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Chapter 8 - Forecasting

Operations Managementby

R. Dan Reid & Nada R. Sanders2nd Edition Wiley 2005


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Decisions that Need ForecastsWhich markets to pursue?What products to produce?How many people to hire?How many units to purchase?

How many units to produce? And so on


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Common Characteristics of

ForecastingForecasts are rarely perfect

Forecasts are more accurate foraggregated data than for individualitems

Forecast are more accurate for shorterthan longer time periods


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Forecasting StepsWhat needs to be forecast?

Level of detail, units of analysis & time horizonrequired

What data is available to evaluate?Identify needed data & whether its available

Select and test the forecasting model

Cost, ease of use & accuracyGenerate the forecastMonitor forecast accuracy over time


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Types of Forecasting ModelsQualitative (technological) methods:

Forecasts generated subjectively by theforecaster

Quantitative (statistical) methods:Forecasts generated through mathematicalmodeling


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Qualitative MethodsType Characteristics Strengths Weaknesses

Executiveopinion

A group of managersmeet & come up with

a forecast

Good for strategic ornew-product

forecasting

One person's opinioncan dominate the

forecast

Marketresearch

Uses surveys &interviews to identifycustomer preferences

Good determinant ofcustomer preferences

It can be difficult todevelop a goodquestionnaire

Delphimethod

Seeks to develop aconsensus among agroup of experts

Excellent forforecasting long-termproduct demand,technological

Time consuming todevelop


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Statistical ForecastingTime Series Models:

Assumes the future will follow same patterns as

the past

Causal Models:Explores cause-and-effect relationshipsUses leading indicators to predict the futureE.g. housing starts and appliance sales


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Composition

of Time Series DataData = historic pattern + randomvariationHistoric pattern may include:

Level (long-term average)Trend

SeasonalityCycle


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Time Series Patterns


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Methods of Forecasting the LevelNave ForecastingSimple MeanMoving AverageWeighted Moving Average

Exponential Smoothing


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Time Series ProblemDetermine forecast forperiods 11

Nave forecast Simple average

3- and 5-period movingaverage

3-period weighted movingaverage with weights 0.5,0.3, and 0.2

Exponential smoothing

with alpha=0.2 and 0.5

Period Orders1 1222 913 1004 775 1156 58

7 758 1289 111

10 8811


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Time Chart of Orders Data

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10


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Simple Average (Mean)Next periods forecast = average of allhistorical data

n A A A

F t t t t .............21

1


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The Effect of the Parameter N

A smaller N makes the forecast more

responsive A larger N makes the forecast morestable


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Weighted Moving Average

1.........

.........

21

11211

N

N t N t t t

C C C

where

AC AC AC F


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The Effect of the Parameter

A smaller makes the forecast more

stable A larger makes the forecast moreresponsive


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Time Series Problem Solution

Simple Simple Weighted Exponential ExponentialNave Simple Moving Moving Moving Smoothing Smoothing

Period Orders (A) Forecast Average Average (N=3) Average(N=5) Average (N=3) ( = 0.2) ( = 0.5)

1 122 122 1222 91 122 122 122 1223 100 91 107 116 1074 77 100 104 104 102 113 1045 115 77 98 89 87 106 916 58 115 101 97 101 101 108 1037 75 58 94 83 88 79 98 81

8 128 75 91 83 85 78 93 789 111 128 96 87 91 98 100 10310 88 111 97 105 97 109 102 107

11 88 97 109 92 103 99 98


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Tracking Forecast ErrorOver Time

Mean Absolute Deviation (MAD): A good measure of the actual errorin a forecast

Mean Square Error (MSE):Penalizes extreme errors

Tracking SignalExposes bias (positive or negative)

n

forecast actual MAD

2

actual - forecastMSE

n

MAD

TS forecast-actual


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Forecasting Trends

Trend-adjusted exponential smoothingThree step process:

Smooth the level of the series:

Smooth the trend:

Calculate the forecast including trend:

))(1( 11 t t t t T S AS

11 )1()( t t t t T S S T

t t t T S FIT 1


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Forecasting trend problem: a company uses exponential smoothing with trend toforecast usage of its lawn care products. At the end of July the company wishes toforecast sales for August. July demand was 62. The trend through June has been 15additional gallons of product sold per month. Average sales have been 57 gallonsper month. The company uses alpha+0.2 and beta +0.10. Forecast for August.

Smooth the level of the series:

Smooth the trend:

Forecast including trend:

14.8150.957700.1)T(1)S(ST 1t1ttJuly

7015570.8620.2)T)(S(1AS 1t1ttJuly

gallons84.814.870TSFIT ttAugust


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Adjusting for Seasonality

Calculate the average demand per season E.g.: average quarterly demand

Calculate a seasonal index for each season ofeach year:

Divide the actual demand of each season by theaverage demand per season for that year

Average the indexes by season E.g .: take the average of all Spring indexes, thenof all Summer indexes, ...


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Adjusting for Seasonality

Forecast demand for the next year & divideby the number of seasons

Use regular forecasting method & divide by fourfor average quarterly demand

Multiply next years average seasonal demandby each average seasonal index

Result is a forecast of demand for each season ofnext year


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Seasonality Problem: Solution

Quarter Year 1 SeasonalIndex

Year 2 SeasonalIndex

Avg.Index

Year3

Fall 24000 1.20 26000 1.24 1.22 27450Winter 23000 1.15 22000 1.05 1.10 24750Spring 19000 0.95 19000 0.90 0.93 20925

Summer 14000 0.70 17000 0.81 0.76 17100

Total 80000 4.00 84000 4.00 4.01 90000 Average 20000 21000 22500


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Linear Regression

X X X

Y X XY b

2

Identify dependent (y) andindependent (x) variablesSolve for the slope of the

line

Solve for the y intercept

Develop your equation forthe trend line

Y=a + bX

XbYa

22 XnX

YXnXYb


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How Good is the Fit?Correlation coefficient (r) measures the direction and strength of the linearrelationship between two variables. The closer the r value is to 1.0 the betterthe regression line fits the data points.

Coefficient of determination ( ) measures the amount of variation in thedependent variable about its mean that is explained by the regression line.

Values of ( ) close to 1.0 are desirable.

.788.982r

.88858987,1654*(205)-4(10,533)

589205)(30,282(4)r

YYn*XXnYXXYnr

22

22

22

22

2r

2r


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Factors for Selecting aForecasting Model

The amount & type of available dataDegree of accuracy requiredLength of forecast horizonPresence of data patterns


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Forecasting Software

SpreadsheetsMicrosoft Excel, Quattro Pro, Lotus 1-2-3

Limited statistical analysis of forecast dataStatistical packages

SPSS, SAS, NCSS, MinitabForecasting plus statistical and graphics

Specialty forecasting packagesForecast Master, Forecast Pro, Autobox, SCA


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