Supply Chain Management Lecture 13. Outline Today –Chapter 7 Thursday –Network design simulation assignment –Chapter 8 Friday –Homework 3 due before 5:00pm.

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

3. Forecast• Forecast for future periods is

• Ft+n = (L + nT)*St+n

0

500

1000

1500

2000

2500

3000

3500

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Quarter

Dem

and

Forecast Ft+n = (L + nT)St+n

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?

Forecast Forecast error

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)

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

8000

9000

10000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

50000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

800000

900000

1000000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

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

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

Forecast Error

-100000

-75000

-50000

-25000

0

25000

50000

75000

100000

1 2 3 4 5 6 7 8 9 10 11 12

Et

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

1 2 3 4 5 6 7 8 9 10 11 12

Et

-500

-400

-300

-200

-100

0

100

200

300

400

500

1 2 3 4 5 6 7 8 9 10 11 12

Et

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

1 2 3 4 5 6 7 8 9 10 11 12

Et

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∑t=1 Et

Forecast Error

8000

9000

10000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

50000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

Bias-19000120007300014000

-15000-400067000-2000

-51000-1000011000

-78000

Bias-300-900

-1800-3000-4500-6300-8400

-10800-13500-16500-19800-23400

Bias-200-500-200-500-300-100

0100

-100-400-90

-390

Bias912.61

1091.151350.811386.801109.80

-2332.49648.46435.64

-754.752789.40

-1361.73-920.13

Undershooting

Forecast mean “on target” but not perfect

800000

900000

1000000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

Forecast Error

• Absolute deviation (A)

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

At = |Et|

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

∑n1n

MADn = ∑t=1 At

= 1.25*MAD

Forecast ErrorMAD

190002500037000425003980035000401434375044333440004190945833

MAD300450600750900

1050120013501500165018001950

MAD200250267275260250229213211220228234

MAD913546450347333851

115510371054130315621469

8000

9000

10000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

50000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

800000

900000

1000000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

Not all that large relative to data

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

Forecast Error

Biased (underforecasting)

TS-1.000.481.970.33

-0.38-0.111.67

-0.05-1.15-0.230.26

-1.70

TS-1.00-2.00-3.00-4.00-5.00-6.00-7.00-8.00-9.00

-10.00-11.00-12.00

TS-1.00-2.00-0.75-1.82-1.15-0.400.000.47

-0.47-1.82-0.39-1.67

TS1.002.003.004.003.34

-2.740.560.42

-0.722.14

-0.87-0.63

0

10000

20000

30000

40000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

1 2 3 4 5 6 7 8 9 10 11 12

Tracking Signal

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

1 2 3 4 5 6 7 8 9 10 11 12

Tracking Signal

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

1 2 3 4 5 6 7 8 9 10 11 12

Tracking Signal

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

1 2 3 4 5 6 7 8 9 10 11 12

Tracking Signal

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)

Et

Dt100∑n∑t=1

n

MAPEn =

Forecast Error

MAPE2.112.884.404.874.533.994.674.995.025.014.785.14

MAPE3.755.216.477.588.579.45

10.2410.9611.6212.2212.7813.29

MAPE2.222.883.143.152.962.852.622.422.392.512.612.65

MAPE11.416.394.643.503.365.986.986.186.598.669.058.39

8000

9000

10000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

0

10000

20000

30000

40000

50000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

800000

900000

1000000

1 2 3 4 5 6 7 8 9 10 11 12

Demand

Forecast

Smallest absolute deviation relative to

demand

MAPE < 10 is considered very good

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

∑n Et2MSEn = ∑t=1

1n

VAR = MSE

Measures of Forecast Error

Measure Description

Error

Absolute Error

Et = Ft – Dt

At = |Et|

Mean Squared Error (MSE) MSEn = ∑t=1Et2

Mean Absolute Deviation (MAD)

MADn = ∑t=1At

Mean Absolute Percentage Error (MAPE)

MAPEn =

Tracking signal (TS) TSt = biast / MADt

∑n1n

∑n1n

Et

Dt100∑n∑t=1

n

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

bias_t=SUM($D$4:D4)=SUM($D$4:D5)=SUM($D$4:D6)=SUM($D$4:D7)

biasn = ∑n∑t=1 Et

Forecast Error in Excel

Absolute Error

AbsoluteErrorA_t

=ABS(D4)=ABS(D5)=ABS(D6)=ABS(D7)

At = |Et|

Forecast Error in Excel

Mean Absolute Deviation

MeanAbs Error

MAD_t=AVERAGE($F$4:F4)=AVERAGE($F$4:F5)=AVERAGE($F$4:F6)=AVERAGE($F$4:F7)

∑n1n

MADn = ∑t=1 At

Forecast Error in Excel

Tracking Signal

TrackingSignalTS_t

=E4/G4=E5/G5=E6/G6=E7/G7

TSt = biast / MADt

Forecast Error in Excel

|%Error|

|%Error|t =

|%Error|

|%Error|=ABS(D4/B4)*100=ABS(D5/B5)*100=ABS(D6/B6)*100=ABS(D7/B7)*100

Et

Dt100

Forecast Error in Excel

Mean Absolute Percentage Error

Mean|%Error|MAPE_t

=AVERAGE($I$4:I4)=AVERAGE($I$4:I5)=AVERAGE($I$4:I6)=AVERAGE($I$4:I7)

|%Error|tnMAPEn =

∑n∑t=1

Forecast Error in Excel

Mean Squared Error

MeanSq ErrorMSE_t

=SUMSQ($D$4:D4)/A4=SUMSQ($D$4:D5)/A5=SUMSQ($D$4:D6)/A6=SUMSQ($D$4:D7)/A7

∑n Et2MSEn = ∑t=1

1n