heizer om10 ch04 - Rajamangala University of Technology ... · Wh l t thi h tWhen you complete this...

44 ForecastingForecasting44 ForecastingForecasting

PowerPoint presentation to accompanyPowerPoint presentation to accompanyPowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, Operations Management, 1010e e Principles of Operations ManagementPrinciples of Operations Management 88eePrinciples of Operations Management, Principles of Operations Management, 88ee

PowerPoint slides by Jeff Heyl

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

OutlineOutlineOutlineOutline Gl b l C P fil Di Global Company Profile: Disney

World What Is Forecasting?

F ti Ti H i Forecasting Time Horizons The Influence of Product Life Cycley Types Of Forecasts


OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued Th St t i I t f The Strategic Importance of

Forecasting Human Resources Capacity Capacity Supply Chain Management

Seven Steps in the Forecasting SystemSystem


OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued F ti A h Forecasting Approaches

Overview of Qualitative Methods Overview of Qualitative Methods Overview of Quantitative Methods

Time-Series Forecasting Decomposition of a Time Series Decomposition of a Time Series Naive Approach


OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued Ti S i F ti ( t ) Time-Series Forecasting (cont.)

Moving Averages Moving Averages Exponential Smoothing Exponential Smoothing with Trend

Adjustment Trend Projections Seasonal Variations in Data Seasonal Variations in Data Cyclical Variations in Data


OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued A i ti F ti M th d Associative Forecasting Methods:

Regression and Correlation A l iAnalysis Using Regression Analysis for g g y

Forecasting Standard Error of the Estimate Standard Error of the Estimate Correlation Coefficients for

Regression LinesRegression Lines Multiple-Regression Analysis


OutlineOutline ContinuedContinuedOutline Outline –– ContinuedContinued Monitoring and Controlling

Forecasts Adaptive Smoothing F F ti Focus Forecasting

Forecasting in the Service Sectorg


Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning ObjectivesWh l t thi h tWh l t thi h tWhen you complete this chapter you When you complete this chapter you should be able to :should be able to :

1. Understand the three time horizons and which models apply for each useand which models apply for each use

2. Explain when to use each of the four lit ti d lqualitative models

3. Apply the naive, moving average, exponential smoothing, and trend methods


Learning ObjectivesLearning ObjectivesLearning ObjectivesLearning ObjectivesWh l t thi h tWh l t thi h tWhen you complete this chapter you When you complete this chapter you should be able to :should be able to :

4. Compute three measures of forecast accuracyaccuracy

5. Develop seasonal indexes6. Conduct a regression and correlation

analysis7. Use a tracking signal


Forecasting at Disney WorldForecasting at Disney WorldForecasting at Disney WorldForecasting at Disney World

Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and g, , y , ,Anaheim

Revenues are derived from people – how Revenues are derived from people how many visitors and how they spend their moneyy

Daily management report contains only the forecast and actual attendance atthe forecast and actual attendance at each park



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

Forecast used by labor management, maintenance operations finance andmaintenance, operations, finance, and park scheduling

F t d t dj t i ti Forecast used to adjust opening times, rides, shows, staffing levels, and guests admittedadmitted



20% of customers come from outside the USA

Economic model includes gross domestic product cross-exchange ratesdomestic product, cross-exchange rates, arrivals into the USA

A staff of 35 analysts and 70 field people A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each yearand travel professionals each year



Inputs to the forecasting model include airline specials, Federal Reserve p ,policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world

Average forecast error for the 5-year g yforecast is 5%

Average forecast error for annual Average forecast error for annual forecasts is between 0% and 3%


What is Forecasting?What is Forecasting?What is Forecasting?What is Forecasting? Process of predicting

a future event Underlying basis

of all business ??

decisions Production Production Inventory Personnel Personnel Facilities


Forecasting Time HorizonsForecasting Time Horizons Short-range forecastForecasting Time HorizonsForecasting Time Horizons

Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce g, j g,

levels, job assignments, production levels Medium-range forecastg

3 months to 3 years Sales and production planning budgeting Sales and production planning, budgeting

Long-range forecast 3+ years New product planning, facility location,

h d d l4 - 15© 2011 Pearson Education, Inc. publishing as Prentice Hall

research and development

Distinguishing DifferencesDistinguishing DifferencesDistinguishing DifferencesDistinguishing Differences

Medium/long rangeMedium/long range forecasts deal with more comprehensive issues and support

t d i i dimanagement decisions regarding planning and products, plants and processesprocesses

ShortShort--termterm forecasting usually employs diff t th d l i th l tdifferent methodologies than longer-term forecasting

