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4 - 1 2011 Pearson Education, Inc. publishing as Prentice Hall

Forecasting

Lectu re 3


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Learn ing Object ives

When you complete this chapter youshould be able to :

1. Understand the three time horizonsand which models apply for each use

2. Explain when to use each of the fourqualitative models

3. Apply the naive, moving average,exponential smoothing, and trendmethods


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Learn ing Object ives

When you complete this chapter youshould be able to :

4. Compute three measures of forecastaccuracy

5. Develop seasonal indices

6. Conduct a regression and correlationanalysis

7. Use a tracking signal


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What is Forecast ing?

Process of predictinga future event

Underlying basis

of all businessdecisions

Production

Inventory Personnel

Facilities

??


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Short-range forecast Up to 1 year, generally less than 3 months

Purchasing, job scheduling, workforcelevels, job assignments, production levels

Medium-range forecast

3 months to 3 years

Sales and production planning, budgeting

Long-range forecast 3+years

New product planning, facility location,research and development

Forecast ing Time Horizons


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Dist ingu ish ing Dif ferences

Medium/long rangeforecasts deal withmore comprehensive issues and supportmanagement decisions regarding

planning and products, plants andprocesses

Short-termforecasting usually employsdifferent methodologies than longer-term

forecasting Short-termforecasts tend to be more

accurate than longer-term forecasts


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Product L i fe Cycle

Best period to

increase market

share

R&D engineering is

critical

Practical to change

price or quality

image

Strengthen niche

Poor time to

change image,

price, or quality

Competitive costs

become critical

Defend market

position

Cost control

critical

Introduction Growth Maturity Decline

Com

panyStrateg

y/Issues

Figure 2.5

Internet search engines

Sales

Drive-throughrestaurants

CD-ROMs

AnalogTVs

iPods

Boeing 787

LCD &plasma TVs

Twitter

Avatars

Xbox 360


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Product L i fe Cycle

Product designanddevelopmentcritical

Frequent

product andprocess designchanges

Short productionruns

High productioncosts

Limited models

Attention toquality

Introduction Growth Maturity Decline

O

MS

trategy/Is

sues

Forecastingcritical

Product andprocessreliability

Competitiveproductimprovementsand options

Increase capacity

Shift towardproduct focus

Enhancedistribution

Standardization

Fewer productchanges, moreminor changes

Optimum

capacity

Increasingstability ofprocess

Long productionruns

Productimprovementand cost cutting

Little productdifferentiation

Costminimization

Overcapacity

in theindustry

Prune line toeliminateitems notreturninggood margin

Reducecapacity

Figure 2.5


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Types o f Forecasts

Economic forecasts

Address business cycleinflation rate,money supply, housing starts, etc.

Technological forecasts

Predict rate of technological progress

Impacts development of new products

Demand forecasts

Predict sales of existing products andservices


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Strateg ic Importance of

Forecast ing

Human ResourcesHiring, training,laying off workers

CapacityCapacity shortages canresult in undependable delivery, lossof customers, loss of market share

Supply Chain ManagementGoodsupplier relations and priceadvantages


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Seven Steps in Forecast ing

1. Determine the use of the forecast

2. Select the items to be forecasted

3. Determine the time horizon of the

forecast

4. Select the forecasting model(s)

5. Gather the data

6. Make the forecast

7. Validate and implement results


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The Realit ies!

Forecasts are seldom perfect

Most techniques assume anunderlying stability in the system

Product family and aggregatedforecasts are more accurate than

individual product forecasts


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Forecast ing App roaches

Used when situation is vague

and little data exist New products

New technology

Involves intuition, experience

e.g., forecasting sales onInternet

Qualitative Methods


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Forecast ing App roaches

Used when situation is stable and

historical data exist Existing products

Current technology

Involves mathematical techniques

e.g., forecasting sales of colortelevisions

Quantitative Methods


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Overview o f Qual i tat ive

Methods

1. Jury of executive opinion

Pool opinions of high-level experts,sometimes augment by statisticalmodels

2. Delphi method

Panel of experts, queried iteratively


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Overview o f Qual i tat ive

Methods

3. Sales force composite

Estimates from individualsalespersons are reviewed forreasonableness, then aggregated

