ch3. demand forecasting

8/2/2019 Ch3. Demand Forecasting

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1 2002 South-Western/Thomson Learning2002 South-Western/Thomson Learning TMTM

Slides preparedSlides prepared

by John Loucksby John Loucks


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Chapter 3

Demand Forecasting


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Overview

IntroductionQualitative Forecasting MethodsQuantitative Forecasting Models

How to Have a Successful Forecasting SystemComputer Software for ForecastingForecasting in Small Businesses and Start-UpVenturesWrap-Up: What World-Class Producers Do


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Demand Management

Independent demand items are the onlyitems demand for which needs to beforecastThese items include:

Finished goods andSpare parts


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Demand Management

A

Independent Demand(finished goods and spare parts)

B(4) C(2)

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

Dependent Demand(components)


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Demand Management

The importance of forecasting in OM


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Introduction

Demand estimates for products and services are thestarting point for all the other planning in operationsmanagement.Management teams develop sales forecasts based inpart on demand estimates.The sales forecasts become inputs to both businessstrategy and production resource forecasts.


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Forecasting is an Integral Partof Business Planning

ForecastMethod(s)

DemandEstimates

SalesForecast

ManagementTeam

Inputs:Market,

Economic,Other

BusinessStrategy

Production ResourceForecasts


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Some Reasons WhyForecasting is Essential in OM

New Facility Planning It can take 5 years to designand build a new factory or design and implement anew production process.Production Planning Demand for products varyfrom month to month and it can take several monthsto change the capacities of production processes.Workforce Scheduling Demand for services (and

the necessary staffing) can vary from hour to hourand employees weekly work schedules must bedeveloped in advance.


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Examples of Production Resource Forecasts

ForecastHorizon Time Span Item Being Forecast Units of Measure

Long-Range Years

Product linesFactory capacitiesPlanning for new productsCapital expenditures

Facility location or expansionR&D

Dollars, tons, etc.

Medium-Range Months

Product groupsDepartment capacitiesSales planningProduction planning and budgeting

Dollars, tons, etc.

Short-Range Weeks

Specific product quantitiesMachine capacitiesPlanningPurchasingSchedulingWorkforce levelsProduction levels

Job assignments

Physical units of products


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Forecasting Methods

Qualitative ApproachesQuantitative Approaches


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Qualitative Approaches

Usually based on judgments about causal factors thatunderlie the demand of particular products or servicesDo not require a demand history for the product orservice, therefore are useful for new products/servicesApproaches vary in sophistication from scientificallyconducted surveys to intuitive hunches about futureevents

The approach/method that is appropriate depends on a products life cycle stage


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Qualitative Methods

Educated guess intuitive hunches Executive committee consensusDelphi method

Survey of sales forceSurvey of customersHistorical analogyMarket research scientifically conducted surveys


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Qualitative Forecasting ApplicationsSmall and Large Firms

Technique Low Sales(less than $100M)

High Sales(more than $500M)

Managers Opinion 40.7% 39.6%

ExecutivesOpinion 40.7% 41.6%

Sales ForceComposite 29.6% 35.4%

Number of Firms 27 48

Source: Nada Sanders and Karl Mandrodt (1994) Practitioners Continue to Rely on Judgmental ForecastingMethods Instead of Quantitative Methods, Interfaces , vol. 24, no. 2, pp. 92-100.Note: More than one response was permitted.


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Quantitative Forecasting Approaches

Based on the assumption that the forces thatgenerated the past demand will generate the futuredemand, i.e., history will tend to repeat itself Analysis of the past demand pattern provides a goodbasis for forecasting future demandMajority of quantitative approaches fall in thecategory of time series analysis


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Quantitative Forecasting ApplicationsSmall and Large Firms

Technique Low Sales(less than $100M)

High Sales(more than $500M)

Moving Average 29.6% 29.2

Simple Linear Regression 14.8% 14.6

Naive 18.5% 14.6

Single ExponentialSmoothing 14.8% 20.8

Multiple Regression 22.2% 27.1

Simulation 3.7% 10.4

Classical Decomposition 3.7% 8.3

Box-Jenkins 3.7% 6.3Number of Firms 27 48

Source: Nada Sanders and Karl Mandrodt (1994) Practitioners Continue to Rely on Judgmental ForecastingMethods Instead of Quantitative Methods, Interfaces , vol. 24, no. 2, pp. 92-100.Note: More than one response was permitted.