ShortShort--termterm forecasts tend to be more accurate than longer-term forecasts


Influence of Product LifeInfluence of Product LifeInfluence of Product Life Influence of Product Life CycleCycle

Introduction Introduction –– Growth Growth –– Maturity Maturity –– DeclineDecline

Introduction and growth require longer forecasts than maturity and declineforecasts than maturity and decline

As product passes through life cycle, f t f l i j tiforecasts are useful in projecting Staffing levels Inventory levels Factory capacity


y p y

Product Life CycleProduct Life CycleProduct Life CycleProduct Life CycleIntroduction Growth Maturity Decline

Best period to increase market share

Practical to change price or quality image

Poor time to change image, price, or quality

Cost control critical

Introduction Growth Maturity Decline

ues

R&D engineering is critical

Strengthen niche Competitive costs become criticalDefend market eg

y/Is

s

position

ny S

trat

e

Internet search enginesDrive-through

restaurantsCD-ROMs

iPods LCD &

Com

pan

Sales

LCD & plasma TVs

Avatars

Xbox 360

C

Analog TVs

Boeing 787

Twitter


Figure 2.5

Product Life CycleProduct Life CycleProduct Life CycleProduct Life CycleIntroduction Growth Maturity Decline

Product design and development

Introduction Growth Maturity Decline

s

Forecasting criticalProduct and

StandardizationFewer product changes more

Little product differentiationCostcritical

Frequent product and process designy/

Issu

es

Product and process reliabilityCompetitive

d t

changes, more minor changesOptimum capacity

Cost minimizationOvercapacity in the i d tprocess design

changesShort production runs

Stra

tegy product

improvements and optionsIncrease capacity

Increasing stability of processLong production

industryPrune line to eliminate items not

High production costsLimited modelsAtt ti t

OM

S

p yShift toward product focusEnhance di t ib ti

Long production runsProduct improvement

d t tti

returning good marginReduce capacityAttention to

qualitydistribution and cost cutting capacity


Figure 2.5

Types of ForecastsTypes of ForecastsTypes of ForecastsTypes of Forecasts

Economic forecasts Address business cycle – inflation rate Address business cycle – inflation rate,

money supply, housing starts, etc. Technological forecasts Technological forecasts

Predict rate of technological progress I t d l t f d t Impacts development of new products

Demand forecasts Predict sales of existing products and

services


St t i I t fSt t i I t fStrategic Importance of Strategic Importance of ForecastingForecastingForecastingForecasting

Human Resources Hiring training Human Resources – Hiring, training, laying off workers

C it C it h t Capacity – Capacity shortages can result in undependable delivery, loss of customers loss of market shareof customers, loss of market share

Supply Chain Management – Good li l ti d isupplier relations and price

advantages


Seven Steps in ForecastingSeven Steps in ForecastingSeven Steps in ForecastingSeven Steps in Forecasting1 Determine the use of the forecast1. Determine the use of the forecast2. Select the items to be forecasted3. Determine the time horizon of the

forecastforecast4. Select the forecasting model(s)5. Gather the data6. Make the forecast6. Make the forecast7. Validate and implement results


The Realities!The Realities!

Forecasts are seldom perfect Most techniques assume an

underlying stability in the systemunderlying stability in the system Product family and aggregated

forecasts are more accurate than individual product forecasts


Forecasting ApproachesForecasting ApproachesForecasting ApproachesForecasting Approaches

U d h i i iQualitative MethodsQualitative Methods

Used when situation is vague and little data exist New products New technology New technology

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

Internet


Internet

Forecasting ApproachesForecasting ApproachesForecasting ApproachesForecasting Approaches

Quantitative MethodsQuantitative Methods

Used when situation is ‘stable’ and historical data exist Existing products C t t h l Current technology

Involves mathematical techniquesq e.g., forecasting sales of color

televisions4 - 25© 2011 Pearson Education, Inc. publishing as Prentice Hall

televisions

Overview of QualitativeOverview of QualitativeOverview of Qualitative Overview of Qualitative MethodsMethods

1 Jury of executive opinion1. Jury of executive opinion Pool opinions of high-level experts,

sometimes augment by statisticalsometimes augment by statistical models

2. Delphi method Panel of experts, queried iteratively Panel of experts, queried iteratively


Overview of QualitativeOverview of QualitativeOverview of Qualitative Overview of Qualitative MethodsMethods

