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Chapter 3Chapter 3Chapter 3Chapter 3
Demand ForecastingDemand Forecasting
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Introduction Introduction Introduction Introduction
Demand estimatesDemand estimates for products and services are the for products and services are the starting point for all the other planning in operations starting point for all the other planning in operations management.management.
Management teams develop Management teams develop sales forecastssales forecasts based in based in part on demand estimates.part on demand estimates.
The sales forecasts become inputs to both business The sales forecasts become inputs to both business strategy and strategy and production resource forecastsproduction resource forecasts..
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Forecasting is an Integral PartForecasting is an Integral Part of Business Planning of Business Planning
Forecasting is an Integral PartForecasting is an Integral Part of Business Planning of Business Planning
ForecastForecastMethod(s)Method(s)
DemandDemandEstimatesEstimates
SalesSalesForecastForecast
ManagementManagementTeamTeam
Inputs:Inputs:Market,Market,
Economic,Economic,OtherOther
BusinessBusinessStrategyStrategy
Production ResourceProduction ResourceForecastsForecasts
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Some Reasons WhySome Reasons WhyForecasting is Essential in OMForecasting is Essential in OM
Some Reasons WhySome Reasons WhyForecasting is Essential in OMForecasting is Essential in OM
New Facility PlanningNew Facility Planning – It can take 5 years to design – It can take 5 years to design and build a new factory or design and implement a and build a new factory or design and implement a new production process.new production process.
Production PlanningProduction Planning – Demand for products vary – Demand for products vary from month to month and it can take several months from month to month and it can take several months to change the capacities of production processes.to change the capacities of production processes.
Workforce SchedulingWorkforce Scheduling – Demand for services (and – Demand for services (and the necessary staffing) can vary from hour to hour the necessary staffing) can vary from hour to hour and employees weekly work schedules must be and employees weekly work schedules must be developed in advance.developed in advance.
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Examples of Production Resource ForecastsExamples of Production Resource ForecastsExamples of Production Resource ForecastsExamples of Production Resource Forecasts
LongLongRangeRange
MediumMediumRangeRange
ShortShortRangeRange
YearsYears
MonthsMonths
Days,Days,WeeksWeeks
Product Lines,Product Lines,Factory CapacitiesFactory Capacities
ForecastForecastHorizonHorizon
TimeTimeSpanSpan
Item BeingItem BeingForecastedForecasted
Unit ofUnit ofMeasureMeasure
Product Groups,Product Groups,Depart. CapacitiesDepart. Capacities
Specific Products,Specific Products,Machine CapacitiesMachine Capacities
Dollars,Dollars,TonsTons
Units,Units,PoundsPounds
Units,Units,HoursHours
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Forecasting MethodsForecasting MethodsForecasting MethodsForecasting Methods
Qualitative ApproachesQualitative Approaches Quantitative ApproachesQuantitative Approaches
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Qualitative ApproachesQualitative ApproachesQualitative ApproachesQualitative Approaches
Usually based on judgments about causal factors that Usually based on judgments about causal factors that underlie the demand of particular products or servicesunderlie the demand of particular products or services
Do not require a demand history for the product or Do not require a demand history for the product or service, therefore are useful for new products/servicesservice, therefore are useful for new products/services
Approaches vary in sophistication from scientifically Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future conducted surveys to intuitive hunches about future eventsevents
The approach/method that is appropriate depends on The approach/method that is appropriate depends on a product’s life cycle stagea product’s life cycle stage
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Qualitative Methods Qualitative Methods Qualitative Methods Qualitative Methods
Educated guessEducated guess intuitive hunchesintuitive hunches Executive committee consensusExecutive committee consensus Delphi methodDelphi method Survey of sales forceSurvey of sales force Survey of customers Survey of customers Historical analogyHistorical analogy Market researchMarket research sscientifically conducted cientifically conducted
surveyssurveys
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Quantitative Forecasting ApproachesQuantitative Forecasting ApproachesQuantitative Forecasting ApproachesQuantitative Forecasting Approaches
Based on the assumption that the “forces” that Based on the assumption that the “forces” that generated the past demand will generate the future generated the past demand will generate the future demand, i.e., history will tend to repeat itselfdemand, i.e., history will tend to repeat itself
Analysis of the past demand pattern provides a good Analysis of the past demand pattern provides a good basis for forecasting future demandbasis for forecasting future demand
Majority of quantitative approaches fall in the Majority of quantitative approaches fall in the category of time series analysiscategory of time series analysis
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A A time seriestime series is a set of numbers where the order or is a set of numbers where the order or sequence of the numbers is important, e.g., historical sequence of the numbers is important, e.g., historical demanddemand
Analysis of the time series identifies patternsAnalysis of the time series identifies patterns Once the patterns are identified, they can be used to Once the patterns are identified, they can be used to
develop a forecastdevelop a forecast
Time Series AnalysisTime Series AnalysisTime Series AnalysisTime Series Analysis
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Components of a Time Series Components of a Time Series Components of a Time Series Components of a Time Series
TrendsTrends are noted by an upward or downward sloping are noted by an upward or downward sloping line.line.