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A time series is a set of numbers where the order orsequence of the numbers is important, e.g., historicaldemandAnalysis of the time series identifies patternsOnce the patterns are identified, they can be used todevelop a forecast

Time Series Analysis


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Components of Time Series

Trends are noted by an upward or downward slopinglineSeasonality is a data pattern that repeats itself overthe period of one year or lessCycle is a data pattern that repeats itself... may takeyearsIrregular variations are jumps in the level of the series

due to extraordinary eventsRandom fluctuation from random variation orunexplained causes


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Seasonal Patterns

Length of Time Number of Before Pattern Length of Seasons

Is Repeated Season in Pattern

Year Quarter 4Year Month 12Year Week 52

Month Day 28-31Week Day 7


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Quantitative Forecasting Approaches

Linear RegressionSimple Moving AverageWeighted Moving Average

Exponential Smoothing (exponentially weightedmoving average)Exponential Smoothing with Trend (doubleexponential smoothing)


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Long-Range Forecasts

Time spans usually greater than one yearNecessary to support strategic decisions aboutplanning products, processes, and facilities


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Simple Linear Regression

Linear regression analysis establishes a relationshipbetween a dependent variable and one or moreindependent variables.In simple linear regression analysis there is only oneindependent variable.If the data is a time series, the independent variable isthe time period.

The dependent variable is whatever we wish toforecast.


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Regression EquationThis model is of the form:

Y = a + bX

Y = dependent variableX = independent variablea = y-axis interceptb = slope of regression line


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Constants a and bThe constants a and b are computed using thefollowing equations:

2

2 2x y- x xya =n x -( x)

2 2

xy- x yb = n x -( x)

n


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Once the a and b values are computed, a future valueof X can be entered into the regression equation and acorresponding value of Y (the forecast) can becalculated.


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Example: College Enrollment

Simple Linear RegressionAt a small regional college enrollments have grownsteadily over the past six years, as evidenced below.Use time series regression to forecast the studentenrollments for the next three years.

Students StudentsYear Enrolled (1000s) Year Enrolled (1000s)

1 2.5 4 3.22 2.8 5 3.33 2.9 6 3.4


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Simple Linear Regression x y x 2 xy1 2.5 1 2.5

2 2.8 4 5.63 2.9 9 8.74 3.2 16 12.85 3.3 25 16.5

6 3.4 36 20.4S x=21 S y=18.1 S x2=91 S xy=66.5


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Y = 2.387 + 0.180X

291(18.1) 21(66.5) 2.387

6(91) (21)a

6(66.5) 21(18.1) 0.180105

b


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Simple Linear RegressionY7 = 2.387 + 0.180(7) = 3.65 or 3,650 studentsY8 = 2.387 + 0.180(8) = 3.83 or 3,830 students

Y9 = 2.387 + 0.180(9) = 4.01 or 4,010 students

Note: Enrollment is expected to increase by 180students per year.


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Simple linear regression can also be used when theindependent variable X represents a variable otherthan time.In this case, linear regression is representative of aclass of forecasting models called causal forecastingmodels.


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Example: Railroad Products Co.

Simple Linear Regression Causal ModelThe manager of RPC wants to project the firms

sales for the next 3 years. He knows that RPCs long -range sales are tied very closely to national freight carloadings. On the next slide are 7 years of relevanthistorical data.

Develop a simple linear regression model

between RPC sales and national freight car loadings.Forecast RPC sales for the next 3 years, given that therail industry estimates car loadings of 250, 270, and300 million.