3 Sales force composite3. Sales force composite Estimates from individual

l i d fsalespersons are reviewed for reasonableness, then aggregated

4. Consumer Market Survey Ask the customer Ask the customer


Jury of Executive OpinionJury of Executive Opinion

Jury of Executive OpinionJury of Executive Opinion Involves small group of high-level

experts and managers Group estimates demand by working

together Combines managerial experience with

statistical models Relatively quick ‘G thi k’ ‘Group-think’

disadvantage


Sales Force CompositeSales Force CompositeSales Force CompositeSales Force Composite

Each salesperson projects his or her salesher sales

Combined at district and national levels

Sales reps know customers’ wants Sales reps know customers wants Tends to be overly optimistic


Delphi MethodDelphi MethodDelphi MethodDelphi Method Iterative group te at e g oup

process, continues until

Decision Makers(Evaluate

responses andcontinues until consensus is reached

responses and make decisions)

reached 3 types of

ti i t

Staff(Administering

survey)participants Decision makers

survey)

Staff Respondents

Respondents(People who can

k l bl4 - 30© 2011 Pearson Education, Inc. publishing as Prentice Hall

Respondents make valuable judgments)

Consumer Market SurveyConsumer Market SurveyConsumer Market SurveyConsumer Market Survey

Ask customers about purchasing plansplans

What consumers say, and what they actually do are often different

Sometimes difficult to answer Sometimes difficult to answer


Overview of QuantitativeOverview of QuantitativeOverview of Quantitative Overview of Quantitative ApproachesApproachespppp

1. Naive approachpp2. Moving averages

time series3. Exponential smoothing

time-series models

g4. Trend projection5. Linear regression associative

model


Time Series ForecastingTime Series ForecastingTime Series ForecastingTime Series Forecasting

Set of evenly spaced numerical data Obtained by observing response

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

no other variables importantno other variables important Assumes that factors influencing

past and present will continuepast and present will continue influence in future


Time Series ComponentsTime Series ComponentsTime Series ComponentsTime Series Components

T d C li lTrend Cyclical

S l R dSeasonal Random


Components of DemandComponents of DemandComponents of DemandComponents of Demand

e

Trend component

or s

ervi

ce Seasonal peaks

prod

uct o

Actual demand line

man

d fo

r

Average demand over 4 years

Dem

| | | |1 2 3 4

Random variation


Time (years)Figure 4.1

Trend ComponentTrend ComponentTrend ComponentTrend Component

Persistent, overall upward or downward patterndownward pattern

Changes due to population, t h l lt ttechnology, age, culture, etc.

Typically several years Typically several years duration


Seasonal ComponentSeasonal Component Regular pattern of up and

Seasonal ComponentSeasonal Component Regular pattern of up and

down fluctuations Due to weather, customs, etc. Occurs within a single year Occurs within a single year

Number ofPeriod Length SeasonsPeriod Length SeasonsWeek Day 7Month Week 4-4.5M th D 28 31Month Day 28-31Year Quarter 4Year Month 12Year Week 52


Year Week 52

Cyclical ComponentCyclical ComponentCyclical ComponentCyclical Component

Repeating up and down movements Affected by business cycle Affected by business cycle,

political, and economic factors Multiple years duration Often causal or Often causal or

associative relationshipsrelationships


0 5 10 15 20

Random ComponentRandom ComponentRandom ComponentRandom Component Erratic, unsystematic, ‘residual’

fluctuationsDue to random variation or unforeseen

eventsevents Short duration

and nonrepeating

4 - 39© 2011 Pearson Education, Inc. publishing as Prentice HallM T W T F

Naive ApproachNaive ApproachNaive ApproachNaive Approach A d d i t Assumes demand in next

period is the same as d d i t t i ddemand in most recent period e.g., If January sales were 68, then e.g., If January sales were 68, then

February sales will be 68 Sometimes cost effective and Sometimes cost effective and

efficient Can be good starting point


Moving Average MethodMoving Average MethodMoving Average MethodMoving Average Method

MA is a series of arithmetic means Used if little or no trend Used often for smoothing Used often for smoothing

Provides overall impression of data tiover time

Moving average =∑ demand in previous n periods

n


Moving Average ExampleMoving Average ExampleMoving Average ExampleMoving Average Example

Actual 3-MonthMonth Shed Sales Moving Average

January 10February 12

10101212y

March 13April 16M 19 (12 13 16)/3 13 2/

1313(1010 + 1212 + 1313)/3 = 11 2/3

May 19June 23July 26

(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3July 26 (16 + 19 + 23)/3 = 19 /3


Graph of Moving AverageGraph of Moving AverageGraph of Moving AverageGraph of Moving AverageM i

