 1.25 MADn
Forecast Error in Excel
• Calculate absolute error At
=ABS(Et)
• Calculate mean absolute deviation MADn
=SUM(A1:An)/n
=AVERAGE(A1:An)
• Calculate mean absolute percentage error MAPEn
=AVERAGE(…)
• Calculate tracking signal TSt
=biast / MADt
• Calculate mean squared error MSEn
=SUMSQ(E1:En)/n
Forecast Error in Excel
Error
E_t
=C4-B4
=C5-B5
=C6-B6
=C7-B7
Et = Ft – Dt
Forecast Error
Forecast Error in Excel
Bias
bias_t
=SUM($D$4:D4)
=SUM($D$4:D5)
=SUM($D$4:D6)
=SUM($D$4:D7)
biasn = ∑nt=1 Et
Bias
Forecast Error in Excel
Absolute
Error
A_t
=ABS(D4)
=ABS(D5)
=ABS(D6)
=ABS(D7)
At = |Et|
Absolute Error
Forecast Error in Excel
Mean
Abs Error
MAD_t
=AVERAGE($F$4:F4)
=AVERAGE($F$4:F5)
=AVERAGE($F$4:F6)
=AVERAGE($F$4:F7)
n A
MADn = 1 ∑t=1
t
n
Mean Absolute Deviation
Forecast Error in Excel
Tracking
Signal
TS_t
=E4/G4
=E5/G5
=E6/G6
=E7/G7
TSt = biast / MADt
Tracking Signal
Forecast Error in Excel
|%Error|
|%Error|
=ABS(D4/B4)*100
=ABS(D5/B5)*100
=ABS(D6/B6)*100
=ABS(D7/B7)*100
Et
|%Error|t =
100
Dt
|%Error|
Forecast Error in Excel
Mean
|%Error|
MAPE_t
=AVERAGE($I$4:I4)
=AVERAGE($I$4:I5)
=AVERAGE($I$4:I6)
=AVERAGE($I$4:I7)
∑nt=1 |%Error|t
MAPEn =
n
Mean Absolute
Percentage Error
Forecast Error in Excel
Mean
Sq Error
MSE_t
=SUMSQ($D$4:D4)/A4
=SUMSQ($D$4:D5)/A5
=SUMSQ($D$4:D6)/A6
=SUMSQ($D$4:D7)/A7
n E2
MSEn = 1 ∑t=1
t
n
Mean Squared Error