Demand Forecasting

McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

IntroductionQualitative Forecasting MethodsQuantitative Forecasting ModelsHow to Have a Successful Forecasting

SystemComputer Software for ForecastingForecasting in Small Businesses and

Start-Up VenturesWrap-Up: What World-Class Producers

Do

Demand estimates for products and services are the starting point for all the other planning in operations management.

Management teams develop sales forecasts based in part on demand estimates.

The sales forecasts become inputs to both business strategy and production resource forecasts.

ForecastForecastMethod(s)Method(s)

DemandDemandEstimatesEstimates

SalesSalesForecastForecast

ManagementManagementTeamTeam

Inputs:Inputs:Market,Market,

Economic,Economic,OtherOther

BusinessBusinessStrategyStrategy

Production ResourceProduction ResourceForecastsForecasts

New Facility Planning – It can take 5 years to design and build a new factory or design and implement a new production process.

Production Planning – Demand for products vary from month to month and it can take several months to change the capacities of production processes.

Workforce Scheduling – Demand for services (and the necessary staffing) can vary from hour to hour and employees weekly work schedules must be developed in advance.

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

Qualitative ApproachesQuantitative Approaches

Usually based on judgments about causal factors that underlie the demand of particular products or services

Do not require a demand history for the product or service, therefore are useful for new products/services

Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events

The approach/method that is appropriate depends on a product’s life cycle stage

Educated guess intuitive hunches

Executive committee consensusDelphi methodSurvey of sales forceSurvey of customers Historical analogyMarket research scientifically

conducted surveys

Based on the assumption that the “forces” that generated the past demand will generate the future demand, i.e., history will tend to repeat itself

Analysis of the past demand pattern provides a good basis for forecasting future demand

Majority of quantitative approaches fall in the category of time series analysis

A time series is a set of numbers where the order or sequence of the numbers is important, e.g., historical demand

Analysis of the time series identifies patterns

Once the patterns are identified, they can be used to develop a forecast

Trends are noted by an upward or downward sloping line.

Cycle is a data pattern that may cover several years before it repeats itself.

Seasonality is a data pattern that repeats itself over the period of one year or less.

Random fluctuation (noise) results from random variation or unexplained causes.

Length of Time Number of Before Pattern Length of Seasons Is Repeated Season in

Pattern

Year Quarter 4 Year Month 12 Year Week 52 Month Day 28-31 Week Day 7

Linear RegressionSimple Moving AverageWeighted Moving AverageExponential Smoothing (exponentially

weighted moving average)Exponential Smoothing with Trend

(double exponential smoothing)

Time spans usually greater than one yearNecessary to support strategic decisions

about planning products, processes, and facilities

Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables.

In simple linear regression analysis there is only one independent variable.

If the data is a time series, the independent variable is the time period.

The dependent variable is whatever we wish to forecast.

Regression EquationThis model is of the form:

Y = a + bX

Y = dependent variable X = independent variable

a = y-axis intercept b = slope of regression line

Constants a and bThe constants a and b are computed using the following equations:

2

2 2

x y- x xya =

n x -( x)

2 2

xy- x yb =

n x -( x)

n

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

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

Students StudentsYear Enrolled (1000s) Year Enrolled (1000s) 1 2.5 4 3.2 2 2.8 5 3.3 3 2.9 6 3.4

Simple Linear Regression

x y x2 xy1 2.5 1 2.52 2.8 4 5.63 2.9 9 8.74 3.2 16 12.85 3.3 25 16.56 3.4 36 20.4

x=21 y=18.1 x2=91 xy=66.5

Simple Linear Regression

Y = 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

Simple Linear Regression

Y7 = 2.387 + 0.180(7) = 3.65 or 3,650 students

Y8 = 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 180 students per year.

Simple linear regression can also be used when the independent variable X represents a variable other than time.

In this case, linear regression is representative of a class of forecasting models called causal forecasting models.

Simple Linear Regression – Causal ModelThe manager of RPC wants to project the firm’s sales for the next 3 years. He knows that RPC’s long-range sales are tied very closely to national freight car loadings. On the next slide are 7 years of relevant historical 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 the rail industry estimates car loadings of 250, 270, and 300 million.

Simple Linear Regression – Causal Model

RPC Sales Car LoadingsYear ($millions) (millions)

1 9.5 1202 11.0 1353 12.0 1304 12.5 1505 14.0 1706 16.0 1907 18.0 220

Simple Linear Regression – Causal Model

x y x2 xy

120 9.5 14,400 1,140135 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

Simple Linear Regression – Causal Model

Y = 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)

Simple Linear Regression – Causal Model

Y8 = 0.528 + 0.0801(250) = $20.55 million Y9 = 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 freight car loadings.