4. Consumer Market Survey

Ask the customer


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Involves small group of high-levelexperts and managers

Group estimates demand by working

together Combines managerial experience with

statistical models

Relatively quick

Group-thinkdisadvantage

Ju ry o f Execu t ive Opinion


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Sales Force Composi te

Each salesperson projects his orher sales

Combined at district and nationallevels

Sales reps know customers wants

Tends to be overly optimistic


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Delph i Method

Iterative groupprocess,continues untilconsensus is

reached

3 types ofparticipants

Decision makers

Staff

Respondents

Staff(Administering

survey)

Decision Makers(Evaluate

responses andmake decisions)

Respondents(People who canmake valuable

judgments)


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Consumer Market Survey

Ask customers about purchasingplans

What consumers say, and whatthey actually do are often different

Sometimes difficult to answer


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Overview of Quanti tative

Approaches1. Naive approach

2. Moving averages3. Exponential

smoothing

4. Trend projection5. Linear regression

time-seriesmodels

associativemodel


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Set of evenly spaced numerical data

Obtained by observing response

variable at regular time periods Forecast based only on past values,

no other variables important

Assumes that factors influencingpast and present will continueinfluence in future

Time Series Forecast ing


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Trend

Seasonal

Cyclical

Random

Time Series Componen ts


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Components of Demand

Deman

dforproductor

service

| | | |

1 2 3 4

Time (years)

Average demandover 4 years

Trendcomponent

Actual demandline

Random variation

Figure 4.1

Seasonal peaks


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Persistent, overall upward ordownward pattern

Changes due to population,technology, age, culture, etc.

Typically several yearsduration

Trend Component


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Regular pattern of up anddown fluctuations

Due to weather, customs, etc.

Occurs within a single year

Seasonal Component

Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52


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Repeating up and down movements

Affected by business cycle,political, and economic factors

Multiple years duration

Often causal or

associativerelationships

Cyc l ical Component

0 5 10 15 20


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Erratic, unsystematic, residualfluctuations

Due to random variation or unforeseenevents

Short durationand nonrepeating

Random Component

M T W T F


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Naive Approach

Assumes demand in nextperiod is the same asdemand in most recent period

e.g., If January sales were 68, thenFebruary sales will be 68

Sometimes cost effective and

efficient Can be good starting point


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MA is a series of arithmetic means

Used if little or no trend

Used often for smoothing

Provides overall impression of dataover time

Mov ing Average Method

Moving average =demand in previous nperiods

n


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Graph o f Moving Average

| | | | | | | | | | | |

J F M A M J J A S O N D

ShedSales

30

28

26

24 22

20

18

16

14

12

10

ActualSales

MovingAverageForecast


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January 10

February 12

March 13

April 16May 19

June 23

July 26

Actual 3-Month Weighted

Month Shed Sales Moving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 141/3

[(3 x 19) + (2 x 16) + (13)]/6 = 17

[(3 x 23) + (2 x 19) + (16)]/6 = 201/2

Weigh ted Mov ing Average

10

12

13

[(3 x 13) + (2 x 12) + (10)]/6 = 121

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Weights Applied Period

3 Last month

2 Two months ago

1 Three months ago

6 Sum of weights


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Increasing nsmooths the forecastbut makes it less sensitive to

changes

Do not forecast trends well

Require extensive historical data

Poten t ial Prob lems With

Moving Average


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Moving Average AndWeigh ted Mov ing Average

30

25

20

15

10

5

Salesdeman

d

| | | | | | | | | | | |


Actualsales

Movingaverage

Weightedmovingaverage

Figure 4.2


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Form of weighted moving average