CycleCycle is a data pattern that may cover several years is a data pattern that may cover several years before it repeats itself.before it repeats itself.
SeasonalitySeasonality is a data pattern that repeats itself over is a data pattern that repeats itself over the period of one year or less.the period of one year or less.
Random fluctuation (noise)Random fluctuation (noise) results from random results from random variation or unexplained causes.variation or unexplained causes.
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Seasonal PatternsSeasonal PatternsSeasonal PatternsSeasonal Patterns
Length of TimeLength of Time Number of Number of
Before Pattern Length ofBefore Pattern Length of Seasons Seasons
Is RepeatedIs Repeated Season Season in Pattern in Pattern
YearYear QuarterQuarter 4 4
YearYear Month Month 1212
YearYear Week Week 5252
MonthMonth Day Day 28-31 28-31
WeekWeek Day Day 7 7
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Quantitative Forecasting ApproachesQuantitative Forecasting ApproachesQuantitative Forecasting ApproachesQuantitative Forecasting Approaches
Linear RegressionLinear Regression Simple Moving AverageSimple Moving Average Weighted Moving AverageWeighted Moving Average Exponential Smoothing (exponentially weighted Exponential Smoothing (exponentially weighted
moving average)moving average) Exponential Smoothing with Trend (double Exponential Smoothing with Trend (double
exponential smoothing)exponential smoothing)
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Long-Range ForecastsLong-Range ForecastsLong-Range ForecastsLong-Range Forecasts
Time spans usually greater than one yearTime spans usually greater than one year Necessary to support strategic decisions about Necessary to support strategic decisions about
planning products, processes, and facilitiesplanning products, processes, and facilities
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Simple Linear RegressionSimple Linear RegressionSimple Linear RegressionSimple Linear Regression
Linear regression analysis establishes a relationship Linear regression analysis establishes a relationship between a dependent variable and one or more between a dependent variable and one or more independent variables.independent variables.
In In simple linear regression analysissimple linear regression analysis there is only one there is only one independent variable.independent variable.
If the data is a time series, the independent variable is If the data is a time series, the independent variable is the time period.the time period.
The dependent variable is whatever we wish to The dependent variable is whatever we wish to forecast.forecast.
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Simple Linear RegressionSimple Linear RegressionSimple Linear RegressionSimple Linear Regression
Regression EquationRegression Equation
This model is of the form:This model is of the form:
Y = a + bXY = a + bX
Y = dependent variableY = dependent variable
X = independent variableX = independent variable
a = y-axis intercepta = y-axis intercept
b = slope of regression lineb = slope of regression line
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Simple Linear RegressionSimple Linear RegressionSimple Linear RegressionSimple Linear Regression
Constants a and bConstants a and b
The constants a and b are computed using the The constants a and b are computed using the following equations:following equations:
2
2 2
x y- x xya =
n x -( x)
2 2
xy- x yb =
n x -( x)
n
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Simple Linear RegressionSimple Linear RegressionSimple Linear RegressionSimple Linear Regression
Once the a and b values are computed, a future value Once the a and b values are computed, a future value of X can be entered into the regression equation and a of X can be entered into the regression equation and a corresponding value of Y (the forecast) can be corresponding value of Y (the forecast) can be calculated.calculated.
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Example: College EnrollmentExample: College EnrollmentExample: College EnrollmentExample: College Enrollment
Simple Linear RegressionSimple Linear Regression
At a small regional college enrollments have grown At a small regional college enrollments have grown steadily over the past six years, as evidenced below. steadily over the past six years, as evidenced below. Use time series regression to forecast the student Use time series regression to forecast the student enrollments for the next three years. enrollments for the next three years.
