Chapter 3

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Chapter 3

Demand Forecasting

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Introduction

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.

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Forecasting is an Integral Part of 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 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.

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Examples of Production Resource Forecasts

LongRange

MediumRange

ShortRange

Years

Months

Days,Weeks

Product Lines,Factory Capacities

ForecastHorizon

TimeSpan

Item BeingForecasted

Unit ofMeasure

Product Groups,Depart. Capacities

Specific Products,Machine Capacities

Dollars,Tons

Units,Pounds

Units,Hours

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Forecasting Methods

Qualitative Approaches Quantitative Approaches

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Qualitative 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

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Qualitative Methods

Educated guess intuitive hunches Executive committee consensus Delphi method Survey of sales force Survey of customers Historical analogy Market research scientifically conducted

surveys

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Quantitative Forecasting Approaches

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

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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

Time Series Analysis

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Components of a Time Series

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.

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Seasonal Patterns

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

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Quantitative Forecasting Approaches

Linear Regression Simple Moving Average Weighted Moving Average Exponential Smoothing (exponentially weighted

moving average) Exponential Smoothing with Trend (double

exponential smoothing)

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Long-Range Forecasts

Time spans usually greater than one year Necessary to support strategic decisions about

planning products, processes, and facilities

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Simple Linear Regression

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.

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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

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

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

2 2xy- x yb = n x -( x)

n

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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.

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Example: College Enrollment

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

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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 Sx=21 Sy=18.1 Sx2=91 Sxy=66.5

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Y = 2.387 + 0.180X

291(18.1) 21(66.5) 2.3876(91) (21)a

6(66.5) 21(18.1) 0.180105b

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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.

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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.

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Example: Railroad Products Co.

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.

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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

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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

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Y = 0.528 + 0.0801X

2185,425(93) 1,115(15,440)a 0.5287(185,425) (1,115)

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

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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.

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Multiple 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)

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Coefficient of Correlation (r)

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.

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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 y

rn x x n y y

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Coefficient of Determination (r2)

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:

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2( )( )Y y

ry y

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Coefficient of Correlation

x y x2 xy y2

120 9.5 14,400 1,140 90.25135 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 Determination

r2 = (.9829)2 = .96696.6% 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 are subject to error.

One way to deal with uncertainty is to develop best-estimate forecasts and the ranges within which the actual data are likely to fall.

The ranges of a forecast are defined by the upper and lower limits of a confidence interval.

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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 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.

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Example: Computer Products Corp.

Seasonalized Times Series Regression AnalysisAn 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.

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Seasonalized Times Series Regression Analysis Representative 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

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Seasonalized Times Series Regression Analysis Compute the Seasonal Indexes

Quarterly SalesYear 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 74.0 Qtr. Avg. 7.85 6.95 5.15 17.05 9.25 Seas.Ind. .849 .751 .557 1.843 4.000

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Seasonalized Times Series Regression Analysis Deseasonalize the Data

Quarterly SalesYear 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 Analysis Perform Regression on Deseasonalized Data

Yr. Qtr. x y x2 xy1 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

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Seasonalized Times Series Regression Analysis Perform Regression on Deseasonalized Data

Y = 8.357 + 0.199X

2204(74.01) 36(341.39)a 8.3578(204) (36)

28(341.39) 36(74.01)b 0.1998(204) (36)

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Seasonalized Times Series Regression Analysis Compute 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.

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Seasonalized Times Series Regression Analysis Seasonalize 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

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Short-Range Forecasts

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

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Evaluating Forecast-Model Performance

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

Impulse response Noise-dampening ability Accuracy

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Impulse Response and Noise-Dampening Ability If 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.

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Accuracy Accuracy is the typical criterion for judging the

performance of a forecasting approach Accuracy is how well the forecasted values match

the actual values

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Monitoring Accuracy

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 ways Standard error of the forecast (covered earlier) Mean absolute deviation (MAD) Mean squared error (MSE)

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Monitoring Accuracy

Mean Absolute Deviation (MAD)

nperiodsn for deviation absolute of Sum=MAD

n

i ii=1

Actual demand -Forecast demandMAD = n

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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)

Monitoring Accuracy

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Short-Range Forecasting Methods

(Simple) Moving Average Weighted Moving Average Exponential Smoothing Exponential Smoothing with Trend

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Simple Moving Average

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

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Simple Moving Average

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)

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Weighted Moving Average

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

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Weighted Moving Average

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.

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The weights used to compute the forecast (moving average) are exponentially distributed.

The forecast is the sum of the old forecast and a portion (a) of the forecast error (A t-1 - Ft-1).

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

. . . more

Exponential Smoothing

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Exponential Smoothing

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

A large a provides a high impulse response forecast. A small a provides a low impulse response forecast.

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Example: Central Call Center

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.

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Moving Average Representative Historical Data

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

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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

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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).

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

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Forecast Accuracy - MADWhich forecasting method (the AP = 3 moving

average or the a = .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.)

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AP = 3 a = .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 4.010 168 195.3 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

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Criteria for Selectinga Forecasting Method

Cost Accuracy Data available Time span Nature of products and services Impulse response and noise dampening

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Cost and Accuracy There is a trade-off between cost and accuracy;

generally, more forecast accuracy can be obtained at a cost.

High-accuracy approaches have disadvantages: Use more data Data are ordinarily more difficult to obtain The models are more costly to design,

implement, and operate Take longer to use

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Cost and Accuracy Low/Moderate-Cost Approaches – statistical

models, historical analogies, executive-committee consensus

High-Cost Approaches – complex econometric models, Delphi, and market research

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Data Available Is the necessary data available or can it be

economically 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 may have to be used.

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Time Span What operations resource is being forecast and for

what purpose? Short-term staffing needs might best be forecast

with moving average or exponential smoothing models.

Long-term factory capacity needs might best be predicted with regression or executive-committee consensus methods.

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

fluctuations?

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Impulse Response and Noise Dampening An appropriate balance must be achieved between:

How responsive we want the forecasting model to be to changes in the actual demand data

Our desire to suppress undesirable chance variation or noise in the demand data

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Reasons for Ineffective Forecasting

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 things Not selecting an appropriate forecasting method Not tracking the accuracy of the forecasting models

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Computer Software for Forecasting

Examples of computer software with forecasting capabilities Forecast Pro Autobox SmartForecasts for Windows SAS SPSS SAP POM Software Libary

Primarily forforecasting

HaveForecasting

modules

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Chapter 3