4 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall 4 4 Forecasting PowerPoint presentation to accompany Heizer and Render Operations Management,

4 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall

44 ForecastingForecasting

PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e

PowerPoint slides by Jeff Heyl

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What is Forecasting?What is Forecasting?

Process of predicting a future event

Underlying basis of all business decisions Production

Inventory

Personnel

Facilities

??

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Short-range forecast Up to 1 year, generally less than 3 months

Purchasing, job scheduling, workforce levels, job assignments, production levels

Medium-range forecast 3 months to 3 years

Sales and production planning, budgeting

Long-range forecast 3+ years

New product planning, facility location, research and development

Forecasting Time HorizonsForecasting Time Horizons

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Types of ForecastsTypes of Forecasts

Economic forecasts Address business cycle – inflation rate,

money supply, housing starts, etc.

Technological forecasts Predict rate of technological progress

Impacts development of new products

Demand forecasts Predict sales of existing products and

services

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Forecasting ApproachesForecasting Approaches

Used when situation is vague and little data exist New products

New technology

Involves intuition, experience e.g., forecasting sales on

Internet

Qualitative MethodsQualitative Methods

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Forecasting ApproachesForecasting Approaches

Used when situation is ‘stable’ and historical data exist Existing products

Current technology

Involves mathematical techniques e.g., forecasting sales of color

televisions

Quantitative MethodsQuantitative Methods

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Overview of Quantitative Overview of Quantitative ApproachesApproaches

1. Naive approach

2. Moving averages

3. Exponential smoothing

4. Trend projection

5. Linear regression

time-series models

associative model

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Set of evenly spaced numerical data Obtained by observing response

variable at regular time periods

Forecast based only on past values, no other variables important Assumes that factors influencing

past and present will continue influence in future

Time Series ForecastingTime Series Forecasting

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Trend

Seasonal

Cyclical

Random

Time Series ComponentsTime Series Components

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Components of DemandComponents of DemandD

eman

d f

or

pro

du

ct o

r se

rvic

e

| | | |1 2 3 4

Time (years)

Average demand over 4 years

Trend component

Actual demand line

Random variation

Figure 4.1

Seasonal peaks

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Persistent, overall upward or downward pattern

Changes due to population, technology, age, culture, etc.

Typically several years duration

Trend ComponentTrend Component

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Regular pattern of up and down fluctuations

Due to weather, customs, etc.

Occurs within a single year

Seasonal ComponentSeasonal Component

Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52

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Repeating up and down movements

Affected by business cycle, political, and economic factors

Multiple years duration

Often causal or associative relationships

Cyclical ComponentCyclical Component

0 5 10 15 20

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Erratic, unsystematic, ‘residual’ fluctuations

Due to random variation or unforeseen events

Short duration and nonrepeating

Random ComponentRandom Component

M T W T F

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MA is a series of arithmetic means

Used if little or no trend

Used often for smoothing Provides overall impression of data

over time

Moving Average MethodMoving Average Method

Moving average =∑ demand in previous n periods

n

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Form of weighted moving average Weights decline exponentially

Most recent data weighted most

Requires smoothing constant () Ranges from 0 to 1

Subjectively chosen

Involves little record keeping of past data

Exponential SmoothingExponential Smoothing

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Exponential SmoothingExponential Smoothing

New forecast = Last period’s forecast+ (Last period’s actual demand

– Last period’s forecast)

Ft = Ft – 1 + (At – 1 - Ft – 1)

where Ft = new forecast

Ft – 1 = previous forecast

= smoothing (or weighting) constant (0 ≤ ≤ 1)

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Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation (MAD)

MAD =∑ |Actual - Forecast|

n

Mean Squared Error (MSE)

MSE =∑ (Forecast Errors)2

n

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Common Measures of ErrorCommon Measures of Error

Mean Absolute Percent Error (MAPE)

MAPE =∑100|Actuali - Forecasti|/Actuali

n

n

i = 1

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Trend ProjectionsTrend Projections

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 = a + bx^

where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable

^

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Seasonal Variations In DataSeasonal Variations In Data

The multiplicative seasonal model can adjust trend data for seasonal variations in demand

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Associative ForecastingAssociative Forecasting

Used when changes in one or more independent variables can be used to predict

the changes in the dependent variable

Most common technique is linear regression analysis

We apply this technique just as we did We apply this technique just as we did in the time series examplein the time series example

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Associative ForecastingAssociative ForecastingForecasting an outcome based on predictor variables using the least squares technique

y = a + bx^

where y= computed value of the variable to be predicted (dependent variable)a= y-axis interceptb= slope of the regression linex= the independent variable though to predict the value of the dependent variable

^

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Associative Forecasting Associative Forecasting ExampleExample

Sales Area Payroll($ millions), y ($ billions), x

2.0 13.0 32.5 42.0 22.0 13.5 7

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sal

es

Area payroll

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Associative Forecasting Associative Forecasting ExampleExample

Sales, y Payroll, x x2 xy

2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5

∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5

x = ∑x/6 = 18/6 = 3

y = ∑y/6 = 15/6 = 2.5

b = = = .25∑xy - nxy

∑x2 - nx2

51.5 - (6)(3)(2.5)

80 - (6)(32)

a = y - bx = 2.5 - (.25)(3) = 1.75

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Associative Forecasting Associative Forecasting ExampleExample

y = 1.75 + .25x^ Sales = 1.75 + .25(payroll)

If payroll next year is estimated to be $6 billion, then:

Sales = 1.75 + .25(6)Sales = $3,250,000

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

No

del

’s s

ales

Area payroll

3.25

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Standard Error of the Standard Error of the EstimateEstimate

A forecast is just a point estimate of a future value

This point is actually the mean of a probability distribution

Figure 4.9

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

No

del

’s s

ales

Area payroll

3.25

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Standard Error of the Standard Error of the EstimateEstimate

where y = y-value of each data point

yc = computed value of the dependent variable, from the regression equation

n = number of data points

Sy,x =∑(y - yc)2

n - 2

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How strong is the linear relationship between the variables?

Correlation does not necessarily imply causality!

Coefficient of correlation, r, measures degree of association Values range from -1 to +1

CorrelationCorrelation

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Correlation CoefficientCorrelation Coefficient

r = nxy - xy

[nx2 - (x)2][ny2 - (y)2]

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Correlation CoefficientCorrelation Coefficient

r = nxy - xy

[nx2 - (x)2][ny2 - (y)2]

y

x(a) Perfect positive correlation: r = +1

y

x(b) Positive correlation: 0 < r < 1

y

x(c) No correlation: r = 0

y

x(d) Perfect negative correlation: r = -1

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Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x Values range from 0 to 1

Easy to interpret

CorrelationCorrelation

For the Nodel Construction example:

r = .901

r2 = .81

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Multiple Regression Multiple Regression AnalysisAnalysis

If more than one independent variable is to be used in the model, linear regression can be

extended to multiple regression to accommodate several independent variables

y = a + b1x1 + b2x2 …^

Computationally, this is quite Computationally, this is quite complex and generally done on the complex and generally done on the

computercomputer

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Multiple Regression Multiple Regression AnalysisAnalysis

y = 1.80 + .30x1 - 5.0x2^

In the Nodel example, including interest rates in the model gives the new equation:

An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales

Sales = 1.80 + .30(6) - 5.0(.12) = 3.00Sales = $3,000,000