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Simple Linear Regression Causal ModelRPC Sales Car Loadings

Year ($millions) (millions)

1 9.5 1202 11.0 1353 12.0 1304 12.5 150

5 14.0 1706 16.0 1907 18.0 220


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Simple Linear Regression Causal Modelx y x 2 xy

120 9.5 14,400 1,140

135 11.0 18,225 1,485130 12.0 16,900 1,560150 12.5 22,500 1,875170 14.0 28,900 2,380190 16.0 36,100 3,040220 18.0 48,400 3,960

1,115 93.0 185,425 15,440


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Simple Linear Regression Causal Model

Y = 0.528 + 0.0801X

2185,425(93) 1,115(15,440)a 0.528

7(185,425) (1,115)

27(15,440) 1,115(93)b 0.08017(185,425) (1,115)


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Simple Linear Regression Causal ModelY8 = 0.528 + 0.0801(250) = $20.55 millionY9 = 0.528 + 0.0801(270) = $22.16 million

Y10 = 0.528 + 0.0801(300) = $24.56 million

Note: RPC sales are expected to increase by$80,100 for each additional million national freightcar loadings.


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Multiple Regression Analysis

Multiple regression analysis is used when there aretwo or more independent variables.An example of a multiple regression equation is:

Y = 50.0 + 0.05X 1 + 0.10X 2 0.03X 3 where: Y = firms annual sales ($millions)

X1 = industry sales ($millions)

X2 = regional per capita income ($thousands)X3 = regional per capita debt ($thousands)


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Coefficient of Correlation ( r )

The coefficient of correlation, r , explains the relativeimportance of the relationship between x and y.The sign of r shows the direction of the relationship.The absolute value of r shows the strength of therelationship.The sign of r is always the same as the sign of b.r can take on any value between 1 and +1.


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Meanings of several values of r :-1 a perfect negative relationship (as x goes up, y

goes down by one unit, and vice versa)+1 a perfect positive relationship (as x goes up, y

goes up by one unit, and vice versa)0 no relationship exists between x and y

+0.3 a weak positive relationship

-0.8 a strong negative relationship


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r is computed by:

2 2 2 2( ) ( )

n xy x yr

n x x n y y


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Coefficient of Determination ( r 2)

The coefficient of determination, r 2

, is the square of the coefficient of correlation.The modification of r to r 2 allows us to shift fromsubjective measures of relationship to a more specificmeasure.r 2 is determined by the ratio of explained variation tototal variation:

22

2( )( )Y yr y y


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Coefficient of Correlationx y x 2 xy y 2

120 9.5 14,400 1,140 90.25

135 11.0 18,225 1,485 121.00130 12.0 16,900 1,560 144.00150 12.5 22,500 1,875 156.25170 14.0 28,900 2,380 196.00190 16.0 36,100 3,040 256.00220 18.0 48,400 3,960 324.00

1,115 93.0 185,425 15,440 1,287.50


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Coefficient of Correlation

r = .9829

2 2

7(15,440) 1,115(93)

7(185,425) (1,115) 7(1,287.5) (93)r


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Coefficient of Determinationr 2 = (.9829) 2 = .966

96.6% of the variation in RPC sales is explained by

national freight car loadings.


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Ranging Forecasts

Forecasts for future periods are only estimates and aresubject to error.One way to deal with uncertainty is to develop best-estimate forecasts and the ranges within which theactual data are likely to fall.The ranges of a forecast are defined by the upper andlower limits of a confidence interval.


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Ranging Forecasts

The standard error (deviation) of the forecast iscomputed as:

2

yx

y - a y - b xys = n - 2


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Ranging ForecastsRecall that linear regression analysis provided a

forecast of annual sales for RPC in year 8 equal to$20.55 million.

Set the limits (ranges) of the forecast so that thereis only a 5 percent probability of exceeding the limitsby chance.


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Ranging ForecastsStep 1: Compute the standard error of the

forecasts, s yx.

Step 2: Determine the appropriate value for t.

n = 7, so degrees of freedom = n 2 = 5.Area in upper tail = .05/2 = .025Appendix B, Table 2 shows t = 2.571.

1287.5 .528(93) .0801(15,440) .57487 2yx

s


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Ranging ForecastsStep 3: Compute upper and lower limits.

Upper limit = 20.55 + 2.571(.5748)

= 20.55 + 1.478= 22.028Lower limit = 20.55 - 2.571(.5748)

= 20.55 - 1.478= 19.072

We are 95% confident the actual sales for year 8will be between $19.072 and $22.028 million.


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Seasonalized Time Series Regression Analysis

Select a representative historical data set.Develop a seasonal index for each season.Use the seasonal indexes to deseasonalize the data.Perform linear regression analysis on thedeseasonalized data.Use the regression equation to compute the forecasts.Use the seasonal indexes to reapply the seasonalpatterns to the forecasts.