Weights decline exponentially

Most recent data weighted most

Requires smoothing constant () Ranges from 0 to 1

Subjectively chosen

Involves little record keeping of pastdata

Exponent ial Smoo thing


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New forecast = Last periods forecast

+ (Last periods actual demand

Last periods forecast)

Ft= Ft1+ (A t1- Ft1)

where Ft= new forecast

Ft1= previous forecast

= smoothing (or weighting)

constant (0 1)


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ExamplePredicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant = .20


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Actual demand = 153


New forecast = 142 + .2(153142)


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Actual demand = 153


New forecast = 142 + .2(153142)

= 142 + 2.2= 144.2 144 cars


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Effect o f

Smoo th ing Constants

Weight Assigned to

Most 2nd Most 3rd Most 4th Most 5th MostRecent Recent Recent Recent RecentSmoothing Period Period Period Period PeriodConstant () (1 - ) (1 - )2 (1 - )3 (1 - )4

= .1 .1 .09 .081 .073 .066

= .5 .5 .25 .125 .063 .031


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Impact o f Dif feren t

225

200

175

150 | | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

Demand

= .1

Actualdemand

= .5 Chose high values of

when underlying averageis likely to change

Choose low values ofwhen underlying averageis stable


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Choos ing

The objective is to obtain the mostaccurate forecast no matter thetechnique

We generally do this by selecting themodel that gives us the lowest forecasterror

Forecast error = Actual demand - Forecast value

= A t- Ft


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Common Measu res o f Error

Mean Absolute Percent Error (MAPE)

MAPE =100|Actuali- Forecasti|/Actuali

n

n

i= 1


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Compar ison o f ForecastError

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.75

4 175 173.18 1.82 165.88 9.12

5 190 173.36 16.64 170.44 19.56

6 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62


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1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.75

4 175 173.18 1.82 165.88 9.12

5 190 173.36 16.64 170.44 19.56

6 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD =|deviations|

n

= 82.45/8 = 10.31

For = .10

= 98.62/8 = 12.33

For = .50


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1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.75

4 175 173.18 1.82 165.88 9.12

5 190 173.36 16.64 170.44 19.56

6 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD 10.31 12.33

= 1,526.54/8 = 190.82

For = .10

= 1,561.91/8 = 195.24

For = .50

MSE = (forecast errors)2

n


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1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.75

4 175 173.18 1.82 165.88 9.12

5 190 173.36 16.64 170.44 19.56

6 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD 10.31 12.33

MSE 190.82 195.24

= 44.75/8 = 5.59%

For = .10

= 54.05/8 = 6.76%

For = .50

MAPE = 100|deviationi|/actuali

n

n

i= 1


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1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.75

4 175 173.18 1.82 165.88 9.12

5 190 173.36 16.64 170.44 19.56

6 205 175.02 29.98 180.22 24.78

7 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD 10.31 12.33

MSE 190.82 195.24

MAPE 5.59% 6.76%


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Exponent ial Smoo thing w i th

Trend Adjus tmentWhen a trend is present, exponentialsmoothing must be modified

Forecastincluding (FITt) =trend

Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend


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Exponent ial Smoo thing w i th

Trend Adjus tment

Ft= (A t- 1) + (1 - )(Ft- 1+ Tt- 1)

Tt= b(Ft - Ft- 1) + (1 - b)Tt- 1Step 1: Compute F

t

Step 2: Compute Tt

Step 3: Calculate the forecast FITt= Ft+ Tt


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Seasonal Variations In Data

1. Find average historical demand for each season

2. Compute the average demand over all seasons

3. Compute a seasonal index for each season

4. Estimate next years total demand

5. Divide this estimate of total demand by the

number of seasons, then multiply it by theseasonal index for that season

Steps in the process:


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Seasonal Index Examp le

Jan 80 85 105 90 94

Feb 70 85 85 80 94

Mar 80 93 82 85 94

Apr 90 95 115 100 94May 113 125 131 123 94

Jun 110 115 120 115 94

Jul 100 102 113 105 94

Aug 88 102 110 100 94

Sept 85 90 95 90 94

Oct 77 78 85 80 94

Nov 75 72 83 80 94

Dec 82 78 80 80 94

Demand Average Average SeasonalMonth 2007 2008 2009 2007-2009 Monthly Index


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Jan 80 85 105 90 94

Feb 70 85 85 80 94

Mar 80 93 82 85 94

Apr 90 95 115 100 94May 113 125 131 123 94

Jun 110 115 120 115 94

Jul 100 102 113 105 94

Aug 88 102 110 100 94

Sept 85 90 95 90 94

Oct 77 78 85 80 94

Nov 75 72 83 80 94

Dec 82 78 80 80 94


0.957

Seasonal index =

Average 2007-2009 monthly demand

Average monthly demand

= 90/94 = .957


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Jan 80 85 105 90 94 0.957

Feb 70 85 85 80 94 0.851

Mar 80 93 82 85 94 0.904

Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309

Jun 110 115 120 115 94 1.223

Jul 100 102 113 105 94 1.117

Aug 88 102 110 100 94 1.064

Sept 85 90 95 90 94 0.957

Oct 77 78 85 80 94 0.851

Nov 75 72 83 80 94 0.851

Dec 82 78 80 80 94 0.851



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Jan 80 85 105 90 94 0.957

Feb 70 85 85 80 94 0.851

Mar 80 93 82 85 94 0.904

Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309

Jun 110 115 120 115 94 1.223

Jul 100 102 113 105 94 1.117

Aug 88 102 110 100 94 1.064

Sept 85 90 95 90 94 0.957

Oct 77 78 85 80 94 0.851

Nov 75 72 83 80 94 0.851

Dec 82 78 80 80 94 0.851


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,20012

Forecast for 2010


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140

130

120

110

100

90

80

70 | | | | | | | | | | | |


Time

Demand

2010 Forecast

2009 Demand

2008 Demand

2007 Demand


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San Diego Hosp ital

10,200

10,000

9,800

9,600

9,400

9,200

9,000 | | | | | | | | | | | |

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

InpatientDa

ys

9530

9551

9573

9594

9616

9637

9659

9680

9702

9724

97459766

Figure 4.6

Trend Data


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San Diego Hosp ital

1.06

1.04

1.02

1.00

0.98

0.96

0.940.92 | | | | | | | | | | | |


Month

In

dexforInpatientDays 1.04

1.021.01

0.99

1.031.04

1.00

0.98

0.97

0.99

0.970.96

Figure 4.7

Seasonal Indices


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San Diego Hosp ital

10,200

10,000

9,800

9,600

9,400

9,200

9,000 | | | | | | | | | | | |


Month

InpatientDa

ys

Figure 4.8

9911

9265

9764

9520

9691

9411

9949

9724

9542

9355

10068

9572

Combined Trend and Seasonal Forecast


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Associat ive Forecast ing

Used when changes in one or moreindependent variables can be used to predict

the changes in the dependent variable

Most common technique is linearregression analysis

We apply this technique just as we didin the time series example


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Associat ive Forecast ing

Forecasting an outcome based onpredictor variables using the least squarestechnique

y= a+ bx^

where y = computed value of the variable tobe predicted (dependent variable)

a = y-axis intercept

b = slope of the regression line

x = the independent variable though topredict the value of the dependentvariable

^


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Forecast ing in the Serv ice

Sector Presents unusual challenges

Special need for short term records

Needs differ greatly as function ofindustry and product

Holidays and other calendar events

Unusual events

F t F d R t t


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Fast Food Restauran tForecast

20%

15%

10%

5%

11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11

(Lunchtime) (Dinnertime)

Hour of day

Percentageofsales

Figure 4.12


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FedEx Call Cen ter Forecast

Figure 4 12

12%

10%

8%

6%

4%

2%

0%

Hour of dayA.M. P.M.

2 4 6 8 10 12 2 4 6 8 10 12

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