Operations Management, 10th Edition chapter 4

5/21/2018 Operations Management, 10th Edition chapter 4

1/114

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

4 Forecasting

PowerPoint presentation to accompanyHeizer and RenderOperations Management, 10ePrinciples of Operations Management, 8e

PowerPoint slides by Jeff Heyl


2/114


Outl ine

Global Company Profile: DisneyWorld

What Is Forecasting?

Forecasting Time Horizons

The Influence of Product Life Cycle

Types Of Forecasts


3/114


Outl ine Con t inued

The Strategic Importance ofForecasting

Human Resources

Capacity

Supply Chain Management

Seven Steps in the ForecastingSystem


4/114



Forecasting Approaches

Overview of Qualitative Methods

Overview of Quantitative Methods

Time-Series Forecasting

Decomposition of a Time Series

Naive Approach


5/114



Time-Series Forecasting (cont.)

Moving Averages

Exponential Smoothing

Exponential Smoothing with TrendAdjustment

Trend Projections

Seasonal Variations in Data

Cyclical Variations in Data


6/114



Associative Forecasting Methods:Regression and CorrelationAnalysis

Using Regression Analysis forForecasting

Standard Error of the Estimate

Correlation Coefficients forRegression Lines

Multiple-Regression Analysis


7/1144 - 7 2011 Pearson Education, Inc. publishing as Prentice Hall


Monitoring and ControllingForecasts

Adaptive Smoothing

Focus Forecasting

Forecasting in the Service Sector



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



Learn ing Object ives

When you complete this chapter youshould be able to :

4. Compute three measures of forecastaccuracy

5. Develop seasonal indexes

6. Conduct a regression and correlationanalysis

7. Use a tracking signal



Forecast ing at Disney World

Global portfolio includes parks in HongKong, Paris, Tokyo, Orlando, andAnaheim

Revenues are derived from peoplehowmany visitors and how they spend theirmoney

Daily management report contains onlythe forecast and actual attendance ateach park




Disney generates daily, weekly, monthly,annual, and 5-year forecasts

Forecast used by labor management,maintenance, operations, finance, andpark scheduling

Forecast used to adjust opening times,

rides, shows, staffing levels, and guestsadmitted


12/114



20% of customers come from outside theUSA

Economic model includes grossdomestic product, cross-exchange rates,arrivals into the USA

A staff of 35 analysts and 70 field people

survey 1 million park guests, employees,and travel professionals each year


13/114



Inputs to the forecasting model includeairline specials, Federal Reservepolicies, Wall Street trends,

vacation/holiday schedules for 3,000school districts around the world

Average forecast error for the 5-yearforecast is 5%

Average forecast error for annualforecasts is between 0% and 3%


14/114


What is Forecast ing?

Process of predictinga future event

Underlying basis

of all businessdecisions

Production

Inventory

Personnel

Facilities

??


15/114


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


16/114


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


17/114


In f luence of Product L i fe

Cycle

Introduction and growth require longerforecasts than maturity and decline

As product passes through life cycle,forecasts are useful in projecting

Staffing levels

Inventory levels

Factory capacity

IntroductionGrowthMaturityDecline


18/114


Product L i fe Cycle

Best period toincrease marketshare

R&D engineering iscritical

Practical to changeprice or qualityimage

Strengthen niche

Poor time tochange image,price, or quality

Competitive costsbecome criticalDefend marketposition

Cost controlcritical

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


19/114


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

capacityIncreasingstability ofprocess

Long productionruns

Productimprovementand cost cutting

Little productdifferentiation

Costminimization

Overcapacity

in theindustry

Prune line toeliminateitems notreturninggood margin

Reducecapacity

Figure 2.5


20/114


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 and

services


21/114


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


22/114


Seven Steps in Forecast ing

1. Determine the use of the forecast2. Select the items to be forecasted

3. Determine the time horizon of the

forecast4. Select the forecasting model(s)

5. Gather the data

6. Make the forecast

7. Validate and implement results


23/114


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


24/114


Forecast ing App roaches

Used when situation is vague

and little data exist New products

New technology

Involves intuition, experience e.g., forecasting sales on

Internet

Qualitative Methods


25/114


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 color

televisions

Quantitative Methods


26/114


Overview o f Qual i tat ive

Methods1. Jury of executive opinion

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

2. Delphi method

Panel of experts, queried iteratively


27/114


Overview o f Qual i tat ive

Methods3. Sales force composite

Estimates from individualsalespersons are reviewed forreasonableness, then aggregated

