Supply Chain Management

1
Supply Chain Management

• Lecture 13

2
Outline

• Today
• Chapter 7
• Thursday
• Network design simulation assignment
• Chapter 8
• Friday
• Homework 3 due before 500pm

3
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 500pm
• March 4
• Simulation results
• Midterm overview
• Homework 4 due
• March 9
• Midterm

4
Summary Static Forecasting Method

• Estimate level and trend
• Deseasonalize the demand data
• Estimate level L and trend T using linear
  regression
• Obtain deasonalized demand Dt
• 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
• Forecast for future periods is
• Ftn (L nT)Stn

Forecast Ftn (L nT)Stn
5
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
years enrollments. Each colleges 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?
6
Time Series Forecasting
Observed demand Systematic component Random
component
L Level (current deseasonalized demand)
T Trend (growth or decline in demand)
S Seasonality (predictable seasonal fluctuation)
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)
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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

8
Examples
9
Measures of Forecast Error
Measure Description
Error Absolute Error Forecast Actual Demand Absolute deviation
Mean Squared Error (MSE) Squared deviation of forecast from demand
Mean Absolute Deviation (MAD) Absolute deviation of forecast from demand
Mean Absolute Percentage Error (MAPE) Absolute deviation of forecast from demand as a percentage of the demand
Tracking signal (TS) Ratio of bias and MAD
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Forecast Error

• Error (E)
• Measures the difference between the forecast and
  the actual demand in period t
• Want error to be relatively small

Et Ft Dt
11
Forecast Error
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Forecast Error

• Bias
• 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

biast
?n
?t1
Et
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Forecast Error
Forecast mean on target but not perfect
Undershooting
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Forecast Error

• Absolute deviation (A)
• Measures the absolute value of error in period t
• Want absolute deviation to be relatively small

At Et
15
Forecast Error

• Mean absolute deviation (MAD)
• 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

?n
MADn ?t1 At
? 1.25MAD
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Forecast Error
Not all that large relative to data
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Forecast Error

• Tracking signal (TS)
• 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

TSt biast / MADt
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Forecast Error
Biased (underforecasting)
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Forecast Error

• Mean absolute percentage error (MAPE)
• 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)

MAPEn
20
Forecast Error
Smallest absolute deviation relative to demand
MAPE lt 10 is considered very good
21
Forecast Error

• Mean squared error (MSE)
• 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

Et2
MSEn ?t1
?n
VAR MSE
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Measures of Forecast Error
Measure Description
Error Absolute Error Et Ft Dt At Et
Mean Squared Error (MSE) MSEn ?t1Et2
Mean Absolute Deviation (MAD) MADn ?t1At
Mean Absolute Percentage Error (MAPE) MAPEn
Tracking signal (TS) TSt biast / MADt
?n
?n
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Summary

• 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
• 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

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Forecast Error in Excel

• Calculate absolute error At ABS(Et)
• Calculate mean absolute deviation
  MADn SUM(A1An)/n AVERAGE(A1An)
• Calculate mean absolute percentage error
  MAPEn AVERAGE()
• Calculate tracking signal TSt biast / MADt
• Calculate mean squared error MSEn SUMSQ(E1En)/n

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Forecast Error in Excel
Et Ft Dt
Forecast Error
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Forecast Error in Excel
biasn
?n
?t1
Et
Bias
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Forecast Error in Excel
At Et
Absolute Error
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Forecast Error in Excel
MADn ?t1 At
?n
Mean Absolute Deviation
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Forecast Error in Excel
TSt biast / MADt
Tracking Signal
30
Forecast Error in Excel
Errort
Error
31
Forecast Error in Excel
Errort
MAPEn
n
Mean Absolute Percentage Error
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Forecast Error in Excel
?n
Et2
MSEn ?t1
Mean Squared Error