30 –28

Moving Average Forecast

es

28 –26 –24 –22

Actual Sales

Shed

Sal 22 –

20 –18 –

S 16 –14 –12 –

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

10 –


W i ht d M i AW i ht d M i A

Weighted Moving AverageWeighted Moving Average Used when some trend might be

present Older data usually less important

W i ht b d i d Weights based on experience and intuition

Weighted∑ (weight for period n)

x (demand in period n)Weightedmoving average =

( )∑ weights


W i ht d M i AW i ht d M i AWeights Applied Period

Weighted Moving AverageWeighted Moving Average33 Last month22 Two months ago11 Th th11 Three months ago6 Sum of weights

Actual 3-Month WeightedMonth Shed Sales Moving Average

January 10February 12

10101212

March 13April 16May 19 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3

1313[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6

May 19June 23July 26

[(3 x 16) + (2 x 13) + (12)]/6 = 14 /3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2


Potential Problems WithPotential Problems WithPotential Problems WithPotential Problems WithMoving AverageMoving Average

Increasing n smooths the forecast

g gg g Increasing n smooths the forecast

but makes it less sensitive to changeschanges

Do not forecast trends well Require extensive historical data


Moving Average AndMoving Average AndMoving Average And Moving Average And Weighted Moving AverageWeighted Moving Average

30 –Weighted moving average

25 –

and

average

20 –

15 –es d

ema Actual

sales

10 –Sale Moving

average

5 –

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


J F M A M J J A S O N DFigure 4.2

Exponential SmoothingExponential SmoothingExponential SmoothingExponential Smoothing

Form of weighted moving average Weights decline exponentially Weights decline exponentially Most recent data weighted most

Requires smoothing constant () Ranges from 0 to 1 Ranges from 0 to 1 Subjectively chosen

Involves little record keeping of past data


data

Exponential SmoothingExponential SmoothingExponential SmoothingExponential Smoothing

New forecast = Last period’s forecast+ (Last period’s actual demand ( p

– Last period’s forecast)

Ft = Ft – 1 + (At – 1 - Ft – 1)

where Ft = new forecastFt – 1 = previous forecast

= smoothing (or weighting) constant (0 ≤ ≤ 1)


Exponential SmoothingExponential SmoothingExponential Smoothing Exponential Smoothing ExampleExampleExampleExample

Predicted demand = 142 Ford MustangsPredicted demand 142 Ford MustangsActual demand = 153Smoothing constant = .20Smoothing constant .20




N f t 142 + 2(153 142)New forecast = 142 + .2(153 – 142)




N f t 142 + 2(153 142)New forecast = 142 + .2(153 – 142)= 142 + 2.2= 144.2 ≈ 144 cars


Effect ofEffect ofEffect ofEffect ofSmoothing ConstantsSmoothing Constantsgg

Weight Assigned toMost 2nd Most 3rd Most 4th Most 5th Most

R t R t R t R t R tRecent 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


Impact of DifferentImpact of Different Impact of Different Impact of Different

225 –

200 –

nd

Actual demand

= .5

175 –Dem

an

150 | | | | | | | | | = .1

150 – | | | | | | | | |1 2 3 4 5 6 7 8 9

Quarter


Quarter

Impact of DifferentImpact of Different Impact of Different Impact of Different

225 –

200 –

nd

Actual demand

= .5 Chose high values of when underlying average

175 –Dem

an when underlying average is likely to change

Choose low values of

| | | | | | | | | = .1

Choose low values of when underlying average is stable150 – | | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

is stable


Quarter

ChoosingChoosing Choosing Choosing

The objective is to obtain the most accurate forecast no matter theaccurate forecast no matter the technique

We generally do this by selecting the We generally do this by selecting the model that gives us the lowest forecastmodel that gives us the lowest forecastmodel that gives us the lowest forecast model that gives us the lowest forecast errorerror

Forecast error = Actual demand - Forecast value

= At - Ft


At Ft

C M f EC M f ECommon Measures of ErrorCommon Measures of Error

Mean Absolute Deviation (MAD)

MAD =∑ |Actual - Forecast|

MAD n

Mean Squared Error (MSE)

∑ (F t E )2

MSE =∑ (Forecast Errors)2

n


C M f EC M f ECommon Measures of ErrorCommon Measures of Error

M Ab l t P t E (MAPE)Mean Absolute Percent Error (MAPE)

MAPE∑100|Actuali - Forecasti|/Actuali

n

i = 1MAPE =n

i = 1


Comparison of ForecastComparison of ForecastComparison of Forecast Comparison of Forecast Error Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

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

1 180 175 5.00 175 5.002 168 175.5 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 19.565 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178 22 3 78 186 30 4 308 182 178.22 3.78 186.30 4.30