StudentsStudents StudentsStudentsYearYear Enrolled (1000s)Enrolled (1000s) YearYear Enrolled (1000s)Enrolled (1000s) 11 2.52.5 44 3.23.2 22 2.82.8 55 3.33.3 33 2.92.9 66 3.43.4
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Example: College EnrollmentExample: College EnrollmentExample: College EnrollmentExample: College Enrollment
Simple Linear RegressionSimple Linear Regression
xx yy xx22 xyxy11 2.52.5 11 2.52.522 2.82.8 44 5.65.633 2.92.9 99 8.78.744 3.23.2 1616 12.812.855 3.33.3 2525 16.516.566 3.43.4 3636 20.420.4
x=21 x=21 y=18.1 y=18.1 xx22=91 =91 xy=66.5xy=66.5
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Example: College EnrollmentExample: College EnrollmentExample: College EnrollmentExample: College Enrollment
Simple Linear RegressionSimple Linear Regression
Y = 2.387 + 0.180XY = 2.387 + 0.180X
2
91(18.1) 21(66.5)2.387
6(91) (21)a
6(66.5) 21(18.1)0.180
105b
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Example: College EnrollmentExample: College EnrollmentExample: College EnrollmentExample: College Enrollment
Simple Linear RegressionSimple Linear Regression
YY77 = 2.387 + 0.180(7) = 3.65 or 3,650 students = 2.387 + 0.180(7) = 3.65 or 3,650 students
YY88 = 2.387 + 0.180(8) = 3.83 or 3,830 students = 2.387 + 0.180(8) = 3.83 or 3,830 students
YY99 = 2.387 + 0.180(9) = 4.01 or 4,010 students = 2.387 + 0.180(9) = 4.01 or 4,010 students
Note: Enrollment is expected to increase by 180Note: Enrollment is expected to increase by 180 students per year.students per year.
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Simple Linear RegressionSimple Linear RegressionSimple Linear RegressionSimple Linear Regression
Simple linear regression can also be used when the Simple linear regression can also be used when the independent variable X represents a variable other independent variable X represents a variable other than time.than time.
In this case, linear regression is representative of a In this case, linear regression is representative of a class of forecasting models called class of forecasting models called causal forecasting causal forecasting modelsmodels..
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Simple Linear Regression – Causal ModelSimple Linear Regression – Causal Model
The manager of RPC wants to project the The manager of RPC wants to project the firm’s sales for the next 3 years. He knows that firm’s sales for the next 3 years. He knows that RPC’s long-range sales are tied very closely to RPC’s long-range sales are tied very closely to national freight car loadings. On the next slide are 7 national freight car loadings. On the next slide are 7 years of relevant historical data.years of relevant historical data.
Develop a simple linear regression model Develop a simple linear regression model between RPC sales and national freight car loadings. between RPC sales and national freight car loadings. Forecast RPC sales for the next 3 years, given that the Forecast RPC sales for the next 3 years, given that the rail industry estimates car loadings of 250, 270, and rail industry estimates car loadings of 250, 270, and 300 million.300 million.
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Simple Linear Regression – Causal ModelSimple Linear Regression – Causal Model
RPC SalesRPC Sales Car LoadingsCar Loadings
YearYear ($millions)($millions) (millions)(millions)11 9.59.5 12012022 11.011.0 13513533 12.012.0 13013044 12.512.5 15015055 14.014.0 17017066 16.016.0 19019077 18.018.0 220220
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Simple Linear Regression – Causal ModelSimple Linear Regression – Causal Model
xx yy xx22 xyxy
120120 9.59.5 14,40014,400 1,1401,140135135 11.011.0 18,22518,225 1,4851,485130130 12.012.0 16,90016,900 1,5601,560150150 12.512.5 22,50022,500 1,8751,875170170 14.014.0 28,90028,900 2,3802,380190190 16.016.0 36,10036,100 3,0403,040220220 18.018.0 48,40048,400 3,9603,960
1,1151,115 93.093.0 185,425185,425 15,44015,440
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Simple Linear Regression – Causal ModelSimple Linear Regression – Causal Model
Y = 0.528 + 0.0801XY = 0.528 + 0.0801X
2
185,425(93) 1,115(15,440)a 0.528
7(185,425) (1,115)
2
7(15,440) 1,115(93)b 0.0801
7(185,425) (1,115)
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Simple Linear Regression – Causal ModelSimple Linear Regression – Causal Model
YY8 8 = 0.528 + 0.0801(250) = $20.55 million = 0.528 + 0.0801(250) = $20.55 million
YY9 9 = 0.528 + 0.0801(270) = $22.16 million = 0.528 + 0.0801(270) = $22.16 million
YY1010 = 0.528 + 0.0801(300) = $24.56 million = 0.528 + 0.0801(300) = $24.56 million
Note: RPC sales are expected to increase by Note: RPC sales are expected to increase by $80,100 for each additional million national freight $80,100 for each additional million national freight car loadings.car loadings.
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Multiple Regression AnalysisMultiple Regression AnalysisMultiple Regression AnalysisMultiple Regression Analysis
Multiple regression analysis is used when there are Multiple regression analysis is used when there are two or more independent variables.two or more independent variables.