Multiple Regression AnalysisMultiple Regression AnalysisMultiple Regression AnalysisMultiple Regression Analysis

Multiple regression analysis is used when there are two or more independent variables.

An example of a multiple regression equation is:

Y = 50.0 + 0.05X1 + 0.10X2 – 0.03X3

where: Y = firm’s annual sales ($millions)

X1 = industry sales ($millions)

X2 = regional per capita income ($thousands)

X3 = regional per capita debt ($thousands)

The coefficient of correlation, r, explains the relative importance 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 the relationship.

The sign of r is always the same as the sign of b.

r can take on any value between –1 and +1.

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

r 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

22

2

( )

( )

Y yr

y y

22

2

( )

( )

Y yr

y y

The coefficient of determination, r2, is the square of the coefficient of correlation.

The modification of r to r2 allows us to shift from subjective measures of relationship to a more specific measure.

r2 is determined by the ratio of explained variation to total variation:

Select a representative historical data set.Develop a seasonal index for each season.Use the seasonal indexes to deseasonalize

the data.Perform lin. regr. analysis on the

deseasonalized data.Use the regression equation to compute

the forecasts.Use the seas. indexes to reapply the

seasonal patterns to the forecasts.

Seasonalized Times Series Regression Analysis

An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales.

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 5.41 4 16.1 2 4 18.0

Seasonalized Times Series Regression AnalysisCompute the Seasonal Indexes

Quarterly SalesYear Q1 Q2 Q3 Q4 Total

1 7.4 6.5 4.9 16.1 34.92 8.3 7.4 5.4 18.0 39.1

Totals15.7 13.9 10.3 34.1 74.0 Qtr. Avg.7.85 6.95 5.15 17.05 9.25 Seas.Ind..849 .751 .557 1.843 4.000

Seasonalized Times Series Regression AnalysisDeseasonalize the Data

Quarterly SalesYear Q1 Q2 Q3 Q4

1 8.72 8.66 8.80 8.742 9.78 9.85 9.69 9.77

Seasonalized Times Series Regression AnalysisPerform Regression on Deseasonalized Data

Yr. Qtr. x y x2 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 48.902 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

Y = 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)

Seasonalized Times Series Regression AnalysisCompute the Deseasonalized Forecasts

Y9 = 8.357 + 0.199(9) = 10.148

Y10 = 8.357 + 0.199(10) = 10.347

Y11 = 8.357 + 0.199(11) = 10.546

Y12 = 8.357 + 0.199(12) = 10.745

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

quarter.

Seasonalized Times Series Regression AnalysisSeasonalize the Forecasts

Seas. Deseas. Seas.Yr. Qtr. Index Forecast Forecast

3 1 .849 10.148 8.623 2 .751 10.347 7.773 3 .557 10.546 5.873 4 1.843 10.745 19.80

Time spans ranging from a few days to a few weeks

Cycles, seasonality, and trend may have little effect

Random fluctuation is main data component

Short-range forecasting models are evaluated on the basis of three characteristics:

Impulse responseNoise-dampening abilityAccuracy

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 data are said to have a high impulse response.

A forecast system that responds quickly to data changes necessarily picks up a great deal of random fluctuation (noise).

Hence, there is a trade-off between high impulse response and high noise dampening.

AccuracyAccuracy is the typical criterion for judging the

performance of a forecasting approachAccuracy is how well the forecasted values

match the actual values

Accuracy of a forecasting approach needs to be monitored to assess the confidence you can have in its forecasts and changes in the market may require reevaluation of the approach

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

Mean Absolute Deviation (MAD)

n

i ii=1

Actual demand -Forecast demandMAD =

n

Mean Squared Error (MSE)

MSE = (Syx)2

A small value for Syx means data points are tightly grouped around the line and error range is small.

When the forecast errors are normally distributed, the values of MAD and syx are related:

MSE = 1.25(MAD)

(Simple) Moving AverageWeighted Moving AverageExponential SmoothingExponential Smoothing with Trend

An averaging period (AP) is given or selected

The forecast for the next period is the arithmetic average of the AP most recent actual demands

It is called a “simple” average because each period used to compute the average is equally weighted

. . . more

It is called “moving” because as new demand data becomes available, the oldest data is not used

By increasing the AP, the forecast is less responsive to fluctuations in demand (low impulse response and high noise dampening)

By decreasing the AP, the forecast is more responsive to fluctuations in demand (high impulse response and low noise dampening)

Technique that averages a number of the most recent actual values in generating a forecast

average moving in the periods ofNumber

1 periodin valueActual

average moving period MA

period for timeForecast

where

MA

1

1

n

tA

n

tF

n

AF

t

n

t

n

iit

nt

3-54Student Slides

This is a variation on the simple moving average where the weights used to compute the average are not equal.

