forecasting - rjerz.com · •describe three measures of forecast accuracy. ... choosing a...

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Forecasting

Dr. Rick Jerz

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Learning Objectives

• Describe why forecasts are used and list the elements of a good forecast.

• Outline the steps in the forecasting process. • Describe at least three qualitative and three

quantitative forecasting techniques, and their advantages and disadvantages.

• Describe three measures of forecast accuracy.• Identify the major factors to consider when

choosing a forecasting technique.

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Making Decisions

• If we know exactly what will happen in the future, operational decisions would be easy.

• Problem – we don’t know the future.

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FORECAST

• A statement about the future

• Used to help managers• Plan the system• Operate the system

• Forecasting time horizons• Short-range• Medium-range• Long-range

????

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Forecasts

• Underlying basis of all business decisions!

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Department Uses of ForecastsAccounting Cost/profit estimatesFinance Cash flow and fundingHuman Resources Hiring/recruiting/trainingMarketing Pricing, promotion, strategyMIS IT/IS systems, servicesOperations Schedules, MRP, workloadsProduct/service design New products and services

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Forecasts Characteristics

• Assumes causal system and system stabilitypast ==> future

• Forecasts rarely perfect because of randomness

• Forecasts more accurate forgroups vs. individuals

• Forecast accuracy decreases as time horizon increases

• Statistics & math are often used

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Elements of a Good Forecast

Timely

AccurateReliable

Meaningful

WrittenEas

y to use

Timely

AccurateReliable

Meaningful

WrittenEas

y to use

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Seven Steps in Forecasting

1. Determine the use of the forecast2. Select the items to be forecasted3. Determine the time horizon of the forecast4. Select the forecasting model(s)5. Gather the data6. Make the forecast7. Validate and implement results

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Types 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 Forecasts“Qualitative”

• Executive opinions• Sales force composite• Consumer surveys• Outside opinion• Opinions of managers and staff• Delphi method

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Time Series Forecasts“Quantitative”

• Trend - long-term movement in data• Seasonality - short-term regular variations in

data• Cycles – wavelike variations, usually more

than one year’s duration• Irregular variations - caused by unusual

circumstances• Random variations - caused by chance

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Forecast Pattern Examples

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Most CommonQuantitative Methods

• Naïve forecasts• Moving average• Weighted moving average• Exponential smoothing• Trend analysis

TimeTime--Series Series ModelsModels

TimeTime--Series Series ModelsModels

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Naïve Forecast

)(1 trendAF tt += -

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

• Can be adjusted with trend

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Naïve Forecasts

• Advantages• Simple to use• Virtually no cost• Data analysis is nonexistent• Easily understandable• Can include trend and seasonality considerations

• Disadvantages• Cannot provide high accuracy• Can be a standard for accuracy

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Moving Average

nAAAF ttnt

t12... --- +++

=

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

Moving average =Moving average = ∑∑ demand in previous n periodsdemand in previous n periodsnnMoving average =Moving average = ∑∑ demand in previous n periodsdemand in previous n periodsnn

∑∑ demand in previous n periodsdemand in previous n periodsnn

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Simple Moving Average Characteristics

• Must choose the number of periods, n• Only use the most recent “n” periods• Gets rid of old data• Premise: newer data is more indicative of

what the future will be• The bigger the “n”, the less “sensitive” the

forecast• The smaller the “n”, the more “reactive” the

forecast• Does not forecast trend well

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Moving Average: Periods

35373941434547

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

Actual

MA3

MA5

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Weighted Moving Average

å---- +++

=w

ttnntnt

AwAwAwF 1121...

• More recent values in a series are given more weight in computing the forecast.

WeightedWeightedmoving averagemoving average ==

∑∑ ((weight for period nweight for period n))x x ((demand in period ndemand in period n))

∑∑ weightsweightsWeightedWeighted

moving averagemoving average ==WeightedWeightedmoving averagemoving average ==


∑∑ weightsweights


∑∑ weightsweights

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Weighted Moving Average Characteristics

• Weights are usually a percent• Sum of the weights equals 1, or 100%• More complex than simple moving average• More responsive to most recent events• Weights based on experience and intuition• Better (than simple moving average) at

forecasting trend

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Exponential Smoothing

)( 111 --- -+= tttt FAFF a

• 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.

New forecast =New forecast = last periodlast period’’s forecasts forecast+ + aa ((last periodlast period’’s actual demand s actual demand

–– last periodlast period’’s forecasts forecast))

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Exponential Smoothing Characteristics

• A form of weighted moving average• Requires a smoothing constant (alpha, α)

that ranges from 0 to 1 • The larger alpha, the more reactive the

forecast model.• Good at forecasting trend• Involves little record keeping of past data

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Trend Analysis

• Linear trends - Fitting a trend line to historical data points to project into the medium-to-long-range

• Linear trends can be found using the least squares technique

y y = = a a + + bxbx^̂y y = = a a + + bxbx^̂

where ywhere y = computed value of the variable to = computed value of the variable to be predicted (dependent variable)be predicted (dependent variable)

aa = y= y--axis interceptaxis interceptbb = slope of the regression line= slope of the regression linexx = the independent variable= the independent variable