An example of a multiple regression equation is:An example of a multiple regression equation is:
Y = 50.0 + 0.05XY = 50.0 + 0.05X11 + 0.10X + 0.10X22 – 0.03X – 0.03X33
where: Y = firm’s annual sales ($millions)where: Y = firm’s annual sales ($millions)
XX11 = industry sales ($millions) = industry sales ($millions)
XX22 = regional per capita income = regional per capita income
($thousands)($thousands)
XX33 = regional per capita debt ($thousands) = regional per capita debt ($thousands)
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Coefficient of Correlation (Coefficient of Correlation (rr))Coefficient of Correlation (Coefficient of Correlation (rr))
The coefficient of correlation, The coefficient of correlation, rr, explains the relative , explains the relative importance of the relationship between importance of the relationship between xx and and yy..
The sign of The sign of rr shows the direction of the relationship. shows the direction of the relationship. The absolute value of The absolute value of rr shows the strength of the shows the strength of the
relationship.relationship. The sign of The sign of rr is always the same as the sign of b. is always the same as the sign of b. rr can take on any value between –1 and +1. can take on any value between –1 and +1.
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Coefficient of Correlation (Coefficient of Correlation (rr))Coefficient of Correlation (Coefficient of Correlation (rr))
Meanings of several values of Meanings of several values of rr::
-1 a perfect negative relationship (as -1 a perfect negative relationship (as xx goes up, goes up, yy goes down by one unit, and vice versa) goes down by one unit, and vice versa)
+1 a perfect positive relationship (as +1 a perfect positive relationship (as xx goes up, goes up, yy goes up by one unit, and vice versa) goes up by one unit, and vice versa)
0 no relationship exists between 0 no relationship exists between xx and and yy
+0.3 a weak positive relationship+0.3 a weak positive relationship
-0.8 a strong negative relationship-0.8 a strong negative relationship
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Coefficient of Correlation (Coefficient of Correlation (rr))Coefficient of Correlation (Coefficient of Correlation (rr))
r r is computed by: is computed by:
2 2 2 2( ) ( )
n xy x yr
n x x n y y
2 2 2 2( ) ( )
n xy x yr
n x x n y y
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Coefficient of Determination (Coefficient of Determination (rr22))Coefficient of Determination (Coefficient of Determination (rr22))
The coefficient of determination, The coefficient of determination, rr22, is the square of , is the square of the coefficient of correlation.the coefficient of correlation.
The modification of The modification of rr to to rr22 allows us to shift from allows us to shift from subjective measures of relationship to a more specific subjective measures of relationship to a more specific measure.measure.
rr22 is determined by the ratio of explained variation to is determined by the ratio of explained variation to total variation:total variation:
22
2
( )
( )
Y yr
y y
22
2
( )
( )
Y yr
y y
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Coefficient of CorrelationCoefficient of Correlation
xx yy xx22 xyxy yy22
120120 9.59.5 14,40014,400 1,1401,140 90.2590.25135135 11.011.0 18,22518,225 1,4851,485 121.00121.00130130 12.012.0 16,90016,900 1,5601,560 144.00144.00150150 12.512.5 22,50022,500 1,8751,875 156.25156.25170170 14.014.0 28,90028,900 2,3802,380 196.00196.00190190 16.016.0 36,10036,100 3,0403,040 256.00256.00220220 18.018.0 48,40048,400 3,9603,960 324.00324.00
1,1151,115 93.093.0 185,425185,425 15,44015,440 1,287.501,287.50
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Coefficient of CorrelationCoefficient of Correlation
r r = .9829 = .9829
2 2
7(15,440) 1,115(93)
7(185,425) (1,115) 7(1,287.5) (93)r
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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.
Coefficient of DeterminationCoefficient of Determination
rr2 2 = (.9829) = (.9829)22 = .966 = .966
96.6% of the variation in RPC sales is explained by 96.6% of the variation in RPC sales is explained by national freight car loadings.national freight car loadings.
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Ranging ForecastsRanging ForecastsRanging ForecastsRanging Forecasts
Forecasts for future periods are only estimates and are Forecasts for future periods are only estimates and are subject to error.subject to error.
One way to deal with uncertainty is to develop best-One way to deal with uncertainty is to develop best-estimate forecasts and the estimate forecasts and the rangesranges within which the within which the actual data are likely to fall.actual data are likely to fall.
The ranges of a forecast are defined by the upper and The ranges of a forecast are defined by the upper and lower limits of a confidence interval.lower limits of a confidence interval.
