Heizer Ch04 Forecasting

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

44 ForecastingForecasting

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OutlineOutline

Global Company Profile: Disney World

What Is Forecasting? Forecasting Time Horizons

The Influence of Product Life Cycle

Types Of Forecasts


Outline – ContinuedOutline – Continued

The Strategic Importance of Forecasting Human Resources

Capacity

Supply Chain Management

Seven Steps in the Forecasting System



Forecasting Approaches Overview of Qualitative Methods

Overview of Quantitative Methods

Time-Series Forecasting Decomposition of a Time Series

Naive Approach



Time-Series Forecasting (cont.) Moving Averages

Exponential Smoothing

Exponential Smoothing with Trend Adjustment

Trend Projections

Seasonal Variations in Data

Cyclical Variations in Data


Outline – ContinuedOutline – Continued Associative Forecasting Methods:

Regression and Correlation Analysis Using Regression Analysis for

Forecasting

Standard Error of the Estimate

Correlation Coefficients for Regression Lines

Multiple-Regression Analysis



Monitoring and Controlling Forecasts Adaptive Smoothing

Focus Forecasting

Forecasting in the Service Sector


Learning ObjectivesLearning Objectives

When you complete this chapter you When you complete this chapter you should be able to :should be able to :

1. Understand the three time horizons and which models apply for each use

2. Explain when to use each of the four qualitative models

3. Apply the naive, moving average, exponential smoothing, and trend methods


Learning ObjectivesLearning Objectives

When you complete this chapter you When you complete this chapter you should be able to :should be able to :

4. Compute three measures of forecast accuracy

5. Develop seasonal indexes

6. Conduct a regression and correlation analysis

7. Use a tracking signal


Forecasting at Disney WorldForecasting at Disney World

Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and Anaheim

Revenues are derived from people – how many visitors and how they spend their money

Daily management report contains only the forecast and actual attendance at each park



Disney generates daily, weekly, monthly, annual, and 5-year forecasts

Forecast used by labor management, maintenance, operations, finance, and park scheduling

Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted



20% of customers come from outside the USA

Economic model includes gross domestic product, cross-exchange rates, arrivals into the USA

A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year



Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world

Average forecast error for the 5-year forecast is 5%

Average forecast error for annual forecasts is between 0% and 3%


What is Forecasting?What is Forecasting?

Process of predicting a future event

Underlying basis of all business decisions Production

Inventory

Personnel

Facilities

??


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


Distinguishing DifferencesDistinguishing Differences

Medium/long rangeMedium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes

Short-termShort-term forecasting usually employs different methodologies than longer-term forecasting

Short-termShort-term forecasts tend to be more accurate than longer-term forecasts


Influence of Product Life Influence of Product Life CycleCycle

Introduction and growth require longer forecasts than maturity and decline

As product passes through life cycle, forecasts are useful in projecting Staffing levels

Inventory levels

Factory capacity

Introduction – Growth – Maturity – DeclineIntroduction – Growth – Maturity – Decline


Product Life CycleProduct Life Cycle

Best period to increase market share

R&D engineering is critical

Practical to change price or quality image

Strengthen niche

Poor time to change image, price, or quality

Competitive costs become criticalDefend market position

Cost control critical

Introduction Growth Maturity Decline

Co

mp

an

y S

tra

teg

y/Is

sue

s

Figure 2.5

Internet search engines

Sales

Drive-through restaurants

CD-ROMs

Analog TVs

iPods

Boeing 787

LCD & plasma TVs

Twitter

Avatars

Xbox 360


Product Life CycleProduct Life Cycle

Product design and development critical

Frequent product and process design changes

Short production runs

High production costs

Limited models

Attention to quality

Introduction Growth Maturity Decline

OM

Str

ate

gy

/Issu

es

Forecasting critical

Product and process reliability

Competitive product improvements and options

Increase capacity

Shift toward product focus

Enhance distribution

Standardization

Fewer product changes, more minor changes

Optimum capacity

Increasing stability of process

Long production runs

Product improvement and cost cutting

Little product differentiation

Cost minimization

Overcapacity in the industry

Prune line to eliminate items not returning good margin

Reduce capacity

Figure 2.5


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


Strategic Importance of Strategic Importance of ForecastingForecasting

Human Resources – Hiring, training, laying off workers

Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share

Supply Chain Management – Good supplier relations and price advantages


Seven Steps in ForecastingSeven Steps in Forecasting

1. Determine the use of the forecast

2. Select the items to be forecasted

3. Determine the time horizon of the forecast

4. Select the forecasting model(s)

5. Gather the data

6. Make the forecast

7. Validate and implement results


The Realities!The Realities!

