McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.

33

Forecasting

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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.

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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.

Identify the major factors to consider when choosing a forecasting technique.

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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

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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

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Assumes causal systempast ==> future

Forecasts rarely perfect because of randomness Forecasts more accurate for

groups vs. individuals Forecast accuracy decreases

as time horizon increases I see that you willget an A this semester.

Features of ForecastsFeatures of Forecasts

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Elements of a Good ForecastElements of a Good Forecast

Timely

AccurateReliable

Meaningful

WrittenEas

y to use

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Steps in the Forecasting ProcessSteps in the Forecasting Process

Step 1 Determine purpose of forecastStep 2 Establish a time horizon

Step 3 Select a forecasting techniqueStep 4 Obtain, clean and analyze data

Step 5 Make the forecastStep 6 Monitor the forecast

“The forecast”

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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

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Judgmental ForecastsJudgmental Forecasts Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi method

Opinions of managers and staff Achieves a consensus forecast

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Time Series ForecastsTime Series Forecasts Trend - long-term movement in data Seasonality - short-term regular

variations in data Cycle – wavelike variations of more than

one year’s duration Irregular variations - caused by unusual

circumstances Random variations - caused by chance

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Forecast VariationsForecast Variations

Trend

Irregularvariation

Seasonal variations

908988

Figure 3.1

Cycles

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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.

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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

Naïve ForecastsNaïve Forecasts

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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 for Naïve ForecastsUses for Naïve Forecasts

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Techniques for AveragingTechniques for Averaging

Moving average

Weighted moving average

Exponential smoothing

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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

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Simple Moving AverageSimple Moving Average

35373941434547

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

Actual

MA3

MA5

Ft = MAn= nAt-n + … At-2 + At-1

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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)

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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)

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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

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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

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Common Nonlinear TrendsCommon Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3.5

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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

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Calculating a and bCalculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b tn

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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

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Linear Trend CalculationLinear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)5

=

b = 5 (2499) - 15(812)5(55) - 225

= 12495-12180275 -225

= 6.3

143.5

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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.

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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

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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

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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

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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

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MAD, MSE, and MAPEMAD, MSE, and MAPE

MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

MAPE = Actual forecas

t

n

/ Actual*100)

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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

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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

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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

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Sources of Forecast errorsSources of Forecast errors Model may be inadequate Irregular variations Incorrect use of forecasting technique

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Tracking SignalTracking Signal

Tracking signal = (Actual-forecast)MAD

•Tracking signal–Ratio of cumulative error to MAD

Bias – Persistent tendency for forecasts to beGreater or less than actual values.

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Choosing a Forecasting Choosing a Forecasting TechniqueTechnique

No single technique works in every situation

Two most important factors Cost Accuracy

Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon

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Operations StrategyOperations Strategy

Forecasts are the basis for many decisions Work to improve short-term forecasts Accurate short-term forecasts improve

Profits Lower inventory levels Reduce inventory shortages Improve customer service levels Enhance forecasting credibility

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Supply Chain ForecastsSupply Chain Forecasts

Sharing forecasts with supply can Improve forecast quality in the supply chain Lower costs Shorter lead times

Gazing at the Crystal Ball (reading in text)

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Exponential SmoothingExponential Smoothing

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Linear Trend EquationLinear Trend Equation

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Simple Linear RegressionSimple Linear Regression