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Seasonalized Time Series Regression AnalysisSeasonalized Time Series Regression AnalysisSeasonalized Time Series Regression AnalysisSeasonalized Time Series Regression Analysis
Select a representative historical data set.Select a representative historical data set. Develop a seasonal index for each season.Develop a seasonal index for each season. Use the seasonal indexes to deseasonalize the data.Use the seasonal indexes to deseasonalize the data. Perform lin. regr. analysis on the deseasonalized data.Perform lin. regr. analysis on the deseasonalized data. Use the regression equation to compute the forecasts.Use the regression equation to compute the forecasts. Use the seas. indexes to reapply the seasonal patterns Use the seas. indexes to reapply the seasonal patterns
to the forecasts.to the forecasts.
39
Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis
An analyst at CPC wants to develop next year’s An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent Epsilon Computers. She believes that the most recent 8 quarters of sales (shown on the next slide) are 8 quarters of sales (shown on the next slide) are representative of next year’s sales.representative of next year’s sales.
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Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis Representative Historical Data SetRepresentative Historical Data Set
YearYear Qtr.Qtr. ($mil.)($mil.) YearYear Qtr.Qtr. ($mil.)($mil.)
11 11 7.47.4 22 11 8.38.311 22 6.56.5 22 22 7.47.411 33 4.94.9 22 33 5.45.411 44 16.116.1 22 44 18.018.0
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Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis Compute the Seasonal IndexesCompute the Seasonal Indexes
Quarterly SalesQuarterly Sales
YearYear Q1Q1 Q2Q2 Q3Q3 Q4Q4 TotalTotal11 7.47.4 6.56.5 4.94.9 16.116.1 34.934.922 8.38.3 7.47.4 5.45.4 18.018.0 39.139.1
TotalsTotals15.715.7 13.913.9 10.310.3 34.134.1 74.074.0 Qtr. Avg.Qtr. Avg.7.857.85 6.956.95 5.155.15 17.0517.05 9.259.25
Seas.Ind.Seas.Ind..849.849 .751.751 .557.557 1.8431.843 4.0004.000
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Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis Deseasonalize the DataDeseasonalize the Data
Quarterly SalesQuarterly Sales
YearYear Q1Q1 Q2Q2 Q3Q3 Q4Q411 8.728.72 8.668.66 8.808.80 8.748.7422 9.789.78 9.859.85 9.699.69 9.779.77
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Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis Perform Regression on Deseasonalized DataPerform Regression on Deseasonalized Data
Yr.Yr. Qtr.Qtr. xx yy xx22 xyxy
11 11 11 8.728.72 11 8.728.7211 22 22 8.668.66 44 17.3217.3211 33 33 8.808.80 99 26.4026.4011 44 44 8.748.74 1616 34.9634.9622 11 55 9.789.78 2525 48.9048.9022 22 66 9.859.85 3636 59.1059.1022 33 77 9.699.69 4949 67.8367.8322 44 88 9.779.77 6464 78.1678.16
TotalsTotals 3636 74.0174.01 204204 341.39341.39
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Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis Perform Regression on Deseasonalized DataPerform Regression on Deseasonalized Data
Y = 8.357 + 0.199XY = 8.357 + 0.199X
2
204(74.01) 36(341.39)a 8.357
8(204) (36)
2
8(341.39) 36(74.01)b 0.199
8(204) (36)
45
Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis Compute the Deseasonalized ForecastsCompute the Deseasonalized Forecasts
YY9 9 = 8.357 + 0.199(9) = 10.148 = 8.357 + 0.199(9) = 10.148
YY10 10 = 8.357 + 0.199(10) = 10.347 = 8.357 + 0.199(10) = 10.347
YY11 11 = 8.357 + 0.199(11) = 10.546 = 8.357 + 0.199(11) = 10.546
YY12 12 = 8.357 + 0.199(12) = 10.745 = 8.357 + 0.199(12) = 10.745
Note: Average sales are expected to increase byNote: Average sales are expected to increase by
.199 million (about $200,000) per .199 million (about $200,000) per quarter.quarter.
46
Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.
Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis Seasonalize the ForecastsSeasonalize the Forecasts
Seas.Seas. Deseas.Deseas. Seas.Seas.Yr.Yr. Qtr.Qtr. IndexIndex ForecastForecast ForecastForecast
33 11 .849.849 10.14810.148 8.628.6233 22 .751.751 10.34710.347 7.777.7733 33 .557.557 10.54610.546 5.875.8733 44 1.8431.843 10.74510.745 19.8019.80
47
Short-Range ForecastsShort-Range ForecastsShort-Range ForecastsShort-Range Forecasts
Time spans ranging from a few days to a few weeks Time spans ranging from a few days to a few weeks Cycles, seasonality, and trend may have little effectCycles, seasonality, and trend may have little effect Random fluctuation is main data componentRandom fluctuation is main data component
48
Evaluating Forecast-Model PerformanceEvaluating Forecast-Model PerformanceEvaluating Forecast-Model PerformanceEvaluating Forecast-Model Performance
Short-range forecasting models are evaluated on the Short-range forecasting models are evaluated on the basis of three characteristics:basis of three characteristics:
Impulse responseImpulse response Noise-dampening abilityNoise-dampening ability AccuracyAccuracy
49
Evaluating Forecast-Model PerformanceEvaluating Forecast-Model PerformanceEvaluating Forecast-Model PerformanceEvaluating Forecast-Model Performance
Impulse Response and Noise-Dampening AbilityImpulse Response and Noise-Dampening Ability If forecasts have little period-to-period fluctuation, If forecasts have little period-to-period fluctuation,
they are said to be they are said to be noise dampeningnoise dampening.. Forecasts that respond quickly to changes in data Forecasts that respond quickly to changes in data
are said to have a high are said to have a high impulse responseimpulse response.. A forecast system that responds quickly to data A forecast system that responds quickly to data
changes necessarily picks up a great deal of changes necessarily picks up a great deal of random fluctuation (random fluctuation (noisenoise).).
Hence, there is a trade-off between high impulse Hence, there is a trade-off between high impulse response and high noise dampening.response and high noise dampening.
50
Evaluating Forecast-Model PerformanceEvaluating Forecast-Model PerformanceEvaluating Forecast-Model PerformanceEvaluating Forecast-Model Performance
AccuracyAccuracy Accuracy is the typical criterion for judging the Accuracy is the typical criterion for judging the
performance of a forecasting approachperformance of a forecasting approach Accuracy is how well the forecasted values match Accuracy is how well the forecasted values match
the actual valuesthe actual values
51
Monitoring Accuracy Monitoring Accuracy Monitoring Accuracy Monitoring Accuracy
Accuracy of a forecasting approach needs to be Accuracy of a forecasting approach needs to be monitored to assess the confidence you can have in monitored to assess the confidence you can have in its forecasts and changes in the market may require its forecasts and changes in the market may require reevaluation of the approachreevaluation of the approach
Accuracy can be measured in several waysAccuracy can be measured in several ways Standard error of the forecast (covered earlier)Standard error of the forecast (covered earlier) Mean absolute deviation (MAD)Mean absolute deviation (MAD) Mean squared error (MSE)Mean squared error (MSE)
52
Monitoring AccuracyMonitoring AccuracyMonitoring AccuracyMonitoring Accuracy
Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)
n
periodsn for deviation absolute of Sum=MAD
n
i ii=1
Actual demand -Forecast demandMAD =
n
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Mean Squared Error (MSE)Mean Squared Error (MSE)
MSE = (SMSE = (Syxyx))22
A small value for SA small value for Syxyx means data points are means data points are
tightly grouped around the line and error range is tightly grouped around the line and error range is small. small.
When the forecast errors are normally When the forecast errors are normally distributed, the values of MAD and sdistributed, the values of MAD and syxyx are related: are related:
MSE = 1.25(MAD)MSE = 1.25(MAD)
Monitoring AccuracyMonitoring AccuracyMonitoring AccuracyMonitoring Accuracy
54
Short-Range Forecasting MethodsShort-Range Forecasting MethodsShort-Range Forecasting MethodsShort-Range Forecasting Methods
(Simple) Moving Average(Simple) Moving Average Weighted Moving AverageWeighted Moving Average Exponential SmoothingExponential Smoothing Exponential Smoothing with TrendExponential Smoothing with Trend
55
Simple Moving AverageSimple Moving AverageSimple Moving AverageSimple Moving Average
An averaging period (AP) is given or selectedAn averaging period (AP) is given or selected The forecast for the next period is the arithmetic The forecast for the next period is the arithmetic
average of the AP most recent actual demandsaverage of the AP most recent actual demands It is called a “simple” average because each period It is called a “simple” average because each period
used to compute the average is equally weightedused to compute the average is equally weighted . . . more. . . more
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Simple Moving AverageSimple Moving AverageSimple Moving AverageSimple Moving Average
It is called “moving” because as new demand data It is called “moving” because as new demand data becomes available, the oldest data is not usedbecomes available, the oldest data is not used
By increasing the AP, the forecast is less responsive By increasing the AP, the forecast is less responsive to fluctuations in demand (low impulse response and to fluctuations in demand (low impulse response and high noise dampening)high noise dampening)
By decreasing the AP, the forecast is more responsive By decreasing the AP, the forecast is more responsive to fluctuations in demand (high impulse response and to fluctuations in demand (high impulse response and low noise dampening)low noise dampening)
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Weighted Moving AverageWeighted Moving AverageWeighted Moving AverageWeighted Moving Average
This is a variation on the simple moving average This is a variation on the simple moving average where the weights used to compute the average are where the weights used to compute the average are not equal.not equal.