82.45 98.62



∑ |deviations|Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

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

MAD =∑ |deviations|

nQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 82.45/8 = 10.31

For = .10

3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.56

For = .505 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178 22 3 78 186 30 4 30

= 98.62/8 = 12.33

8 182 178.22 3.78 186.30 4.3082.45 98.62



∑ (forecast errors)2Rounded Absolute Rounded Absolute

Actual Forecast Deviation Forecast DeviationTonnage with for with for

Quarter Unloaded = 10 = 10 = 50 = 50

MSE =∑ (forecast errors)

nQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 1,526.54/8 = 190.82

For = .10

3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.56

,

For = .505 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178 22 3 78 186 30 4 30

= 1,561.91/8 = 195.24

8 182 178.22 3.78 186.30 4.3082.45 98.62

MAD 10.31 12.33


Comparison of ForecastComparison of ForecastComparison of Forecast Comparison of Forecast Error Error ∑100|deviationi|/actuali

n


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

MAPE =∑100|deviationi|/actuali

ni = 1

Quarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50= 44.75/8 = 5.59%

For = .10

3 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.56

%

For = .505 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178 22 3 78 186 30 4 30

= 54.05/8 = 6.76%

8 182 178.22 3.78 186.30 4.3082.45 98.62

MAD 10.31 12.33


MSE 190.82 195.24



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

1 180 175 5.00 175 5.002 168 175.5 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 19.565 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178 22 3 78 186 30 4 308 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33


MSE 190.82 195.24MAPE 5.59% 6.76%

Exponential Smoothing withExponential Smoothing withExponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustmentjj

When a trend is present, exponentialWhen a trend is present, exponential smoothing must be modified

Forecast including (FITt) =

Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)

trend forecast trend


Exponential Smoothing withExponential Smoothing withExponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustmentjj

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

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

Step 1: Compute Ft

St 2 C t TStep 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt


t t t

Exponential Smoothing withExponential Smoothing withExponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example

ForecastActual Smoothed Smoothed Including

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

1 12 11 2 13.002 172 173 204 195 245 246 217 318 288 289 36

10


Table 4.1




1 12 11 2 13.002 172 173 204 195 24 Step 1: Forecast for Month 25 246 217 318 28

F2 = A1 + (1 - )(F1 + T1)F ( 2)(12) (1 2)(11 2)

Step 1: Forecast for Month 2

8 289 36

10

F2 = (.2)(12) + (1 - .2)(11 + 2)= 2.4 + 10.4 = 12.8 units


Table 4.1




1 12 11 2 13.002 17 12.802 17 12.803 204 195 24 Step 2: Trend for Month 25 246 217 318 28

T2 = (F2 - F1) + (1 - )T1

T ( 4)(12 8 11) (1 4)(2)

Step 2: Trend for Month 2

8 289 36

10

T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 units


Table 4.1




1 12 11 2 13.002 17 12.80 1.922 17 12.80 1.923 204 195 24 Step 3: Calculate FIT for Month 25 246 217 318 28

FIT2 = F2 + T2

FIT 12 8 1 92

Step 3: Calculate FIT for Month 2

8 289 36

10

FIT2 = 12.8 + 1.92= 14.72 units


Table 4.1




1 12 11 2 13.002 17 12.80 1.92 14.722 17 12.80 1.92 14.723 204 195 24

15.18 2.10 17.2817.82 2.32 20.1419 91 2 23 22 145 24

6 217 318 28

19.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827 14 2 45 29 598 28

9 3610

27.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16


Table 4.1


35 –Actual demand (A )

man

d

30 –

25 –

Actual demand (At)

duct

dem 20 –

15 –

Prod

10 –

5

Forecast including trend (FITt)with = .2 and = .4

| | | | | | | | |1 2 3 4 5 6 7 8 9

5 –

0 –


Figure 4.31 2 3 4 5 6 7 8 9

Time (month)

Trend ProjectionsTrend ProjectionsTrend ProjectionsTrend ProjectionsFitting a trend line to historical data pointsFitting a trend line to historical data points to project into the medium to long-range

Linear trends can be found using the least squares technique

y = a + bx^

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

i i t t

^

a = y-axis interceptb = slope of the regression linex = the independent variable


x the independent variable

L t S M th dL t S M th dLeast Squares MethodLeast Squares Methodia

ble

Deviation7Actual observation (y-value)

ent V

ar

Deviation5 Deviation6

(y-value)

Dep

end

Deviation4

Deviation3

ues

of D

Deviation1(error) Deviation2

4

T d li + b^

Valu 2 Trend line, y = a + bx


Time period Figure 4.4

L t S M th dL t S M th dLeast Squares MethodLeast Squares Method

iabl

e

Deviation7Actual observation (y-value)

ent V

ar

Deviation5 Deviation6

(y-value)

