Demand Managementand

Forecasting

Chapter 15 15

Focus on two short-range forecasting techniques– Moving Average– Exponential Smoothing

OBJECTIVES

15-2

Simple Moving Average Formula

F = A + A + A +...+A

ntt-1 t-2 t-3 t-nF =

A + A + A +...+A

ntt-1 t-2 t-3 t-n

• The simple moving average model assumes an average is a good estimator of future behavior

• The formula for the simple moving average is:

Ft = Forecast for the coming period N = Number of periods to be averagedA t-1 = Actual occurrence in the past period for up to “n” periods

15-3

Simple Moving Average Problem (1)

Week Demand1 6502 6783 7204 7855 8596 9207 8508 7589 892

10 92011 78912 844

F = A + A + A +...+A

ntt-1 t-2 t-3 t-nF =

A + A + A +...+A

ntt-1 t-2 t-3 t-n

Question: What are the 3-week and 6-week moving average forecasts for demand?

Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts

Question: What are the 3-week and 6-week moving average forecasts for demand?

Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts

15-4

Week Demand 3-Week 6-Week1 6502 6783 7204 785 682.675 859 727.676 920 788.007 850 854.67 768.678 758 876.33 802.009 892 842.67 815.33

10 920 833.33 844.0011 789 856.67 866.5012 844 867.00 854.83

F4=(650+678+720)/3

=682.67F7=(650+678+720 +785+859+920)/6

=768.67

Calculating the moving averages gives us:

©The McGraw-Hill Companies, Inc., 2004

15-5

500

600

700

800

900

1000

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

Week

Dem

and

Demand

3-Week

6-Week

Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example

Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example

Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother

Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother

15-6

Simple Moving Average Problem (2) Data

Week Demand1 8202 7753 6804 6555 6206 6007 575

Question: What is the 3 week moving average forecast for this data?

Assume you only have 3 weeks and 5 weeks of actual demand data for the respective forecasts

Question: What is the 3 week moving average forecast for this data?

Assume you only have 3 weeks and 5 weeks of actual demand data for the respective forecasts

15-7

Simple Moving Average Problem (2) Solution

Week Demand 3-Week 5-Week1 8202 7753 6804 655 758.335 620 703.336 600 651.67 710.007 575 625.00 666.00

F4=(820+775+680)/3

=758.33F6=(820+775+680 +655+620)/5 =710.00

15-8

Exponential Smoothing Model

• Premise: The most recent observations might have the highest predictive value

• Therefore, we should give more weight to the more recent time periods when forecasting

Ft = Ft-1 + (At-1 - Ft-1)Ft = Ft-1 + (At-1 - Ft-1)

constant smoothing Alpha

period epast t tim in the occurance ActualA

period past time 1in alueForecast vF

period t timecoming for the lueForcast vaF

:Where

1-t

1-t

t

15-9

Exponential Smoothing Problem (1) Data

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775

10

Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using =0.10 and =0.60?

Assume F1=D1

Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using =0.10 and =0.60?

Assume F1=D1

15-10

Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

15-11

Exponential Smoothing Problem (1) Plotting

500

600

700

800

900

1 2 3 4 5 6 7 8 9 10

Week

Dem

and

Demand

0.1

0.6

Note how that the smaller alpha results in a smoother line in this example

Note how that the smaller alpha results in a smoother line in this example

15-12

Exponential Smoothing Problem (2) Data

Question: What are the exponential smoothing forecasts for periods 2-5 using a =0.5?

Assume F1=D1

Question: What are the exponential smoothing forecasts for periods 2-5 using a =0.5?

Assume F1=D1

Week Demand1 8202 7753 6804 6555

15-13

Exponential Smoothing Problem (2) Solution

Week Demand 0.51 820 820.002 775 820.003 680 797.504 655 738.755 696.88

F1=820+(0.5)(820-820)=820 F3=820+(0.5)(775-820)=797.75

15-14

The MAD Statistic to Determine Forecasting Error

MAD = A - F

n

t tt=1

n

MAD =

A - F

n

t tt=1

n

1 MAD 0.8 standard deviation

1 standard deviation 1.25 MAD

• The ideal MAD is zero which would mean there is no forecasting error

• The larger the MAD, the less the accurate the resulting model

15-15

MAD Problem Data

Month Sales Forecast1 220 n/a2 250 2553 210 2054 300 3205 325 315

Question: What is the MAD value given the forecast values in the table below?

Question: What is the MAD value given the forecast values in the table below?

15-16

MAD Problem Solution

MAD = A - F

n=

40

4= 10

t tt=1

n

MAD =

A - F

n=

40

4= 10

t tt=1

n

Month Sales Forecast Abs Error1 220 n/a2 250 255 53 210 205 54 300 320 205 325 315 10

40

Note that by itself, the MAD only lets us know the mean error in a set of forecasts

Note that by itself, the MAD only lets us know the mean error in a set of forecasts

15-17

MAPE

• Mean Absolute Percentage Error (MAPE) is another measure often used to evaluate forecasting accuracy

n

actual

forecastactual

100MAPE

n

1i i

ii

A MAPE of under 8% is acceptable for most applications

Computing MAD and MAPE: Problem (1)

Time ACTUAL FORECAST ERROR ABS ERROR APE1 820 820.00 --- --- ---2 775 820.00 -45.00 45.00 5.813 680 815.50 -135.50 135.50 19.934 655 801.95 -146.95 146.95 22.445 750 787.26 -37.26 37.26 4.976 802 783.53 18.47 18.47 2.307 798 785.38 12.62 12.62 1.588 689 786.64 -97.64 97.64 14.179 775 776.88 -1.88 1.88 0.2410 776.69

61.91 8.93MAD MAPE

Question Bowl

Which of the following is an example of a “Time Series Analysis” type of forecasting technique or model?

a. Simulationb. Exponential smoothingc. Panel consensusd. All of the abovee. None of the above

Answer: b. Exponential smoothing (Also includes Simple Moving Average, Weighted Moving Average, Regression Analysis, Box Jenkins, Shiskin Time Series, and Trend Projections.)

15-20

Question Bowl

Which of the following are reasons why the Exponential Smoothing model has been a well accepted forecasting methodology?

a. It is accurateb. It is easy to usec. Computer storage requirements

are smalld. All of the abovee. None of the above

Answer: d. All of the above

15-21

Question Bowl

The value for alpha or α must be between which of the following when used in an Exponential Smoothing model?

a. 1 to 10b. 1 to 2c. 0 to 1d. -1 to 1e. Any number at all

Answer: c. 0 to 1

15-22

Question Bowl

Which of the following are sources of error in forecasts?

a. Biasb. Randomc. Employing the wrong trend

lined. All of the abovee. None of the above

Answer: d. All of the above

15-23

Question Bowl

Which of the following would be the “best” MAD values in an analysis of the accuracy of a forecasting model?

a. 1000b. 100c. 10d. 1e. 0

Answer: e. 0

15-24

1-25

End of Chapter 15

15-25