Forecasts are seldom perfect

Most techniques assume an underlying stability in the system

Product family and aggregated forecasts are more accurate than individual product forecasts


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


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


Overview of Qualitative Overview of Qualitative MethodsMethods

1. Jury of executive opinion Pool opinions of high-level experts,

sometimes augment by statistical models

2. Delphi method Panel of experts, queried iteratively


Overview of Qualitative Overview of Qualitative MethodsMethods

3. Sales force composite Estimates from individual

salespersons are reviewed for reasonableness, then aggregated

4. Consumer Market Survey Ask the customer


Involves small group of high-level experts and managers

Group estimates demand by working together

Combines managerial experience with statistical models

Relatively quick

‘Group-think’disadvantage

Jury of Executive OpinionJury of Executive Opinion


Sales Force CompositeSales Force Composite

Each salesperson projects his or her sales

Combined at district and national levels

Sales reps know customers’ wants

Tends to be overly optimistic


Delphi MethodDelphi Method Iterative group

process, continues until consensus is reached

3 types of participants Decision makers

Staff

Respondents

Staff(Administering

survey)

Decision Makers(Evaluate

responses and make decisions)

Respondents(People who can make valuable

judgments)


Consumer Market SurveyConsumer Market Survey

Ask customers about purchasing plans

What consumers say, and what they actually do are often different

Sometimes difficult to answer


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


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


Trend

Seasonal

Cyclical

Random

Time Series ComponentsTime Series Components


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


Persistent, overall upward or downward pattern

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

Typically several years duration

Trend ComponentTrend Component


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


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


Erratic, unsystematic, ‘residual’ fluctuations

Due to random variation or unforeseen events

Short duration and nonrepeating

Random ComponentRandom Component

M T W T F


Naive ApproachNaive Approach

Assumes demand in next period is the same as demand in most recent period e.g., If January sales were 68, then

February sales will be 68

Sometimes cost effective and efficient

Can be good starting point


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


January 10February 12March 13April 16May 19June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

(12 + 13 + 16)/3 = 13 2/3

(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

Moving Average ExampleMoving Average Example

101012121313

(1010 + 1212 + 1313)/3 = 11 2/3


Graph of Moving AverageGraph of Moving Average

| | | | | | | | | | | |

J F M A M J J A S O N D

Sh

ed S

ales

30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –

Actual Sales

Moving Average Forecast


Used when some trend might be present Older data usually less important

Weights based on experience and intuition

Weighted Moving AverageWeighted Moving Average

Weightedmoving average =

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

∑ weights


January 10February 12March 13April 16May 19June 23July 26

Actual 3-Month WeightedMonth Shed Sales Moving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 141/3

[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2

Weighted Moving AverageWeighted Moving Average

101012121313

[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6

Weights Applied Period

33 Last month22 Two months ago11 Three months ago

6 Sum of weights


Increasing n smooths the forecast but makes it less sensitive to changes

Do not forecast trends well

Require extensive historical data

Potential Problems WithPotential Problems With Moving Average Moving Average


Moving Average And Moving Average And Weighted Moving AverageWeighted Moving Average

30 –

25 –

20 –

15 –

10 –

5 –

Sa

les

de

man

d

| | | | | | | | | | | |

J F M A M J J A S O N D

Actual sales

Moving average

Weighted moving average

Figure 4.2


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


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)


Exponential Smoothing Exponential Smoothing ExampleExample

Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20




New forecast = 142 + .2(153 – 142)




New forecast = 142 + .2(153 – 142)

= 142 + 2.2

= 144.2 ≈ 144 cars


Effect ofEffect of Smoothing Constants Smoothing Constants

Weight Assigned to

Most 2nd Most 3rd Most 4th Most 5th MostRecent Recent Recent Recent Recent

Smoothing Period Period Period Period PeriodConstant () (1 - ) (1 - )2 (1 - )3 (1 - )4