Dep

end

Deviation4

Deviation3Least squares method

minimizes the sum of the squared errors (deviations)

ues

of D

Deviation1(error) Deviation2

4

T d li + b^

squared errors (deviations)

Valu 2 Trend line, y = a + bx


Time period Figure 4.4

L t S M th dL t S M th dLeast Squares MethodLeast Squares MethodEquations to calculate the regression variables

y = a + bx^

b =xy - nxy

b =x2 - nx2

a = y - bx


Least Squares ExampleLeast Squares ExampleLeast Squares ExampleLeast Squares ExampleTime Electrical Power

Y P i d ( ) D d 2Year Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252007 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

b = = = 10.54∑xy - nxy∑x2 - nx2

3,063 - (7)(4)(98.86)140 - (7)(42)


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

Least Squares ExampleLeast Squares ExampleTime Electrical Power

Y P i d ( ) D d 2

Least Squares ExampleLeast Squares ExampleYear Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 525

The trend line is

y = 56 70 + 10 54x^2007 5 105 25 5252008 6 142 36 8522009 7 122 49 854

y = 56.70 + 10.54x

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

b = = = 10.54∑xy - nxy∑x2 - nx2

3,063 - (7)(4)(98.86)140 - (7)(42)


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

Least Squares ExampleLeast Squares ExampleLeast Squares ExampleLeast Squares ExampleT d li160 –

150 –140

Trend line,y = 56.70 + 10.54x^

140 –130 –120 –em

and

110 –100 –

90 –Pow

er d

e

80 –70 –60

P

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

60 –50 –


2003 2004 2005 2006 2007 2008 2009 2010 2011Year

L S R iL S R iLeast Squares RequirementsLeast Squares Requirements

1. We always plot the data to insure a linear relationship

2 We do not predict time periods far2. We do not predict time periods far beyond the database

3. Deviations around the least squares line are assumed to be random


Seasonal Variations In DataSeasonal Variations In DataSeasonal Variations In DataSeasonal Variations In Data

The multiplicative seasonal modelseasonal model can adjust trend data for seasonaldata for seasonal variations in demanddemand


Seasonal Variations In DataSeasonal Variations In DataSeasonal Variations In DataSeasonal Variations In Data

1 Find average historical demand for each season

Steps in the process:Steps in the process:

1. Find average historical demand for each season 2. Compute the average demand over all seasons

C f3. Compute a seasonal index for each season 4. Estimate next year’s total demand5. Divide this estimate of total demand by the

number of seasons, then multiply it by the seasonal index for that seasonseasonal index for that season


Seasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleDemand Average Average Seasonal

Jan 80 85 105 90 94F b 70 85 85 80 94

g gMonth 2007 2008 2009 2007-2009 Monthly Index

Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94pMay 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94


Dec 82 78 80 80 94


Jan 80 85 105 90 94F b 70 85 85 80 94


0.957Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94Seasonal index =

Average 2007-2009 monthly demandAverage monthly demandp

May 113 125 131 123 94Jun 110 115 120 115 94

Average monthly demand

= 90/94 = .957

Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94


Dec 82 78 80 80 94


Jan 80 85 105 90 94 0.957F b 70 85 85 80 94 0 851


Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064pMay 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851


Dec 82 78 80 80 94 0.851


Jan 80 85 105 90 94 0.957F b 70 85 85 80 94 0 851


Forecast for 2010Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064Expected annual demand = 1,200

Forecast for 2010

pMay 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223

p

Jan x 957 = 961,200

Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957

Jan x .957 = 9612

Feb x 851 = 851,200

Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851

Feb x .851 = 8512


Dec 82 78 80 80 94 0.851

Seasonal Index ExampleSeasonal Index ExampleSeasonal Index ExampleSeasonal Index Example2010 Forecast

140 –

130

2010 Forecast2009 Demand 2008 Demand130 –

120 –

110nd

2008 Demand2007 Demand

110 –

100 –

90

Dem

an

90 –

80 –

70 –| | | | | | | | | | | |J F M A M J J A S O N D


Time

San Diego HospitalSan Diego HospitalSan Diego HospitalSan Diego HospitalTrend Data

10,200 –

Trend Data

10,000 –

9,800 –Day

s

9659 9702 9745,

9,600 –

9 400patie

nt D

9530

9551

9573

9594

9616

9637

96599680

9702

9724 9766

9,400 –

9,200 –

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

Inp

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


MonthFigure 4.6

San Diego HospitalSan Diego HospitalSan Diego HospitalSan Diego HospitalSeasonal Indices