4. Consumer Market Survey

Ask the customer


28/114


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


29/114


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


30/114


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)


31/114


Consumer Market Survey

Ask customers about purchasingplans

What consumers say, and whatthey actually do are often different

Sometimes difficult to answer


32/114


Overview of Quanti tative

Approaches1. Naive approach

2. Moving averages

3. Exponentialsmoothing

4. Trend projection5. Linear regression

time-seriesmodels

associativemodel


33/114


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


34/114


Trend

Seasonal

Cyclical

Random

Time Series Componen ts


35/114


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


36/114


Persistent, overall upward ordownward pattern

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

Typically several yearsduration

Trend Component


37/114


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 28-31

Year Quarter 4Year Month 12Year Week 52


38/114


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


39/114


Erratic, unsystematic, residualfluctuations

Due to random variation or unforeseenevents

Short durationand nonrepeating

Random Component

M T W T F


40/114


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


41/114


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


42/114


January 10

February 12March 13April 16May 19

June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

(12 + 13 + 16)/3 = 13 2/3

(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

Mov ing Average Examp le

10

1213

(10+ 12+ 13)/3 = 11 2/3


43/114


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


44/114


Used when some trend might bepresent

Older data usually less important

Weights based on experience andintuition

Weigh ted Mov ing Average

Weightedmoving average =

(weight for period n)

x (demand in period n)

weights


45/114


January 10February 12March 13

April 16May 19June 23July 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

101213

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

/6

Weights Applied Period

3 Last month2 Two months ago1 Three months ago

6 Sum of weights


46/114


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


47/114


Moving Average AndWeigh ted Mov ing Average

30

25

20

15

10

5

Salesdeman

d

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


Actualsales

Movingaverage

Weightedmovingaverage

Figure 4.2


48/114


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 past

data

Exponent ial Smoo thing


49/114



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)


50/114



ExamplePredicted demand = 142 Ford MustangsActual demand = 153

Smoothing constant = .20


51/114





New forecast = 142 + .2(153142)


52/114





New forecast = 142 + .2(153142)

= 142 + 2.2= 144.2 144 cars


53/114


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


54/114


Impact o f Dif feren t

225

200

175

150 | | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

Demand

= .1

Actualdemand

= .5


55/114


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 of when underlying averageis stable


56/114


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


57/114


Common Measu res o f Error

Mean Absolute Deviation (MAD)

MAD =

|Actual - Forecast|

n

Mean Squared Error (MSE)

MSE =(Forecast Errors)2

n


58/114


Common Measu res o f Error

Mean Absolute Percent Error (MAPE)

MAPE =100|Actuali- Forecasti|/Actuali

n

n

i= 1


59/114


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 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 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


60/114





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 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 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


61/114





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 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 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 98.62MAD 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

C i f F


62/114





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 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 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 98.62MAD 10.31 12.33MSE 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

C i f F t


63/114





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 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 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 98.62MAD 10.31 12.33MSE 190.82 195.24

MAPE 5.59% 6.76%


64/114


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


65/114


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- 1

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt= Ft+ Tt


66/114


Exponent ial Smoo thing w ithTrend Adjustment Example

ForecastActual Smoothed Smoothed Including

Month(t) Demand (A t) Forecast, Ft Trend, Tt Trend, FITt

1 12 11 2 13.00

2 173 204 195 246 21

7 318 289 36

10

Table 4.1


67/114





1 12 11 2 13.00

2 173 204 195 246 21

7 318 289 36

10

Table 4.1

F2 = A 1+ (1 - )(F1+ T1)F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2


68/114





1 12 11 2 13.00

2 17 12.803 204 195 246 21

7 318 289 36

10

Table 4.1

T2 = b(F2- F1) + (1 - b)T1T2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2


69/114





1 12 11 2 13.00

2 17 12.80 1.923 204 195 246 21

7 318 289 36

10

Table 4.1

FIT2 = F

2+ T

2

FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FITfor Month 2


70/114





1 12 11 2 13.00

2 17 12.80 1.92 14.723 204 195 246 21

7 318 289 36

10

Table 4.1

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.89

24.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16


71/114



Figure 4.3

| | | | | | | | |

1 2 3 4 5 6 7 8 9

Time (month)

Productdem

and

35

30

25

20

15

10

5

0

Actual demand (A t)