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Example: Computer Products Corp.

Seasonalized Times Series Regression AnalysisAn analyst at CPC wants to develop next years

quarterly forecasts of sales revenue for CPCs line of Epsilon Computers. She believes that the most recent8 quarters of sales (shown on the next slide) arerepresentative of next years sales.


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Seasonalized Times Series Regression AnalysisRepresentative Historical Data Set

Year Qtr. ($mil.) Year Qtr. ($mil.)

1 1 7.4 2 1 8.31 2 6.5 2 2 7.41 3 4.9 2 3 5.4

1 4 16.1 2 4 18.0


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Seasonalized Times Series Regression AnalysisCompute the Seasonal Indexes

Quarterly Sales

Year Q1 Q2 Q3 Q4 Total1 7.4 6.5 4.9 16.1 34.92 8.3 7.4 5.4 18.0 39.1

Totals 15.7 13.9 10.3 34.1 74.0Qtr. Avg. 7.85 6.95 5.15 17.05 9.25Seas.Ind. .849 .751 .557 1.843 4.000


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Seasonalized Times Series Regression AnalysisDeseasonalize the Data

Quarterly Sales

Year Q1 Q2 Q3 Q41 8.72 8.66 8.80 8.742 9.78 9.85 9.69 9.77


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Seasonalized Times Series Regression AnalysisPerform Regression on Deseasonalized Data

Yr. Qtr. x y x 2 xy

1 1 1 8.72 1 8.721 2 2 8.66 4 17.321 3 3 8.80 9 26.401 4 4 8.74 16 34.962 1 5 9.78 25 48.90

2 2 6 9.85 36 59.102 3 7 9.69 49 67.832 4 8 9.77 64 78.16

Totals 36 74.01 204 341.39


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Seasonalized Times Series Regression AnalysisPerform Regression on Deseasonalized Data

Y = 8.357 + 0.199X

2204(74.01) 36(341.39)a 8.357

8(204) (36)

28(341.39) 36(74.01)b 0.199

8(204) (36)


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Seasonalized Times Series Regression AnalysisCompute the Deseasonalized Forecasts

Y9 = 8.357 + 0.199(9) = 10.148

Y10 = 8.357 + 0.199(10) = 10.347Y11 = 8.357 + 0.199(11) = 10.546Y12 = 8.357 + 0.199(12) = 10.745

Note: Average sales are expected to increase by.199 million (about $200,000) per quarter.

l d


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Seasonalized Times Series Regression AnalysisSeasonalize the Forecasts

Seas. Deseas. Seas.

Yr. Qtr. Index Forecast Forecast3 1 .849 10.148 8.623 2 .751 10.347 7.77

3 3 .557 10.546 5.873 4 1.843 10.745 19.80

Sh R F


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Short-Range Forecasts

Time spans ranging from a few days to a few weeksCycles, seasonality, and trend may have little effectRandom fluctuation is main data component

E l i F M d l P f


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Evaluating Forecast-Model Performance

Short-range forecasting models are evaluated on thebasis of three characteristics:Impulse responseNoise-dampening abilityAccuracy

E l i F M d l P f


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Impulse Response and Noise-Dampening AbilityIf forecasts have little period-to-period fluctuation,they are said to be noise dampening.Forecasts that respond quickly to changes in dataare said to have a high impulse response.A forecast system that responds quickly to datachanges necessarily picks up a great deal of

random fluctuation (noise).Hence, there is a trade-off between high impulseresponse and high noise dampening.

E l i F M d l P f


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AccuracyAccuracy is the typical criterion for judging theperformance of a forecasting approachAccuracy is how well the forecasted values matchthe actual values

M it i A


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Monitoring Accuracy

Accuracy of a forecasting approach needs to bemonitored to assess the confidence you can have in itsforecasts and changes in the market may requirereevaluation of the approach

Accuracy can be measured in several waysStandard error of the forecast (covered earlier)Mean absolute deviation (MAD)

Mean squared error (MSE)

M it i A


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Monitoring Accuracy

Mean Absolute Deviation (MAD)

n

periodsnfordeviationabsoluteof Sum=MAD

n

i ii=1

Actual demand -Forecast demandMAD =

n

M it i g A


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Mean Squared Error (MSE)MSE = (S yx)2

A small value for S yx means data points aretightly grouped around the line and error range issmall.