This allows more recent demand data to have a This allows more recent demand data to have a greater effect on the moving average, therefore the greater effect on the moving average, therefore the forecast.forecast.
. . . more. . . more
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Weighted Moving AverageWeighted Moving AverageWeighted Moving AverageWeighted Moving Average
The weights must add to 1.0 and generally decrease The weights must add to 1.0 and generally decrease in value with the age of the data.in value with the age of the data.
The distribution of the weights determine the impulse The distribution of the weights determine the impulse response of the forecast.response of the forecast.
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The weights used to compute the forecast (moving The weights used to compute the forecast (moving average) are exponentially distributed.average) are exponentially distributed.
The forecast is the sum of the old forecast and a The forecast is the sum of the old forecast and a portion (portion () of the forecast error (A) of the forecast error (A t-1 t-1--FFt-1t-1).).
FFtt = F = Ft-1t-1 + + (A(A t-1 t-1--FFt-1t-1))
. . . more. . . more
Exponential SmoothingExponential SmoothingExponential SmoothingExponential Smoothing
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Exponential SmoothingExponential SmoothingExponential SmoothingExponential Smoothing
The smoothing constant, The smoothing constant, , must be between 0.0 and , must be between 0.0 and 1.0.1.0.
A large A large provides a high impulse response forecast. provides a high impulse response forecast. A small A small provides a low impulse response forecast. provides a low impulse response forecast.
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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center
Moving AverageMoving Average
CCC wishes to forecast the number of CCC wishes to forecast the number of incoming calls it receives in a day from the customers incoming calls it receives in a day from the customers of one of its clients, BMI. CCC schedules the of one of its clients, BMI. CCC schedules the appropriate number of telephone operators based on appropriate number of telephone operators based on projected call volumes.projected call volumes.
CCC believes that the most recent 12 days of CCC believes that the most recent 12 days of call volumes (shown on the next slide) are call volumes (shown on the next slide) are representative of the near future call volumes.representative of the near future call volumes.
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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center
Moving AverageMoving Average Representative Historical DataRepresentative Historical Data
DayDay CallsCalls DayDay CallsCalls11 159159 77 20320322 217217 88 19519533 186186 99 18818844 161161 1010 16816855 173173 1111 19819866 157157 1212 159159
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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center
Moving AverageMoving Average
Use the moving average method with an AP = Use the moving average method with an AP = 3 days to develop a forecast of the call volume in Day 3 days to develop a forecast of the call volume in Day 13.13.
FF1313 = (168 + 198 + 159)/3 = 175.0 calls = (168 + 198 + 159)/3 = 175.0 calls
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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center
Weighted Moving AverageWeighted Moving Average
Use the weighted moving average method with Use the weighted moving average method with an AP = 3 days and weights of .1 (for oldest an AP = 3 days and weights of .1 (for oldest datum), .3, and .6 to develop a forecast of the call datum), .3, and .6 to develop a forecast of the call volume in Day 13.volume in Day 13.
FF1313 = .1(168) + .3(198) + .6(159) = 171.6 calls = .1(168) + .3(198) + .6(159) = 171.6 calls
Note: The WMA forecast is lower than the MA Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).(.60) as it does in the MA (.33).
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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center
Exponential SmoothingExponential Smoothing
If a smoothing constant value of .25 is used If a smoothing constant value of .25 is used and the exponential smoothing forecast for Day 11 and the exponential smoothing forecast for Day 11 was 180.76 calls, what is the exponential smoothing was 180.76 calls, what is the exponential smoothing forecast for Day 13?forecast for Day 13?
FF1212 = 180.76 + .25(198 – 180.76) = 185.07 = 180.76 + .25(198 – 180.76) = 185.07
FF1313 = 185.07 + .25(159 – 185.07) = 178.55 = 185.07 + .25(159 – 185.07) = 178.55
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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center
Forecast Accuracy - MADForecast Accuracy - MAD
Which forecasting method (the AP = 3 moving Which forecasting method (the AP = 3 moving average or the average or the = .25 exponential smoothing) is = .25 exponential smoothing) is preferred, based on the MAD over the most recent 9 preferred, based on the MAD over the most recent 9 days? (Assume that the exponential smoothing days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call forecast for Day 3 is the same as the actual call volume.)volume.)