Forecast including trend (FITt)

with = .2 and b= .4


72/114


Trend Project ions

Fitting a trend line to historical data pointsto project into the medium to long-range

Linear trends can be found using the leastsquares technique

y= a+ bx^

where y = computed value of the variable to

be predicted (dependent variable)a = y-axis interceptb = slope of the regression linex = the independent variable

^


73/114


Least Squares Method

Time period

Value

sofDepende

ntVariable

Figure 4.4

Deviation1

(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation(y-value)

Trend line, y= a+ bx^


74/114



Time period

Value

sofDepende

ntVariable

Figure 4.4

Deviation1

(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation(y-value)

Trend line, y= a+ bx^

Least squares methodminimizes the sum of the

squared errors (deviations)


75/114



Equations to calculate the regression variables

b =Sxy - nxy

Sx2- nx2

y = a + bx^

a = y - bx


76/114


Least Squares Example

b= = = 10.54xy- nxy

x2- nx2

3,063 - (7)(4)(98.86)

140 - (7)(42)

a= y- bx= 98.86 - 10.54(4) = 56.70

Time Electrical Power

Year Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 360

2007 5 105 25 5252008 6 142 36 8522009 7 122 49 854

x= 28 y= 692 x2= 140 xy= 3,063x= 4 y= 98.86


77/114


b= = = 10.54xy- nxy

x2- nx2

3,063 - (7)(4)(98.86)

140 - (7)(42)

a= y- bx= 98.86 - 10.54(4) = 56.70

Time Electrical Power

Year Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 360

2007 5 105 25 5252008 6 142 36 8522009 7 122 49 854

x= 28 y= 692 x2= 140 xy= 3,063x= 4 y= 98.86


The trend line is

y= 56.70 + 10.54x^


78/114



| | | | | | | | |2003 2004 2005 2006 2007 2008 2009 2010 2011

160

150

140

130

120 110

100

90

80

70

60

50

Year

Powerdemand

Trend line,y= 56.70 + 10.54x^


79/114


Seasonal Variations In Data

The multiplicative

seasonal modelcan adjust trenddata for seasonalvariations indemand


80/114


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:

S


81/114


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

S l I d E l


82/114



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

S l I d E l


83/114



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


S l I d E l


84/114



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

S l I d E l


85/114



140

130

120

110

100

90

80

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


Time

Demand

2010 Forecast2009 Demand

2008 Demand

2007 Demand

San Diego Hosp ital


86/114


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

InpatientDays

9530

9551

9573

9594

9616

9637

9659

9680

9702

9724

97459766

Figure 4.6

Trend Data

San Diego Hosp ital


87/114


San Diego Hosp ital

1.06

1.04

1.02

1.00

0.98

0.96

0.94

0.92 | | | | | | | | | | | |


Month

IndexforInpatie

ntDays 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

San Diego Hosp ital


88/114


San Diego Hosp ital

10,200

10,000

9,800

9,600

9,400

9,200

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


Month

InpatientDays

Figure 4.8

9911

9265

9764

9520

9691

9411

9949

9724

9542

9355

10068

9572

Combined Trend and Seasonal Forecast

A i t i F t i


89/114


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

A i t i F t i


90/114



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

^



91/114


Associat ive Forecast ingExample

Sales Area Payroll($ millions), y ($ billions), x

2.0 13.0 3

2.5 42.0 22.0 13.5 7

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

Sales

Area payroll



92/114



Sales, y Payroll, x x2 xy

2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.0

2.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5

y= 15.0 x= 18 x2= 80 xy= 51.5

x= x/6 = 18/6 = 3

y= y/6 = 15/6 = 2.5

b= = = .25xy - nxy

x2- nx2

51.5 - (6)(3)(2.5)80 - (6)(32)

a= y- bx = 2.5 - (.25)(3) = 1.75



93/114



y= 1.75 + .25x^ Sales = 1.75 + .25(payroll)

If payroll next year

is estimated to be$6 billion, then:

Sales = 1.75 + .25(6)Sales = $3,250,000

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

N

odels

sales

Area payroll

3.25

Standard Erro r o f the


94/114


Standard Erro r o f theEst imate

A forecast is just a point estimate of afuture value

This point is

actually themean of aprobabilitydistribution

Figure 4.9

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

N

odels

sales

Area payroll

3.25



95/114



where y = y-value of each data point

yc = computed value of the dependentvariable, from the regressionequation

n = number of data points

Sy,x=(y - yc)

2

n - 2



96/114



Computationally, this equation isconsiderably easier to use

We use the standard error to set upprediction intervals around thepoint estimate

Sy,x=y2- ay - bxy

n - 2



97/114



4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

No

dels

sales

Area payroll

3.25

Sy,x= =y2- ay - bxy

n - 2

39.5 - 1.75(15) - .25(51.5)

6 - 2

Sy,x= .306

The standard errorof the estimate is

$306,000 in sales

Correlat ion


98/114


How strong is the linearrelationship between the variables?