When the forecast errors are normally

distributed, the values of MAD and s yx are related:MSE = 1.25(MAD)

Monitoring Accuracy

Sh t R g F ti g M th d


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Short-Range Forecasting Methods

(Simple) Moving AverageWeighted Moving AverageExponential SmoothingExponential Smoothing with Trend

Simple Mo ing A erage


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Simple Moving Average

An averaging period (AP) is given or selectedThe forecast for the next period is the arithmeticaverage of the AP most recent actual demandsIt is called a simple average because each periodused to compute the average is equally weighted. . . more



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It is called moving because as new demand databecomes available, the oldest data is not usedBy increasing the AP, the forecast is less responsiveto fluctuations in demand (low impulse response and

high noise dampening)By decreasing the AP, the forecast is more responsiveto fluctuations in demand (high impulse response andlow noise dampening)

Weighted Moving Average


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This is a variation on the simple moving averagewhere the weights used to compute the average arenot equal.This allows more recent demand data to have a

greater effect on the moving average, therefore theforecast.. . . more



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The weights must add to 1.0 and generally decreasein value with the age of the data.The distribution of the weights determine the impulseresponse of the forecast.

Exponential Smoothing


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The weights used to compute the forecast (movingaverage) are exponentially distributed.The forecast is the sum of the old forecast and aportion ( a ) of the forecast error (A t-1 - Ft-1).

Ft = F t-1 + a (A t-1 - Ft-1)

. . . more




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The smoothing constant,a

, must be between 0.0 and1.0.A large a provides a high impulse response forecast.A small a provides a low impulse response forecast.

Example: Central Call Center


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Moving AverageCCC wishes to forecast the number of incomingcalls it receives in a day from the customers of one of its clients, BMI. CCC schedules the appropriate

number of telephone operators based on projected callvolumes.

CCC believes that the most recent 12 days of callvolumes (shown on the next slide) are representativeof the near future call volumes.



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Moving AverageRepresentative Historical Data

Day Calls Day Calls

1 159 7 2032 217 8 1953 186 9 1884 161 10 168

5 173 11 1986 157 12 159



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Moving AverageUse the moving average method with an AP = 3days to develop a forecast of the call volume in Day13.

F13 = (168 + 198 + 159)/3 = 175.0 calls



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Weighted Moving AverageUse the weighted moving average method with anAP = 3 days and weights of .1 (for oldest datum), .3,and .6 to develop a forecast of the call volume in Day

13.F13 = .1(168) + .3(198) + .6(159) = 171.6 calls

Note: The WMA forecast is lower than the MAforecast because Day 13s relatively low call volumecarries almost twice as much weight in the WMA(.60) as it does in the MA (.33).



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Exponential SmoothingIf a smoothing constant value of .25 is used andthe exponential smoothing forecast for Day 11 was180.76 calls, what is the exponential smoothing

forecast for Day 13?

F12 = 180.76 + .25(198 180.76) = 185.07F13 = 185.07 + .25(159 185.07) = 178.55



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Forecast Accuracy - MADWhich forecasting method (the AP = 3 movingaverage or the a = .25 exponential smoothing) ispreferred, based on the MAD over the most recent 9

days? (Assume that the exponential smoothingforecast for Day 3 is the same as the actual callvolume.)



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AP = 3 a = .25Day Calls Forec. |Error| Forec. |Error|

4 161 187.3 26.3 186.0 25.05 173 188.0 15.0 179.8 6.8

6 157 173.3 16.3 178.1 21.17 203 163.7 39.3 172.8 30.28 195 177.7 17.3 180.4 14.69 188 185.0 3.0 184.0 4.0

10 168 195.3 27.3 185.0 17.011 198 183.7 14.3 180.8 17.212 159 184.7 25.7 185.1 26.1

MAD 20.5 18.0

Exponential Smoothing with Trend


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As we move toward medium-range forecasts, trendbecomes more important.Incorporating a trend component into exponentiallysmoothed forecasts is called double exponential

smoothing.The estimate for the average and the estimate for thetrend are both smoothed.