1.06 –

s 1 04 1 04

Seasonal Indices

1.04 –

1.02 –

ient

Day

s 1.041.02

1.01

1.031.04

1 001.00 –

0.98 –or

Inpa

ti 0.99 1.00

0.980.99

0.96 –

0.94 –| | | | | | | | | | | |

Inde

x fo

0.97 0.970.96

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


MonthFigure 4.7

San Diego HospitalSan Diego HospitalSan Diego HospitalSan Diego HospitalCombined Trend and Seasonal Forecast

10,200 – 10068

Combined Trend and Seasonal Forecast

10,000 –

9,800 –Day

s 99119764

9691

9949

9724,

9,600 –

9 400patie

nt D

9520

9691

9542

9572

9,400 –

9,200 –

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

Inp

9265

95209411

9355

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


MonthFigure 4.8

Associative ForecastingAssociative ForecastingAssociative ForecastingAssociative Forecasting

Used when changes in one or more independent variables can be used to predictindependent variables can be used to predict

the changes in the dependent variable

Most common technique is linear regression analysisg y

We apply this technique just as we didWe apply this technique just as we didWe apply this technique just as we did We apply this technique just as we did in the time series examplein the time series example


Associative ForecastingAssociative ForecastingAssociative ForecastingAssociative ForecastingForecasting an outcome based onForecasting an outcome based on predictor variables using the least squares techniquetechnique

y = a + bx^

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

^

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

predict the value of the dependent


p pvariable

Associative ForecastingAssociative ForecastingAssociative Forecasting Associative Forecasting ExampleExample

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

2.0 13.0 32.5 4 4 02.0 22.0 13 5 7

4.0 –

3.0 –

es3.5 72.0 –

1 0

Sal

1.0 –

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


0 1 2 3 4 5 6 7Area payroll


Sales, y Payroll, x x2 xy2 0 1 1 2 02.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02 0 2 4 4 02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5

∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5

b 2∑xy - nxy 51.5 - (6)(3)(2.5)

x = ∑x/6 = 18/6 = 3

y = ∑y/6 = 15/6 = 2 5

b = = = .25∑ y y∑x2 - nx2

( )( )( )80 - (6)(32)

a = y - bx = 2 5 - ( 25)(3) = 1 75


y = ∑y/6 = 15/6 = 2.5 a = y - bx = 2.5 - (.25)(3) = 1.75


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

If payroll next year is estimated to be 4.0 –

$6 billion, then: 3.0 –

2 0

sale

s 3.25

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

2.0 –

1.0 –Nod

el’s

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

Area payroll


p y

Standard Error of theStandard Error of theStandard Error of the Standard Error of the EstimateEstimate

A forecast is just a point estimate of a future valuefuture value

This point is actually the

4.0 –actually the mean of a probability

3.0 –

2 0

sale

s 3.25

probability distribution

2.0 –

1.0 –Nod

el’s

Fi 4 9

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

Area payroll


Figure 4.9 p y


∑(y y )2Sy,x =

∑(y - yc)2

n - 2

where y = y-value of each data pointyc = computed value of the dependent

variable, from the regression equationequation

n = number of data points



Computationally, this equation is considerably easier to useconsiderably easier to use

∑y2 a∑y b∑xySy,x =

∑y2 - a∑y - b∑xyn - 2

We use the standard error to set up di i i l d hprediction intervals around the

point estimate



Sy,x = =∑y2 - a∑y - b∑xyn - 2

39.5 - 1.75(15) - .25(51.5)6 - 2

4.0 –Sy x = .306

3.0 –

sale

s 3.25y,x

The standard error2.0 –

1.0 –Nod

el’s

sThe standard error of the estimate is $306,000 in sales

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

N

A ll


Area payroll

CorrelationCorrelationCorrelationCorrelation

How strong is the linear relationship between the variables?p

Correlation does not necessarily imply causality!imply causality!

Coefficient of correlation, r, , ,measures degree of association Values range from -1 to +1 Values range from -1 to +1


Correlation CoefficientCorrelation CoefficientCorrelation CoefficientCorrelation Coefficient

r = nxy - xy

[ 2 ( )2][ 2 ( )2][nx2 - (x)2][ny2 - (y)2]


Correlation CoefficientCorrelation Coefficienty yCorrelation CoefficientCorrelation Coefficienty y

r = nxy - xy

[ 2 ( )2][ 2 ( )2][nx2 - (x)2][ny2 - (y)2]x(a) Perfect positive correlation: r = +1

x(b) Positive correlation: 0 < r < 10 r 1

y y

x( ) N l ti x(d) Perfect negative


x(c) No correlation: r = 0

x(d) Perfect negative correlation: r = -1

CorrelationCorrelation C ffi i t f D t i ti 2

CorrelationCorrelation Coefficient of Determination, r2,

measures the percent of change in y predicted by the change in x Values range from 0 to 1 Values range from 0 to 1 Easy to interpret

