heizer om10 ch04

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44 ForecastingForecasting

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

PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e

PowerPoint slides by Jeff Heyl

OutlineOutline

Global Company Profile: Disney WorldWhat Is Forecasting?

F ti Ti H i


Forecasting Time HorizonsThe Influence of Product Life CycleTypes Of Forecasts

Outline Outline –– ContinuedContinuedThe Strategic Importance of Forecasting

Human ResourcesCapacity


CapacitySupply Chain Management

Seven Steps in the Forecasting System

Outline Outline –– ContinuedContinuedForecasting Approaches

Overview of Qualitative MethodsOverview of Quantitative Methods


Time-Series ForecastingDecomposition of a Time SeriesNaive Approach

Outline Outline –– ContinuedContinuedTime-Series Forecasting (cont.)

Moving AveragesExponential Smoothing


Exponential Smoothing with Trend AdjustmentTrend ProjectionsSeasonal Variations in DataCyclical Variations in Data

Outline Outline –– ContinuedContinuedAssociative Forecasting Methods: Regression and Correlation Analysis

Using Regression Analysis for


g g yForecastingStandard Error of the EstimateCorrelation Coefficients for Regression LinesMultiple-Regression Analysis

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Outline Outline –– ContinuedContinuedMonitoring and Controlling Forecasts

Adaptive SmoothingF F ti


Focus ForecastingForecasting in the Service Sector

Learning ObjectivesLearning ObjectivesWhen 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 use


and which models apply for each use2. Explain when to use each of the four

qualitative models3. Apply the naive, moving average,

exponential smoothing, and trend methods

Learning ObjectivesLearning ObjectivesWhen 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 accuracy


accuracy5. Develop seasonal indexes6. Conduct a regression and correlation

analysis7. Use a tracking signal

Forecasting at Disney WorldForecasting at Disney World

Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and AnaheimRevenues are derived from people – how


Revenues are derived from people how many visitors and how they spend their moneyDaily management report contains only the forecast and actual attendance at each park


Disney generates daily, weekly, monthly, annual, and 5-year forecastsForecast used by labor management, maintenance operations finance and


maintenance, operations, finance, and park schedulingForecast used to adjust opening times, rides, shows, staffing levels, and guests admitted


20% of customers come from outside the USAEconomic model includes gross domestic product cross-exchange rates


domestic product, cross-exchange rates, arrivals into the USAA staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year

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


school districts around the worldAverage forecast error for the 5-year forecast is 5%Average forecast error for annual forecasts is between 0% and 3%

What is Forecasting?What is Forecasting?Process of predicting a future eventUnderlying basis of all business

??


decisionsProductionInventoryPersonnelFacilities

Short-range forecastUp to 1 year, generally less than 3 monthsPurchasing, job scheduling, workforce levels, job assignments, production levels

Medium-range forecast

Forecasting Time HorizonsForecasting Time Horizons


g3 months to 3 yearsSales and production planning, budgeting

Long-range forecast3+ yearsNew product planning, facility location, research and development

Distinguishing DifferencesDistinguishing Differences

Medium/long rangeMedium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes


processesShortShort--termterm forecasting usually employs different methodologies than longer-term forecastingShortShort--termterm forecasts tend to be more accurate than longer-term forecasts

Influence of Product Life Influence of Product Life CycleCycle

Introduction and growth require longer forecasts than maturity and decline

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


forecasts than maturity and declineAs product passes through life cycle, forecasts are useful in projecting

Staffing levelsInventory levelsFactory capacity

Product Life CycleProduct Life CycleBest 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 criticalDefend market

Cost control critical

Introduction Growth Maturity Decline

egy/

Issu

es


position

Com

pany

Str

ate

Figure 2.5

Internet search engines

Sales

Drive-through restaurants

CD-ROMs

Analog TVs

iPods

Boeing 787

LCD & plasma TVs

Twitter

Avatars

Xbox 360

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Product Life CycleProduct Life CycleProduct design and development criticalFrequent product and process design

Introduction Growth Maturity Decline

y/Is

sues

Forecasting criticalProduct and process reliabilityCompetitive

d t

StandardizationFewer product changes, more minor changesOptimum capacity

Little product differentiationCost minimizationOvercapacity in the i d t


process design changesShort production runsHigh production costsLimited modelsAttention to quality

OM

Str

ateg

y product improvements and optionsIncrease capacityShift toward product focusEnhance distribution

Increasing stability of processLong production runsProduct improvement and cost cutting

industryPrune line to eliminate items not returning good marginReduce capacity

Figure 2.5

Types of ForecastsTypes of Forecasts

Economic forecastsAddress business cycle – inflation rate, money supply, housing starts, etc.