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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center
AP = 3AP = 3 = .25 = .25DayDay CallsCalls Forec.Forec. |Error||Error| Forec.Forec. |Error||Error|
44 161161 187.3187.3 26.326.3 186.0186.0 25.025.055 173173 188.0188.0 15.015.0 179.8179.8 6.86.866 157157 173.3173.3 16.316.3 178.1178.1 21.121.177 203203 163.7163.7 39.339.3 172.8172.8 30.230.288 195195 177.7177.7 17.317.3 180.4180.4 14.614.699 188188 185.0185.0 3.03.0 184.0184.0 4.04.0
1010 168168 195.3195.3 27.327.3 185.0185.0 17.017.01111 198198 183.7183.7 14.314.3 180.8180.8 17.217.21212 159159 184.7184.7 25.725.7 185.1185.1 26.126.1
MADMAD 20.520.5 18.018.0
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Criteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting MethodCriteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting Method
CostCost AccuracyAccuracy Data availableData available Time spanTime span Nature of products and servicesNature of products and services Impulse response and noise dampeningImpulse response and noise dampening
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Criteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting MethodCriteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting Method
Cost and AccuracyCost and Accuracy There is a trade-off between cost and accuracy; There is a trade-off between cost and accuracy;
generally, more forecast accuracy can be obtained generally, more forecast accuracy can be obtained at a cost.at a cost.
High-accuracy approaches have disadvantages:High-accuracy approaches have disadvantages: Use more dataUse more data Data are ordinarily more difficult to obtainData are ordinarily more difficult to obtain The models are more costly to design, The models are more costly to design,
implement, and operateimplement, and operate Take longer to useTake longer to use
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Criteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting MethodCriteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting Method
Cost and AccuracyCost and Accuracy Low/Moderate-Cost ApproachesLow/Moderate-Cost Approaches – statistical – statistical
models, historical analogies, executive-committee models, historical analogies, executive-committee consensusconsensus
High-Cost ApproachesHigh-Cost Approaches – complex econometric – complex econometric models, Delphi, and market researchmodels, Delphi, and market research
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Criteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting MethodCriteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting Method
Data AvailableData Available Is the necessary data available or can it be Is the necessary data available or can it be
economically obtained?economically obtained? If the need is to forecast sales of a If the need is to forecast sales of a newnew product, product,
then a customer survey may not be practical; then a customer survey may not be practical; instead, historical analogy or market research may instead, historical analogy or market research may have to be used.have to be used.
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Criteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting MethodCriteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting Method
Time SpanTime Span What operations resource is being forecast and for What operations resource is being forecast and for
what purpose?what purpose? Short-term staffing needs might best be forecast Short-term staffing needs might best be forecast
with moving average or exponential smoothing with moving average or exponential smoothing models.models.
Long-term factory capacity needs might best be Long-term factory capacity needs might best be predicted with regression or executive-committee predicted with regression or executive-committee consensus methods.consensus methods.
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Criteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting MethodCriteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting Method
Nature of Products and ServicesNature of Products and Services Is the product/service high cost or high volume?Is the product/service high cost or high volume? Where is the product/service in its life cycle?Where is the product/service in its life cycle? Does the product/service have seasonal demand Does the product/service have seasonal demand
fluctuations?fluctuations?
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Criteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting MethodCriteria for SelectingCriteria for Selectinga Forecasting Methoda Forecasting Method
Impulse Response and Noise DampeningImpulse Response and Noise Dampening An appropriate balance must be achieved between:An appropriate balance must be achieved between:
How responsive we want the forecasting model How responsive we want the forecasting model to be to changes in the actual demand datato be to changes in the actual demand data
Our desire to suppress undesirable chance Our desire to suppress undesirable chance variation or noise in the demand datavariation or noise in the demand data
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Reasons for Ineffective ForecastingReasons for Ineffective ForecastingReasons for Ineffective ForecastingReasons for Ineffective Forecasting
Not involving a broad cross section of peopleNot involving a broad cross section of people Not recognizing that forecasting is integral to Not recognizing that forecasting is integral to
business planningbusiness planning Not recognizing that forecasts will always be wrongNot recognizing that forecasts will always be wrong Not forecasting the right thingsNot forecasting the right things Not selecting an appropriate forecasting methodNot selecting an appropriate forecasting method Not tracking the accuracy of the forecasting modelsNot tracking the accuracy of the forecasting models
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Computer Software for ForecastingComputer Software for ForecastingComputer Software for ForecastingComputer Software for Forecasting
Examples of computer software with forecasting Examples of computer software with forecasting capabilitiescapabilities Forecast ProForecast Pro AutoboxAutobox SmartForecasts for WindowsSmartForecasts for Windows SASSAS SPSSSPSS SAPSAP POM Software LibaryPOM Software Libary
Primarily forPrimarily forforecastingforecasting
HaveHaveForecastingForecasting
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