This allows more recent demand data to have a greater effect on the moving average, therefore the forecast.

. . . more

The weights must add to 1.0 and generally decrease in value with the age of the data.

The distribution of the weights determine the impulse response of the forecast.

The most recent values in a time series are given more weight in computing a forecastThe choice of weights, w, is somewhat

arbitrary and involves some trial and error

etc. ,1 periodfor valueactual the , periodfor valueactual the

etc. ,1 periodfor weight , periodfor weight

where

)(...)()(

1

1

11

tAtA

twtw

AwAwAwF

tt

tt

ntntttttt

3-57Student Slides

A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error

period previous thefrom salesor demand Actual

constant Smoothing=

period previous for theForecast

periodfor Forecast

where

)(

1

1

111

t

t

t

tttt

A

F

tF

FAFF

3-58Student Slides

The smoothing constant, , must be between 0.0 and 1.0.

A large provides a high impulse response forecast.

A small provides a low impulse response forecast.

Moving AverageCCC wishes to forecast the number of

incoming calls 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 call volumes.

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

Moving AverageRepresentative Historical Data

Day Calls Day Calls1 159 7 2032 217 8 1953 186 9 1884 161 10 1685 173 11 1986 157 12 159

Moving AverageUse the moving average method

with an AP = 3 days to develop a forecast of the call volume in Day 13.

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

Weighted Moving AverageUse the weighted moving average method

with an AP = 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 MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).

Example: Central Call CenterExample: Central Call Center

Exponential Smoothing

If a smoothing constant value of .25 is used and the exponential smoothing forecast for Day 11 was 180.76 calls, what is the exponential smoothing forecast for Day 13?

F12 = 180.76 + .25(198 – 180.76) = 185.07

F13 = 185.07 + .25(159 – 185.07) = 178.55

Forecast Accuracy - MADWhich forecasting method (the AP =

3 moving average or the = .25 exponential smoothing) is preferred, based on the MAD over the most recent 9 days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call volume.)

AP = 3 = .25

Day Calls Forec.|Error| Forec. |Error|

4 161 187.3 26.3 186.0 25.05 173 188.0 15.0 179.8 6.86 157 173.3 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

CostAccuracyData availableTime spanNature of products and servicesImpulse response and noise dampening

Not involving a broad cross section of people

Not recognizing that forecasting is integral to business planning

Not recognizing that forecasts will always be wrong

Not forecasting the right thingsNot selecting an appropriate forecasting

methodNot tracking the accuracy of the

forecasting models

Tracking Signal (TS)The TS measures the cumulative forecast error

over n periods in terms of MAD

If the forecasting model is performing well, the TS should be around zero

The TS indicates the direction of the forecasting error; if the TS is positive -- increase the forecasts, if the TS is negative -- decrease the forecasts.

n

i i1

(Actual demand - Forecast demand )TS =

MADin

i i1

(Actual demand - Forecast demand )TS =

MADi

Tracking SignalThe value of the TS can be used to

automatically trigger new parameter values of a model, thereby correcting model performance.

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

If the limits are set too wide, the parameter values will not be changed often enough and accuracy will suffer.

Examples of computer software with forecasting capabilitiesForecast ProAutoboxSmartForecasts for WindowsSASSPSSSAPPOM Software Libary

Primarily forPrimarily forforecastingforecasting

HaveHaveForecastingForecasting

modulesmodules

Forecasting for these businesses can be difficult for the following reasons:Not enough personnel with the time to forecastPersonnel lack the necessary skills to develop

good forecastsSuch businesses are not data-rich

environmentsForecasting for new products/services is

always difficult, even for the experienced forecaster

Government agencies at the local, regional, state, and federal levels

Industry associationsConsulting companies

Consumer Confidence IndexConsumer Price Index (CPI)Gross Domestic Product (GDP)Housing StartsIndex of Leading Economic IndicatorsPersonal Income and ConsumptionProducer Price Index (PPI)Purchasing Manager’s IndexRetail Sales

Predisposed to have effective methods of forecasting because they have exceptional long-range business planning

Formal forecasting effortDevelop methods to monitor the

performance of their forecasting modelsDo not overlook the short run....

excellent short range forecasts as well

n

100

Actual

ForecastActual

MAPE t

tt

n

tt ForecastActualMAD

2

tt

1

ForecastActualMSE

n

MAD weights all errors evenly

MSE weights errors according to their squared values

MAPE weights errors according to relative error

3-76Student Slides