Technological forecasts


Technological forecastsPredict rate of technological progressImpacts development of new products

Demand forecastsPredict sales of existing products and services

Strategic Importance of Strategic Importance of ForecastingForecasting

Human Resources – Hiring, training, laying off workersC it C it h t


Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market shareSupply Chain Management – Good supplier relations and price advantages

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

forecast


o ecast4. Select the forecasting model(s)5. Gather the data6. Make the forecast7. Validate and implement results

The Realities!The Realities!

Forecasts are seldom perfectMost techniques assume an underlying stability in the system


underlying stability in the systemProduct family and aggregated forecasts are more accurate than individual product forecasts

Forecasting ApproachesForecasting Approaches

Used when situation is vague and little data exist

Qualitative MethodsQualitative Methods


New productsNew technology

Involves intuition, experiencee.g., forecasting sales on Internet

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Forecasting ApproachesForecasting Approaches

Used when situation is ‘stable’ and historical data exist

Quantitative MethodsQuantitative Methods


Existing productsCurrent technology

Involves mathematical techniquese.g., forecasting sales of color televisions

Overview of Qualitative Overview of Qualitative MethodsMethods

1. Jury of executive opinionPool opinions of high-level experts, sometimes augment by statistical


sometimes augment by statistical models

2. Delphi methodPanel of experts, queried iteratively

Overview of Qualitative Overview of Qualitative MethodsMethods

3. Sales force compositeEstimates from individual

l i d f


salespersons are reviewed for reasonableness, then aggregated

4. Consumer Market SurveyAsk the customer

Involves small group of high-level experts and managersGroup estimates demand by working together

Jury of Executive OpinionJury of Executive Opinion


Combines managerial experience with statistical modelsRelatively quick‘Group-think’disadvantage

Sales Force CompositeSales Force Composite

Each salesperson projects his or her salesCombined at district and national


levelsSales reps know customers’ wantsTends to be overly optimistic

Delphi MethodDelphi MethodIterative group process, continues until consensus is reached

Decision Makers(Evaluate

responses and make decisions)


reached3 types of participants

Decision makersStaffRespondents

Staff(Administering

survey)

Respondents(People who can make valuable

judgments)

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Consumer Market SurveyConsumer Market Survey

Ask customers about purchasing plansWhat consumers say, and what


they actually do are often differentSometimes difficult to answer

Overview of Quantitative Overview of Quantitative ApproachesApproaches

1. Naive approach2. Moving averages

time series


3. Exponential smoothing

4. Trend projection5. Linear regression

time-series models

associative model

Set of evenly spaced numerical dataObtained by observing response variable at regular time periods

Time Series ForecastingTime Series Forecasting


Forecast based only on past values, no other variables important

Assumes that factors influencing past and present will continue influence in future

Trend Cyclical

Time Series ComponentsTime Series Components


Seasonal Random

Components of DemandComponents of Demand

or s

ervi

ce

Trend component

Seasonal peaks


Dem

and

for p

rodu

ct o

| | | |1 2 3 4

Time (years)

Average demand over 4 years

Actual demand line

Random variation

Figure 4.1

Persistent, overall upward or downward patternChanges due to population, t h l lt t

Trend ComponentTrend Component


technology, age, culture, etc.Typically several years duration

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Regular pattern of up and down fluctuationsDue to weather, customs, etc.Occurs within a single year

Seasonal ComponentSeasonal Component


Occurs within a single year Number of

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

Repeating up and down movementsAffected by business cycle, political, and economic factors

Cyclical ComponentCyclical Component


Multiple years durationOften causal or associative relationships

0 5 10 15 20

Erratic, unsystematic, ‘residual’ fluctuationsDue to random variation or unforeseen events

