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2.22.2

Forecasting

OUTLINEOUTLINE

Introduction Steps in forecasting process Types of forecasting Naïve Forecasts Averaging Forecasts Linear Trend Forecasts Associative Forecasts Forecast Accuracy

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Learning ObjectivesLearning Objectives

List the elements of a good forecast. Outline the steps in the forecasting

process. Describe at least three qualitative

forecasting techniques and the advantages and disadvantages of each.

Compare and contrast qualitative and quantitative approaches to forecasting.

Learning ObjectivesLearning Objectives

Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems.

Describe two measures of forecast accuracy.

Describe two ways of evaluating and controlling forecasts.

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FORECAST: A statement about the future value of a

variable of interest such as demand. Forecasting is used to make informed

decisions. Long-range Short-range

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ForecastsForecasts

Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing MIS Operations Product/service design

Accounting Cost/profit estimates

Finance Cash flow and funding

Human resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design New products and services

Uses of ForecastsUses of Forecasts

I see that you willget an A this semester.

Assumes causal systempast ==> future

Forecasts rarely perfect because of randomness

Forecasts more accurate forgroups vs. individuals

Forecast accuracy decreases as time horizon increases

Features of ForecastsFeatures of Forecasts

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Elements of a Good ForecastElements of a Good Forecast

Timely

AccurateReliable

Mea

ningfu

l

Written

Easy

to u

se

Steps in the Forecasting ProcessSteps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Establish a time horizon

Step 3 Select a forecasting technique

Step 4 Obtain, clean and analyze data

Step 5 Make the forecast

Step 6 Monitor the forecast

“The forecast”

Types of ForecastsTypes of Forecasts

Judgmental: uses subjective inputs

Time series: uses historical data, assuming the future will be like the past

Associative models: uses explanatory variables to predict the future

Judgmental ForecastsJudgmental Forecasts

Executive opinions

Sales force opinions

Consumer surveys

Outside opinion

Delphi method Opinions of managers and staff Achieves a consensus forecast

Time Series ForecastsTime Series Forecasts

Trend: long-term movement in data Seasonality: short-term regular

variations in data Cycles: wavelike variations of more than

one year’s duration Irregular variations: caused by unusual

circumstances Random variations: caused by chance

Forecast VariationsForecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Figure 3.1

Cycles

Naive ForecastsNaive Forecasts

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

The forecast for any period equals the previous period’s actual value.

Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy

Naive ForecastsNaive Forecasts

Stable time series data F(t) = A(t-1)

Seasonal variations F(t) = A(t-n)

Data with trends F(t) = A(t-1) + (A(t-1) – A(t-2))

Uses of Naive ForecastsUses of Naive Forecasts

Techniques for AveragingTechniques for Averaging

Moving average

Weighted moving average

Exponential smoothing

Moving AveragesMoving Averages

Moving average: A technique that averages a number of recent actual values, updated as new values become available.

Weighted moving average: More recent values in a series are given more weight in computing the forecast.

Ft = MAn= n

At-n + … At-2 + At-1

Ft = WMAn= n

wnAt-n + … wn-1At-2 + w1At-1

Simple Moving AverageSimple Moving Average

35

37

39

41

43

45

47

1 2 3 4 5 6 7 8 9 10 11 12

Actual

MA3

MA5

Ft = MAn= n

At-n + … At-2 + At-1

Exponential SmoothingExponential Smoothing

Premise: The most recent observations might have the highest predictive value. Therefore, we should give more weight to

the more recent time periods when forecasting.

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

Exponential SmoothingExponential Smoothing

Weighted averaging method based on previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

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

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92

Example 3: Exponential SmoothingExample 3: Exponential Smoothing

Picking a Smoothing ConstantPicking a Smoothing Constant

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and .1

.4

Actual

Common Nonlinear TrendsCommon Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3.5

Linear Trend EquationLinear Trend Equation

Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

Ft

Calculating a and bCalculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b t

n

Linear Trend Equation ExampleLinear Trend Equation Example

t yW e e k t 2 S a l e s t y

1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5

Linear Trend CalculationLinear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 =

b = 5 (2499) - 15(812)

5(55) - 225 =

12495-12180

275 -225 = 6.3

143.5

Techniques for SeasonalityTechniques for Seasonality

Seasonal variations Regularly repeating movements in series values

that can be tied to recurring events

Seasonal relative Percentage of average or trend

Centered moving average A moving average positioned at the center of the

data that were used to compute it

Associative ForecastingAssociative Forecasting

Predictor variables: used to predict values of variable interest

Regression: technique for fitting a line to a set of points

Least squares line: minimizes sum of squared deviations around the line

Linear Model Seems ReasonableLinear Model Seems Reasonable

A straight line is fitted to a set of sample points.

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

Linear Regression AssumptionsLinear Regression Assumptions

Variations around the line are random Deviations around the line normally distributed Predictions are being made only within the

range of observed values For best results:

Always plot the data to verify linearity Check for data being time-dependent Small correlation may imply that other variables

are important

Forecast AccuracyForecast Accuracy

Error: difference between actual value and predicted value

Mean Absolute Deviation (MAD) Average absolute error

Mean Squared Error (MSE) Average of squared error

Mean Absolute Percent Error (MAPE) Average absolute percent error

MAD, MSE, and MAPEMAD, MSE, and MAPE

MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

MAPE = Actual forecas

t

n

/ Actual*100)

MAD, MSE, and MAPEMAD, MSE, and MAPE

MAD Easy to compute Weights errors linearly

MSE Squares error More weight to large errors

MAPE Puts errors in perspective

Example 10Example 10

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75MSE= 10.86

MAPE= 1.28

Controlling the ForecastControlling the Forecast

Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors

Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are

present

Sources of Forecast ErrorsSources of Forecast Errors

Model may be inadequate Irregular variations Incorrect use of forecasting technique