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Chapter 13

Forecasting

Demand Management

Qualitative Forecasting Methods

Simple & Weighted Moving Average Forecasts

Exponential Smoothing

Simple Linear Regression

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Types of Forecasts

Qualitative (Judgmental)

Quantitative– Time Series Analysis– Causal Relationships– Simulation

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Delphi Method

4. Summarize again, refining forecasts and conditions, and again develop new questions.

5. Repeat Step 4 if necessary. Distribute the final results to all participants.

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Components of Demand

1 2 3 4

x

x xx

xx

x xx

xx x x x

xxxxxx x x

xx

x x xx

xx

xx

x

xx

xx

xx

xx

xx

xx

x

x

Year

Sal

es

What’s going on here?

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A Trend is Worth Noting

Start by identifying the trend

What is the trend in the sales of personal computers?

Are there any seasonal effects, cyclical factors or other predicted events that might affect the sales of personal computers?

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Delphi Method

l. Choose the experts to participate. There should be a variety of knowledgeable people in different areas.

2. Through a questionnaire (or E-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants.

3. Summarize the results and redistribute them to the participants along with appropriate new questions.

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Judgmental Forecasting ApplicationsSmall and Large Firms

Technique

LowSales

< $100M

HighSales

> $500M

Manager’s opinion 40.7% 39.6%Jury of executive opinion 40.7% 41.6%Sales force composite 29.6% 35.4%Number of Firms 27 48

Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100.

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Quantitative Forecasting ApplicationsSmall and Large Firms

Technique

LowSales

< $100M

HighSales

> $500M

Moving average 29.6% 29.2%Straight line projection 14.8% 14.6%Naive 18.5% 14.6%Exponential smoothing 14.8% 20.8%Regression 22.2% 27.1%Simulation 3.7% 10.4%Classical decomposition 3.7% 8.3%Box-Jenkins 3.7% 6.3%Number of Firms 27 48

Source: Nada Sanders and Karl Mandrodt (1994) “Practitioners Continue to Rely on Judgmental Forecasting Methods Instead of Quantitative Methods,” Interfaces, vol. 24, no. 2, pp. 92-100.

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Time Series Analysis

Pick a model based on:

1. Time horizon to forecast

2. Data availability

3. Accuracy required

4. Size of forecasting budget

5. Availability of qualified personnel

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Forecast Errors

MAD = A - F

n

t tt=1

n

Study the formula for a moment

Now, what does MAD tell you?

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Example--MAD

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

Determine the MAD for the four forecast periods

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Solution

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

40

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Simple Moving Average

Week Demand1 6502 6783 7204 7855 8596 9207 8508 7589 89210 92011 78912 844

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

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

Let’s develop 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

Week Demand 3-Week 6-Week1 6502 6783 7204 785 682.675 859 727.676 920 788.007 850 854.67 768.678 758 876.33 802.009 892 842.67 815.3310 920 833.33 844.0011 789 856.67 866.5012 844 867.00 854.83

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500

600

700

800

900

1000

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

Week

Demand Demand

3-Week

6-Week

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Hill

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In-Class Exercise

Week Demand1 8202 7753 6804 6555 6206 6007 575

Develop 3-week and 5-week moving average forecasts for demand.

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

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In-Class Exercise (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

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Weighted Moving Average

F = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t-n

w = 1ii=1

n

Determine the 3-period weighted moving average forecast for period 4.

Weights: t-1 .5t-2 .3t-3 .2

Week Demand1 6502 6783 7204

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Solution

Week Demand Forecast1 6502 6783 7204 693.4

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In-Class Exercise

Determine the 3-period weighted moving average forecast for period 5.

Weights: t-1 .7t-2 .2t-3 .1

Week Demand1 8202 7753 6804 655

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Solution

Week Demand Forecast1 8202 7753 6804 6555 672

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Exponential Smoothing

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)

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Exponential Smoothing Example

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 77510

Determine exponential smoothing forecasts for periods 2-10 using =.10 and =.60.

Let F1=D1

Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 820.004 655 801.95 817.305 750 787.26 808.096 802 783.53 795.597 798 785.38 788.358 689 786.64 786.579 775 776.88 786.6110 776.69 780.77

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Effect of on Forecast

500

600

700

800

900

1 2 3 4 5 6 7 8 9 10

Week

Demand Demand

0.1

0.6

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In-Class Exercise

Determine exponential smoothing forecasts for periods 2-5 using =.50

Let F1=D1

Week Demand1 8202 7753 6804 6555

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In-Class Exercise (Solution)

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

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Simple Linear Regression Model

b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope

Yt = a + bx

0 1 2 3 4 5 x (weeks)

Y

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Calculating a and b

a = y - bx

b =xy - n(y)(x)

x - n(x2 2

)

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Regression Equation Example

Week Sales1 1502 1573 1624 1665 177

Develop a regression equation to predict sales based on these five points.

Week Week*Week Sales Week*Sales1 1 150 1502 4 157 3143 9 162 4864 16 166 6645 25 177 8853 55 162.4 2499

Average Sum Average Sum

b =xy - n(y)(x)

x - n(x=

2499 - 5(162.4)(3)=

a = y - bx = 162.4 - (6.3)(3) =

2 2

) ( )55 5 9

63

106.3

143.538©The McGraw-Hill Companies,

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y = 143.5 + 6.3t

135140145150155

160165170175180

1 2 3 4 5

Period

Sales

Sales

Forecast

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