Random ComponentRandom Component


eventsShort duration and nonrepeating

M T W T F

Naive ApproachNaive ApproachAssumes demand in next period is the same as demand in most recent period

e.g., If January sales were 68, then


e g , Ja ua y sa es e e 68, t eFebruary sales will be 68

Sometimes cost effective and efficientCan be good starting point

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

Moving Average MethodMoving Average Method


Used often for smoothingProvides overall impression of data over time

Moving average =∑ demand in previous n periods

n

January 10February 12

Actual 3-MonthMonth Shed Sales Moving Average

Moving Average ExampleMoving Average Example

10101212


yMarch 13April 16May 19June 23July 26

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

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

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Graph of Moving AverageGraph of Moving Average

es

30 –28 –26 –24 –22

Actual Sales

Moving Average Forecast


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

Shed

Sal 22 –

20 –18 –16 –14 –12 –10 –

Used when some trend might be present

Older data usually less importantW i ht b d i d

Weighted Moving AverageWeighted Moving Average


Weights based on experience and intuition

Weightedmoving average =

∑ (weight for period n)x (demand in period n)

∑ weights

Actual 3-Month WeightedMonth Shed Sales Moving Average

Weighted Moving AverageWeighted Moving AverageWeights Applied Period

33 Last month22 Two months ago11 Three months ago6 Sum of weights


January 10February 12March 13April 16May 19June 23July 26

[(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

101012121313

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

Increasing n smooths the forecast but makes it less sensitive to changes

Potential Problems WithPotential Problems WithMoving AverageMoving Average


changesDo not forecast trends wellRequire extensive historical data

Moving Average And Moving Average And Weighted Moving AverageWeighted Moving Average

30 –

25 –

and

Weighted moving average


20 –

15 –

10 –

5 –

Sale

s de

ma

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

Actual sales

Moving average

Figure 4.2

Form of weighted moving averageWeights decline exponentiallyMost recent data weighted most

Exponential SmoothingExponential Smoothing


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

Involves little record keeping of past data

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Exponential SmoothingExponential Smoothing

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

– Last period’s forecast)


Ft = Ft – 1 + α(At – 1 - Ft – 1)

where Ft = new forecastFt – 1 = previous forecast

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

Exponential Smoothing Exponential Smoothing ExampleExample

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


Smoothing constant α .20





New forecast = 142 + .2(153 – 142)





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

Effect ofEffect ofSmoothing ConstantsSmoothing Constants

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

R t R t R t R t R t


Recent Recent Recent Recent RecentSmoothing Period Period Period Period PeriodConstant (α) α(1 - α) α(1 - α)2 α(1 - α)3 α(1 - α)4

α = .1 .1 .09 .081 .073 .066

α = .5 .5 .25 .125 .063 .031

Impact of Different Impact of Different αα

225 –

200 –

nd

Actual demand

α = .5


175 –

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

Quarter

Dem

an

α = .1

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Impact of Different Impact of Different αα

225 –

200 –

nd

Actual demand

α = .5Chose high values of αwhen underlying average


175 –

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

Quarter

Dem

an

α = .1

when underlying average is likely to changeChoose low values of αwhen underlying average is stable

Choosing Choosing αα

The objective is to obtain the most accurate 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 forecast model that gives us the lowest forecast errorerror

Forecast error = Actual demand - Forecast value

= At - Ft

Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation (MAD)

MAD =∑ |Actual - Forecast|


MAD n

Mean Squared Error (MSE)

MSE =∑ (Forecast Errors)2

n

Common Measures of ErrorCommon Measures of Error

Mean Absolute Percent Error (MAPE)


MAPE =∑100|Actuali - Forecasti|/Actuali

n

n

i = 1

Comparison of Forecast Comparison of Forecast Error Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

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

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50


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 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62




1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50

MAD =∑ |deviations|

n

= 82.45/8 = 10.31For α = .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 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

= 98.62/8 = 12.33For α = .50

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

For α = .10

MSE =∑ (forecast errors)2

n


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 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33

,

= 1,561.91/8 = 195.24For α = .50




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

For α = .10

MAPE =∑100|deviationi|/actuali

n

n

i = 1


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 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24

%

= 54.05/8 = 6.76%For α = .50




1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.50


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 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%

Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

When a trend is present, exponential smoothing must be modified


Forecast including (FITt) = trend

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

Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

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


Tt = β(Ft - Ft - 1) + (1 - β)Tt - 1

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt

Exponential 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 17


2 173 204 195 246 217 318 289 3610

Table 4.1

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1 12 11 2 13.002 17


2 173 204 195 246 217 318 289 3610

Table 4.1

F2 = αA1 + (1 - α)(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2




1 12 11 2 13.002 17 12.80


2 17 12.803 204 195 246 217 318 289 3610

Table 4.1

T2 = β(F2 - F1) + (1 - β)T1

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

Step 2: Trend for Month 2




1 12 11 2 13.002 17 12.80 1.92


2 17 12.80 1.923 204 195 246 217 318 289 3610

Table 4.1

FIT2 = F2 + T2

FIT2 = 12.8 + 1.92= 14.72 units

Step 3: Calculate FIT for Month 2




1 12 11 2 13.002 17 12.80 1.92 14.72


2 17 12.80 1.92 14.723 204 195 246 217 318 289 3610

Table 4.1

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16


man

d

35 –

30 –

25 –

Actual demand (At)


Figure 4.3

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

Time (month)

Prod

uct d

em 20 –

15 –

10 –

5 –

0 –

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

Trend ProjectionsTrend ProjectionsFitting 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)

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

^

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Least Squares MethodLeast Squares Methoden

t Var

iabl

e

Deviation5

Deviation7

Deviation6

Actual observation (y-value)


Time period

Valu

es o

f Dep

end

Figure 4.4

Deviation1(error) Deviation2

Deviation4

Deviation3

Trend line, y = a + bx^

Least Squares MethodLeast Squares Method

ent V

aria

ble

Deviation5

Deviation7

Deviation6

Actual observation (y-value)


Time period

Valu

es o

f Dep

end

Figure 4.4

Deviation1(error) Deviation2

Deviation4

Deviation3

Trend line, y = a + bx^

Least squares method minimizes the sum of the

squared errors (deviations)

Least Squares MethodLeast Squares MethodEquations to calculate the regression variables

y = a + bx^


b =Σxy - nxyΣx2 - nx2

a = y - bx

Least Squares ExampleLeast Squares ExampleTime Electrical Power

Year Period (x) Demand x2 xy

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


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

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

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 3602007 5 105 25 525

Least Squares ExampleLeast Squares Example

The trend line is

y = 56 70 + 10 54x^


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

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

y = 56.70 + 10.54x

Least Squares ExampleLeast Squares Example

160 –150 –140 –130 –120 –em

and

Trend line,y = 56.70 + 10.54x^


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

110 –100 –

90 –80 –70 –60 –50 –

Year

Pow

er d

e

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Least Squares RequirementsLeast Squares Requirements

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

2 We do not predict time periods far


2. 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 Data

The multiplicative seasonal model


seasonal model can adjust trend data for seasonal variations in demand

Seasonal Variations In DataSeasonal Variations In Data

1. Find average historical demand for each season 2. Compute the average demand over all seasons 3 C l i d f h

Steps in the process:Steps in the process:


3. 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 season

Seasonal Index ExampleSeasonal Index Example

Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94

Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index


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


Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94


0.957

Seasonal index = Average 2007-2009 monthly demand

Average monthly demand


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

Average monthly demand

= 90/94 = .957


Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064



pMay 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 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851

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Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064


Expected annual demand = 1,200

Forecast for 2010


pMay 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 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851

p

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12


140 –

130 –

120 –

110nd

2010 Forecast2009 Demand 2008 Demand2007 Demand


110 –

100 –

90 –

80 –

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

Time

Dem

an

San Diego HospitalSan Diego Hospital

10,200 –

10,000 –

9,800 –Day

s

9659 9702 9745

Trend Data


,

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

Inpa

tient

D

9530

9551

9573

9594

9616

9637

96599680

9702

9724 9766

Figure 4.6


1.06 –

1.04 –

1.02 –

ent D

ays 1.04

1.021.01

1.031.04

1 00

Seasonal Indices


1.00 –

0.98 –

0.96 –

0.94 –

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

Month

Inde

x fo

r Inp

ati 0.99 1.00

0.98

0.97

0.990.97

0.96

Figure 4.7


10,200 –

10,000 –

9,800 –Day

s

99119764

9691

9949

9724

10068

Combined Trend and Seasonal Forecast


,

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

Inpa

tient

D

Figure 4.8

9265

9520

9691

94119542

9355

9572

Associative ForecastingAssociative Forecasting

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

the changes in the dependent variable


Most common technique is linear regression analysis

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

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Associative ForecastingAssociative ForecastingForecasting an outcome based on predictor variables using the least squares 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 though to

predict the value of the dependent variable

^

Associative Forecasting Associative Forecasting ExampleExample

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

2.0 13.0 32.5 4 4 0


2.0 22.0 13.5 7

4.0 –

3.0 –

2.0 –

1.0 –

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

Sale

s

Area payroll


Sales, y Payroll, x x2 xy2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02 0 2 4 4 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 = = = .25∑xy - nxy∑x2 - nx2