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Model Form

FT t = S t-1 + T t-1where:

FT t = forecast with trend in period tSt-1 = smoothed forecast (average) in period t-1Tt-1 = smoothed trend estimate in period t-1



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Smoothing the Average

St = FT t + a (A t FT t)

Smoothing the Trend

Tt = T t-1 + b (FT t FT t-1 - T t-1)

where: a = smoothing constant for the average

b = smoothing constant for the trend

Criteria for Selecting


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a Forecasting Method

CostAccuracyData availableTime spanNature of products and servicesImpulse response and noise dampening



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Cost and AccuracyThere is a trade-off between cost and accuracy;generally, more forecast accuracy can be obtainedat a cost.

High-accuracy approaches have disadvantages:Use more dataData are ordinarily more difficult to obtain

The models are more costly to design,implement, and operateTake longer to use



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Cost and AccuracyLow/Moderate-Cost Approaches statisticalmodels, historical analogies, executive-committeeconsensus

High-Cost Approaches complex econometricmodels, Delphi, and market research

Criteria for Selectingh d


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Data AvailableIs the necessary data available or can it beeconomically obtained?If the need is to forecast sales of a new product,then a customer survey may not be practical;instead, historical analogy or market research mayhave to be used.

Criteria for SelectingF i M h d


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Time SpanWhat operations resource is being forecast and forwhat purpose?Short-term staffing needs might best be forecastwith moving average or exponential smoothingmodels.Long-term factory capacity needs might best be

predicted with regression or executive-committeeconsensus methods.



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Nature of Products and ServicesIs the product/service high cost or high volume?Where is the product/service in its life cycle?Does the product/service have seasonal demandfluctuations?



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Impulse Response and Noise DampeningAn appropriate balance must be achieved between:

How responsive we want the forecasting modelto be to changes in the actual demand dataOur desire to suppress undesirable chancevariation or noise in the demand data

Reasons for Ineffective Forecasting


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g

Not involving a broad cross section of peopleNot recognizing that forecasting is integral tobusiness planningNot recognizing that forecasts will always be wrongNot forecasting the right thingsNot selecting an appropriate forecasting methodNot tracking the accuracy of the forecasting models

Monitoring and ControllingF ti M d l


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a Forecasting Model

Tracking Signal (TS)The TS measures the cumulative forecast errorover n periods in terms of MAD

If the forecasting model is performing well, the TSshould be around zeroThe TS indicates the direction of the forecastingerror; if the TS is positive -- increase the forecasts,if the TS is negative -- decrease the forecasts.

n

i i1

(Actual demand - Forecast demand )TS =

MADi

Monitoring and ControllingF ti M d l


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a Forecasting Model

Tracking SignalThe value of the TS can be used to automaticallytrigger new parameter values of a model, therebycorrecting model performance.

If the limits are set too narrow, the parametervalues will be changed too often.If the limits are set too wide, the parameter values

will not be changed often enough and accuracywill suffer.

Tracking Signal: What do you notice?


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Tracking Signal: What do you notice?

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9 10 11Period

S a

l e s

Computer Software for Forecasting


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p g

Examples of computer software with forecastingcapabilities

Forecast ProAutoboxSmartForecasts for WindowsSASSPSS

SAPPOM Software Library

Primarily for

forecasting

Have

Forecastingmodules

Forecasting in Small Businessesand Start Up Vent res


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and Start-Up Ventures

Forecasting for these businesses can be difficult forthe following reasons:

Not enough personnel with the time to forecastPersonnel lack the necessary skills to develop goodforecastsSuch businesses are not data-rich environmentsForecasting for new products/services is always

difficult, even for the experienced forecaster

Sources of Forecasting Data and Help


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Government agencies at the local, regional, state, andfederal levelsIndustry associationsConsulting companies


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Wrap-Up: World-Class Practice


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Predisposed to have effective methods of forecastingbecause they have exceptional long-range businessplanningFormal forecasting effort

Develop methods to monitor the performance of theirforecasting modelsDo not overlook the short run.... excellent short rangeforecasts as well

End of Chapter 3


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ch3. demand forecasting

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