1 Forecasting. 2 Demand Management Qualitative Forecasting Methods Simple & Weighted Moving Average Forecasts Exponential Smoothing Simple Linear Regression.

1

Forecasting

2

Demand Management Qualitative Forecasting Methods Simple & Weighted Moving

Average Forecasts Exponential Smoothing Simple Linear Regression

OBJECTIVES

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Because there must be a better way!

Why study demand management & forecasting?

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Demand Management

B(1) C(2)

D(2) E(1) D(3) F(2)

How does a firm actively or passively manage independent demand? Outside it’s dependence on independent demand, how can a firm

control dependent demand?

A

Independent Demand:Finished Goods

Dependent Demand:Raw Materials, Component parts,Sub-assemblies, etc.

CUSTOMER DEMAND

5D

em

an

dD

em

an

d

Time

Time

Decomposition of a Time Series

Components: Average demand for a

period of time, level

Trend

Seasonal element

Cyclical elements

Random variation

Autocorrelation

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Decomposition of FedEx Share Price

Original

Seasonal

Random

Cyclical

Trend

Level

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Types of Forecasts

Qualitative (Judgmental)

Quantitative– Time Series Analysis– Causal Relationships– Simulation

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Qualitative Methods

Grass Roots

Market Research

Panel Consensus

Executive Judgment

Historical analogy

Delphi Method

Qualitative

Methods

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Quantitative Methods

Time Series Analysis Time series forecasting models try to

predict the future based on past data You can pick models 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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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

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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

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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

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13

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

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Simple Moving Average Problem (2) Data

Week Demand1 8202 7753 6804 6555 6206 6007 575

Question: What is the 3 and 5 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 and 5 week moving average forecast for this data?

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

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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

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Weighted Moving Average Formula

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

w = 1ii=1

n

w = 1ii=1

n

While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods

While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods

wt = weight given to time period “t” occurrence (weights must add to one)

wt = weight given to time period “t” occurrence (weights must add to one)

The formula for the moving average is:The formula for the moving average is:

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Weighted Moving Average Problem (1) Data

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

Week Demand1 6502 6783 7204

Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?

Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?

Note: weights place more emphasis on the most recent data, that is time period “t-1”weights must total “1”weight assignment is based on experience over time

Note: weights place more emphasis on the most recent data, that is time period “t-1”weights must total “1”weight assignment is based on experience over time

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Weighted Moving Average Problem (1) Solution

Week Demand Forecast1 6502 6783 7204 693.4

F4 = 0.5(720)+0.3(678)+0.2(650)=693.4

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Weighted Moving Average Problem

(2) Data

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

Week Demand1 8202 7753 6804 655

Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?

Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?

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Weighted Moving Average Problem (2) Solution

Week Demand Forecast1 8202 7753 6804 6555 672

F5 = (0.7)(655)+(0.2)(680)+(0.1)(775)= 672

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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 alueForecast vF

:Where

1-t

1-t

t

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Exponential Smoothing Problem (1) Data

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775

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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

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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.

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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

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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

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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)=797.5

F4=797.5+(0.5)(680-797.5)=738.75

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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

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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?

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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

Is the error in this forecast within normal range?

10 x 3.75sd = 37.5 Yes, no single abs error exceeds 37.5.

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Tracking Signal Formula

The Tracking Signal or TS is a measure that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand.

Depending on the number of MAD’s selected, the TS can be used like a quality control chart indicating when the model is generating too much error in its forecasts.

The TS formula is:

TS =RSFE

MAD=

Running sum of forecast errors

Mean absolute deviationTS =

RSFE

MAD=

Running sum of forecast errors

Mean absolute deviation

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Simple Linear Regression Model

Yt = a + bx0 1 2 3 4 5 x (Time)

YThe simple linear regression model seeks to fit a line through various data over time

The simple linear regression model seeks to fit a line through various data over time

Is the linear regression modelIs the linear regression model

a

Yt is the regressed forecast value or dependent variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. 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.

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Simple Linear Regression Formulas

for Calculating “a” and “b”

a = y - bx

b =xy - n(y)(x)

x - n(x2 2

)

a = y - bx

b =xy - n(y)(x)

x - n(x2 2

)

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Simple Linear Regression Problem Data

Week Sales1 1502 1573 1624 1665 177

Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?

Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?

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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

143.5

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

143.5

Answer: First, using the linear regression formulas, we can compute “a” and “b”

Answer: First, using the linear regression formulas, we can compute “a” and “b”

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35

Yt = 143.5 + 6.3x

180

Period

135140145150155160165170175

1 2 3 4 5

Sal

es

Sales

Forecast

The resulting regression model is:

Now if we plot the regression generated forecasts against the actual sales we obtain the following chart:

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Yt = 143.5+(6.3)(5)

Yt = 143.5+31.5

Yt = 175