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

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:

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

3.0 –

2.0 –

1.0 –

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

Nod

el’s

sal

es

Area payroll

3.25

Standard Error of the Standard Error of the EstimateEstimate

A forecast is just a point estimate of a future valueThis point is actually the

4.0 –


actually the mean of a probability distribution

Figure 4.9

3.0 –

2.0 –

1.0 –

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

Nod

el’s

sal

es

Area payroll

3.25


Sy,x =∑(y - yc)2

n - 2


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

variable, from the regression equation

n = number of data points

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Computationally, this equation is considerably easier to use

∑y2 a∑y b∑xy


We use the standard error to set up prediction intervals around the

point estimate

Sy,x =∑y2 - a∑y - b∑xy

n - 2


4.0 –

Sy,x = =∑y2 - a∑y - b∑xyn - 2

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

Sy x = .306


3.0 –

2.0 –

1.0 –

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

Nod

el’s

sal

es

Area payroll

3.25y,x

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

How strong is the linear relationship between the variables?Correlation does not necessarily imply causality!

CorrelationCorrelation


imply causality!Coefficient of correlation, r, measures degree of association

Values range from -1 to +1

Correlation CoefficientCorrelation Coefficient

r = nΣxy - ΣxΣy

[nΣx2 - (Σx)2][nΣy2 - (Σy)2]


Correlation CoefficientCorrelation Coefficient

r = nΣxy - ΣxΣy

[nΣx2 - (Σx)2][nΣy2 - (Σy)2]

y

x(a) Perfect positive correlation: r = +1

y

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


0 r 1

y

x(c) No correlation: r = 0

y

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

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

Values range from 0 to 1

CorrelationCorrelation


Values range from 0 to 1Easy to interpret

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

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Multiple Regression Multiple Regression AnalysisAnalysis

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 bl


accommodate several independent variables

y = a + b1x1 + b2x2 …^

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

computercomputer

Multiple Regression Multiple Regression AnalysisAnalysis

y = 1 80 + 30x 5 0x^

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


y = 1.80 + .30x1 - 5.0x2

An 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

Measures how well the forecast is di ti t l l

Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking SignalTracking Signal


predicting actual valuesRatio of cumulative forecast errors to mean absolute deviation (MAD)

Good tracking signal has low valuesIf forecasts are continually high or low, the forecast has a bias error

Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking signal

Cumulative errorMAD=


Tracking signal =

∑(Actual demand in period i -

Forecast demand in period i)

(∑|Actual - Forecast|/n)

Tracking SignalTracking Signal

Tracking signal

+Upper control limit

Signal exceeding limit


0 MADs

–Lower control limit

Time

Acceptable range

Tracking 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 7.5


3 115 100 +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

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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 7.5

Tracking Signal ExampleTracking Signal ExampleTrackingSignal

(Cumm Error/MAD)

-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 11.06 140 110 +30 +35 30 85 14.2

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

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

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

Adaptive ForecastingAdaptive Forecasting

It’s possible to use the computer to continually monitor forecast error and adjust the values of the α and βcoefficients used in exponential


coefficients used in exponential smoothing to continually minimize forecast errorThis technique is called adaptive smoothing

Focus ForecastingFocus ForecastingDeveloped at American Hardware Supply, based on two principles:1. Sophisticated forecasting models are not

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


g qbe used for all products or services

This approach uses historical data to test multiple forecasting models for individual itemsThe forecasting model with the lowest error is then used to forecast the next demand

Forecasting in the Service Forecasting in the Service SectorSector

Presents unusual challengesSpecial need for short term recordsN d diff tl f ti f


Needs differ greatly as function of industry and productHolidays and other calendar eventsUnusual events

Fast Food Restaurant Fast Food Restaurant ForecastForecast

20% –

15% –

10%ntag

e of

sal

es


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

Perc

en

Figure 4.12

FedEx Call Center ForecastFedEx Call Center Forecast

12% –

10% –

8% –


Figure 4.12

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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