^̂where ywhere y = computed value of the variable to = computed value of the variable to be predicted (dependent variable)be predicted (dependent variable)

aa = y= y--axis interceptaxis interceptbb = slope of the regression line= slope of the regression linexx = the independent variable= the independent variable

^̂

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Least Squares Method

Time periodTime period

Valu

es o

f Dep

ende

nt V

aria

ble

Time periodTime period

Valu

es o

f Dep

ende

nt V

aria

ble

DeviationDeviation11







DeviationDeviation11DeviationDeviation11







Actual observation Actual observation (y value)(y value)

Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂Trend line, y = a + bxTrend line, y = a + bx^̂Trend line, y = a + bxTrend line, y = a + bx^̂

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Equations to Calculatethe Regression Variables

b =b = SSxy xy -- nxynxySSxx22 -- nxnx22

b =b = SSxy xy -- nxynxySSxx22 -- nxnx22SSxy xy -- nxynxySSxx22 -- nxnx22

y y = = a a + + bxbx^̂y y = = a a + + bxbx^̂

a = y a = y -- bxbxa = y a = y -- bxbx© 2018 rjerz.com26

Least Squares Example

b b = = = 10.5= = = 10.544SSxy xy -- nxynxySSxx22 -- nxnx22

3,063 3,063 -- (7)(4)(98.86)(7)(4)(98.86)140 140 -- (7)(4(7)(422))b b = = = 10.5= = = 10.544

SSxy xy -- nxynxySSxx22 -- nxnx22b b = = = 10.5= = = 10.544SSxy xy -- nxynxySSxx22 -- nxnx22

3,063 3,063 -- (7)(4)(98.86)(7)(4)(98.86)140 140 -- (7)(4(7)(422))

3,063 3,063 -- (7)(4)(98.86)(7)(4)(98.86)140 140 -- (7)(4(7)(422))

aa = = yy -- bxbx = 98.86 = 98.86 -- 10.54(4) = 56.7010.54(4) = 56.70aa = = yy -- bxbx = 98.86 = 98.86 -- 10.54(4) = 56.7010.54(4) = 56.70

TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy

19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854

SSxx = 28= 28 SSyy = 692= 692 SSxx22 = 140= 140 SSxyxy = 3,063= 3,063xx = 4= 4 yy = 98.86= 98.86


19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854



19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854


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Least Squares Example

| | | | | | | | |19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007

160 160 –150 150 –140 140 –130 130 –120 120 –110 110 –100 100 –

90 90 –80 80 –70 70 –60 60 –50 50 –

YearYear

Pow

er d

eman

dPo

wer

dem

and

| | | | | | | | |19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007

160 160 –150 150 –140 140 –130 130 –120 120 –110 110 –100 100 –

90 90 –80 80 –70 70 –60 60 –50 50 –

| | | | | | | | |19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007

160 160 –150 150 –140 140 –130 130 –120 120 –110 110 –100 100 –

90 90 –80 80 –70 70 –60 60 –50 50 –

YearYear

Pow

er d

eman

dPo

wer

dem

and

Trend line,Trend line,y y = 56.70 + 10.54x= 56.70 + 10.54x^̂Trend line,Trend line,y y = 56.70 + 10.54x= 56.70 + 10.54x^̂Trend line,Trend line,y y = 56.70 + 10.54x= 56.70 + 10.54x^̂

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Trend Line Characteristics

• Great, if data has trend• Variations around the line are assumed to be

random• If trend is not linear, cannot use trend line• Trend could be curves, but math becomes

more difficult• Plot the data to insure a linear relationship• Be careful forecasting far beyond the

database

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More Advanced Techniques

• Associative forecasting• Predictor variables not “time”

• Multiple linear regression• More than one predictor variable

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Forecast Accuracy

• We generally do this by selecting the model that gives us the lowest forecast error

• 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 percentage error (MAPE)• Average of the percent errors

• Correlation coefficient – for trend line

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Mean Error

nForecastActual

ErrorMean å -=

|)(|

• Difference between actual and forecast• Absolute value used

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Mean Squared Error

• The error is squared• “Variance”

• Note: Some authors divide by n-1

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Mean AbsolutePercentage Error

• The absolute error is divided by the actual to calculate the percent errors

• These errors are averaged

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Correlation and Linear Regression

• Are two sets of data related?• Correlation analysis

• Is the relationship “linear”?• Linear regression analysis

• How strong is the relationship?• Correlation• Coefficient of Correlations (denoted by r).• Values range from -1 to +1• Values close to 0.0 indicate a weak correlation• Negative values indicate an inverse relationship

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Correlation

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Correlation

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Correlation Coefficient Equation to Calculate “r”

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Choosing a Forecasting Method

• Cost• Accuracy• Timely• Understandable• Serves purpose• In writing

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Operations 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

• Consider accountability of person making the forecast

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forecasting - rjerz.com · •describe three measures of forecast accuracy. ... choosing a...

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