Correlation does not necessarily

imply causality!

Coefficient of correlation, r,measures degree of association

Values range from -1 to +1

Correlat ion

C l t i C ff i i t


99/114


Correlat ion Coeff ic ient

r =nSxy- SxSy

[nSx2- (Sx)2][nSy2- (Sy)2]

C l t i C ff i i t

y y


100/114


Correlat ion Coeff ic ient

r =nSxy- SxSy

[nSx2- (Sx)2][nSy2- (Sy)2]

y

x(a) Perfect positivecorrelation:

r= +1

y

x(b) Positivecorrelation:

0 < r< 1

y

x(c) No correlation:r= 0

y

x(d) Perfect negativecorrelation:r= -1

Correlat ion


101/114


Coefficient of Determination, r2,measures the percent of change inypredicted by the change in x

Values range from 0 to 1 Easy to interpret

Correlat ion

For the Nodel Construction example:

r = .901

r2= .81

M lt i l R i


102/114


Mult ip le Regress ion

Analys isIf more than one independent variable is to be

used in the model, linear regression can beextended to multiple regression to

accommodate several independent variables

y = a + b1x1+ b2x2^

Computationally, this is quitecomplex and generally done on the

computer

M lt i l R i


103/114


Mult ip le Regress ion

Analys is

y = 1.80 + .30x1- 5.0x2^

In the Nodel example, including interest rates inthe model gives the new equation:

An improved correlation coefficient of r= .96means this model does a better job of predicting

the change in construction sales

Sales= 1.80 + .30(6) - 5.0(.12) = 3.00Sales= $3,000,000

Moni tor ing and Con tro ll ing


104/114


Measures how well the forecast ispredicting actual values

Ratio of cumulative forecast errors tomean absolute deviation (MAD)

Good tracking signal has low values If forecasts are continually high or low, the

forecast has a bias error


ForecastsTracking Signal



105/114



Forecasts

Trackingsignal

Cumulative errorMAD

=

Trackingsignal =

(Actual demand inperiod i-

Forecast demandin period i)

|Actual - Forecast|/n)

Track ing Signal


106/114


Track ing Signal

Tracking signal

+

0 MADs

Upper control limit

Lower control limit

Time

Signal exceeding limit

Acceptablerange

Track ing Signal Example


107/114



CumulativeAbsolute Absolute

Actual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD

1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2



108/114


CumulativeAbsolute Absolute

Actual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD

1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2


TrackingSignal

(Cumm Error/MAD)

-10/10 = -1-15/7.5 = -2

0/10 = 0-10/10 = -1

+5/11 = +0.5+35/14.2 = +2.5

The variation of the tracking signalbetween -2.0 and +2.5 is within acceptablelimits

Adap t ive Forecast ing


109/114


Adap t ive Forecast ing

Its possible to use the computer tocontinually monitor forecast errorand adjust the values of the

andb

coefficients used in exponentialsmoothing to continually minimizeforecast error

This technique is called adaptivesmoothing

Focus Forecast ing


110/114


Focus Forecast ing

Developed at American Hardware Supply,based on two principles:

1. Sophisticated forecasting models are notalways better than simple ones

2. There is no single technique that shouldbe used for all products or services

This approach uses historical data to testmultiple forecasting models for individual

items The forecasting model with the lowest

error is then used to forecast the nextdemand

Forecast ing in the Serv ice


111/114


Forecast ing in the Serv iceSector

Presents unusual challenges

Special need for short term records

Needs differ greatly as function ofindustry and product

Holidays and other calendar events

Unusual events

Fast Food Restauran t


112/114


Forecast20%

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

Percen

tageofsales

Figure 4.12

FedEx Call Cen ter Forecast


113/114


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


114/114

All rights reserved. No part of this publication may be reproduced, stored in a retrieval

system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,

recording, or otherwise, without the prior written permission of the publisher.

Printed in the United States of America.

Operations Management, 10th Edition chapter 4

Documents