For the Nodel Construction example:r = .901r2 = 81


r2 = .81

M lti l R iM lti l R iMultiple Regression Multiple Regression AnalysisAnalysisAnalysisAnalysis

If more than one independent variable is to be used in the model, linear regression can be

extended to multiple regression to d t l i d d t i blaccommodate several independent variables

y = a + b x + b xy = a + b1x1 + b2x2 …

Computationally this is quiteComputationally this is quiteComputationally, this is quite Computationally, this is quite complex and generally done on the complex and generally done on the

computercomputer4 - 103© 2011 Pearson Education, Inc. publishing as Prentice Hall

computercomputer

M lti l R iM lti l R iMultiple Regression Multiple Regression AnalysisAnalysisAnalysisAnalysis

In the Nodel example, including interest rates in th d l i th ti

y = 1 80 + 30x 5 0x^

the model gives the new equation:

y = 1.80 + .30x1 - 5.0x2

An improved correlation coefficient of r = 96An improved correlation coefficient of r = .96 means 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


Sales = $3,000,000

Monitoring and ControllingMonitoring and ControllingMonitoring and Controlling Monitoring and Controlling ForecastsForecastsForecastsForecasts

Tracking SignalTracking Signal

Measures how well the forecast is di ti t l l

g gg g

predicting actual values Ratio of cumulative forecast errors to

mean absolute deviation (MAD) Good tracking signal has low valuesg g If forecasts are continually high or low, the

forecast has a bias error


Monitoring and ControllingMonitoring and ControllingMonitoring and Controlling Monitoring and Controlling ForecastsForecastsForecastsForecasts

Tracking signal

Cumulative errorMAD=

∑(Actual demand in i d i

T ki

period i -Forecast demand

in period i)Tracking signal =

in period i)∑|Actual - Forecast|/n)


Tracking SignalTracking SignalTracking SignalTracking Signal

Tracking signal

Signal exceeding limit

Tracking signal

+Upper control limit

0 MADs Acceptable range

–Lower control limito e co t o t

Time


Tracking Signal ExampleTracking Signal ExampleTracking Signal ExampleTracking Signal ExampleCumulative

Absolute AbsoluteActual Forecast Cumm Forecast Forecast

Qtr 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 05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2


Tracking Signal ExampleTracking Signal ExampleTracking Signal ExampleTracking Signal ExampleCumulative

Absolute AbsoluteActual Forecast Cumm Forecast Forecast

Qtr Demand Demand Error Error Error Error MAD

TrackingSignal

(Cumm Error/MAD)

1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.5

( )

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

3 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11 0

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

+5/11 +0 55 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2

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

The variation of the tracking signal between -2.0 and +2.5 is within acceptable


plimits

Adaptive ForecastingAdaptive ForecastingAdaptive ForecastingAdaptive Forecasting

It’s possible to use the computer to continually monitor forecast errorcontinually monitor forecast error and adjust the values of the and coefficients used in exponentialcoefficients used in exponential smoothing to continually minimize forecast errorforecast error

This technique is called adaptive smoothing


Focus ForecastingFocus ForecastingFocus ForecastingFocus Forecasting Developed at American Hardware Supply, p pp y,

based on two principles:1. Sophisticated forecasting models are not1. Sophisticated forecasting models are not

always better than simple ones2. There is no single technique that should g q

be used for all products or services This approach uses historical data to test pp

multiple forecasting models for individual items

The forecasting model with the lowest error is then used to forecast the next


demand

Forecasting in the ServiceForecasting in the ServiceForecasting in the Service Forecasting in the Service SectorSector

Presents unusual challengesg Special need for short term records N d diff tl f ti f Needs differ greatly as function of

industry and product Holidays and other calendar events Unusual events Unusual events


Fast Food Restaurant Fast Food Restaurant ForecastForecast

20%20% –

15%

sale

s

15% –

10%ntag

e of

10% –

5%

Perc

en

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)


(Lunchtime) (Dinnertime)Hour of day Figure 4.12

FedEx Call Center ForecastFedEx Call Center ForecastFedEx Call Center ForecastFedEx Call Center Forecast

12% –

10% –10%

8% –

6% –

4% –

2% –

0% –

Hour of dayA.M. P.M.

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


Figure 4.12Hour of day

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.


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