= .1 .1 .09 .081 .073 .066

= .5 .5 .25 .125 .063 .031


Impact of Different Impact of Different

225 –

200 –

175 –

150 –| | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

De

ma

nd

= .1

Actual demand

= .5


Impact of Different Impact of Different

225 –

200 –

175 –

150 –| | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

De

ma

nd

= .1

Actual demand

= .5 Chose high values of when underlying average is likely to change

Choose low values of when underlying average is stable


Choosing Choosing

The objective is to obtain the most accurate forecast no matter the technique

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

Forecast error = Actual demand - Forecast value

= At - Ft


Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation (MAD)

MAD =∑ |Actual - Forecast|

n

Mean Squared Error (MSE)

MSE =∑ (Forecast Errors)2

n


Common Measures of ErrorCommon Measures of Error

Mean Absolute Percent Error (MAPE)

MAPE =∑100|Actuali - Forecasti|/Actuali

n

n

i = 1


Comparison of Forecast Comparison of Forecast Error Error

Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62





1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD =∑ |deviations|

n

= 82.45/8 = 10.31

For = .10

= 98.62/8 = 12.33

For = .50





1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33

= 1,526.54/8 = 190.82

For = .10

= 1,561.91/8 = 195.24

For = .50

MSE =∑ (forecast errors)2

n





1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24

= 44.75/8 = 5.59%

For = .10

= 54.05/8 = 6.76%

For = .50

MAPE =∑100|deviationi|/actuali

n

n

i = 1





1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%


Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

When a trend is present, exponential smoothing must be modified

Forecast including (FITt) = trend

Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend


Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

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

Tt = (Ft - Ft - 1) + (1 - )Tt - 1

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt


Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example

ForecastActual Smoothed Smoothed Including

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt

1 12 11 2 13.002 173 204 195 246 217 318 289 36

10

Table 4.1





1 12 11 2 13.002 173 204 195 246 217 318 289 36

10

Table 4.1

F2 = A1 + (1 - )(F1 + T1)

F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2





1 12 11 2 13.002 17 12.803 204 195 246 217 318 289 36

10

Table 4.1

T2 = (F2 - F1) + (1 - )T1

T2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2





1 12 11 2 13.002 17 12.80 1.923 204 195 246 217 318 289 36

10

Table 4.1

FIT2 = F2 + T2

FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2





1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 217 318 289 36

10

Table 4.1

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16



Figure 4.3

| | | | | | | | |

1 2 3 4 5 6 7 8 9

Time (month)

Pro

du

ct d

eman

d

35 –

30 –

25 –

20 –

15 –

10 –

5 –

0 –

Actual demand (At)

Forecast including trend (FITt)with = .2 and = .4


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

^


Least Squares MethodLeast Squares Method

Time period

Va

lue

s o

f D

ep

end

en

t V

ari

able

Figure 4.4

Deviation1

(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation (y-value)

Trend line, y = a + bx^



Time period

Va

lue

s o

f D

ep

end

en

t V

ari

able

Figure 4.4

Deviation1

(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation (y-value)

Trend line, y = a + bx^

Least squares method minimizes the sum of the

squared errors (deviations)



Equations to calculate the regression variables

b =xy - nxy

x2 - nx2

y = a + bx^

a = y - bx


Least Squares ExampleLeast Squares Example

b = = = 10.54∑xy - nxy

∑x2 - nx2

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

140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

Time Electrical Power Year Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854

∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86


b = = = 10.54∑xy - nxy

∑x2 - nx2

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

140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

Time Electrical Power Year Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854

∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063x = 4 y = 98.86


The trend line is

y = 56.70 + 10.54x^



| | | | | | | | |2003 2004 2005 2006 2007 2008 2009 2010 2011

160 –150 –140 –130 –120 –110 –100 –90 –80 –70 –60 –50 –

Year

Po

wer

dem

and

Trend line,y = 56.70 + 10.54x^


Seasonal Variations In DataSeasonal Variations In Data

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


Seasonal Variations In DataSeasonal Variations In Data

1. Find average historical demand for each season

2. Compute the average demand over all seasons

3. Compute a seasonal index for each season

4. Estimate next year’s total demand

5. Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season

Steps in the process:Steps in the process:


Seasonal Index ExampleSeasonal Index Example

Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94

Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index



Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94


0.957

Seasonal index = Average 2007-2009 monthly demand

Average monthly demand

= 90/94 = .957



Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851




Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12

Forecast for 2010



140 –

130 –

120 –

110 –

100 –

90 –

80 –

70 –| | | | | | | | | | | |J F M A M J J A S O N D

Time

Dem

and

2010 Forecast

2009 Demand

2008 Demand

2007 Demand


San Diego HospitalSan Diego Hospital

10,200 –

10,000 –

9,800 –

9,600 –

9,400 –

9,200 –

9,000 –| | | | | | | | | | | |

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

Inp

atie

nt

Day

s

9530

9551

9573

9594

9616

9637

9659

9680

9702

9724

9745

9766

Figure 4.6

Trend Data



1.06 –

1.04 –

1.02 –

1.00 –

0.98 –

0.96 –

0.94 –

0.92 – | | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

Ind

ex f

or

Inp

atie

nt

Day

s 1.04

1.021.01

0.99

1.031.04

1.00

0.98

0.97

0.99

0.970.96

Figure 4.7

Seasonal Indices



10,200 –

10,000 –

9,800 –

9,600 –

9,400 –

9,200 –

9,000 –| | | | | | | | | | | |

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

Inp

atie

nt

Day

s

Figure 4.8

9911

9265

9764

9520

9691

9411

9949

9724

9542

9355

10068

9572

Combined Trend and Seasonal Forecast


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


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

^


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



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



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


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



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



Computationally, this equation is considerably easier to use

We use the standard error to set up prediction intervals around the

point estimate

Sy,x =∑y2 - a∑y - b∑xy

n - 2



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

Sy,x = =∑y2 - a∑y - b∑xyn - 2

39.5 - 1.75(15) - .25(51.5)6 - 2

Sy,x = .306

The standard error of the estimate is $306,000 in sales


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


Correlation CoefficientCorrelation Coefficient

r = nxy - xy

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


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


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


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


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


Measures how well the forecast is predicting actual values

Ratio of cumulative forecast errors to mean absolute deviation (MAD) Good tracking signal has low values

If forecasts are continually high or low, the forecast has a bias error

Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking SignalTracking Signal


Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking signal

Cumulative errorMAD

=

Tracking signal =

∑(Actual demand in period i -

Forecast demand in period i)

∑|Actual - Forecast|/n)


Tracking SignalTracking Signal

Tracking signal

+

0 MADs

–

Upper control limit

Lower control limit

Time

Signal exceeding limit

Acceptable range


Tracking Signal ExampleTracking Signal Example

CumulativeAbsolute Absolute

Actual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD

1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2


CumulativeAbsolute Absolute

Actual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD

1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2

Tracking Signal ExampleTracking Signal Example

TrackingSignal

(Cumm Error/MAD)

-10/10 = -1-15/7.5 = -2

0/10 = 0-10/10 = -1

+5/11 = +0.5+35/14.2 = +2.5

The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits


Adaptive ForecastingAdaptive Forecasting

It’s possible to use the computer to continually monitor forecast error and adjust the values of the and coefficients used in exponential smoothing to continually minimize forecast error

This technique is called adaptive smoothing


Focus ForecastingFocus Forecasting Developed at American Hardware Supply,

based on two principles:1. Sophisticated forecasting models are not

always better than simple ones

2. There is no single technique that should be used for all products or services

This approach uses historical data to test multiple forecasting models for individual items

The forecasting model with the lowest error is then used to forecast the next demand


Forecasting in the Service Forecasting in the Service SectorSector

Presents unusual challenges Special need for short term records

Needs differ greatly as function of industry and product

Holidays and other calendar events

Unusual events


Fast Food Restaurant Fast Food Restaurant ForecastForecast

20% –

15% –

10% –

5% –

11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11

(Lunchtime) (Dinnertime)Hour of day

Per

cen

tag

e o

f sa

les

Figure 4.12


FedEx Call Center ForecastFedEx Call Center Forecast

Figure 4.12

12% –

10% –

8% –

6% –

4% –

2% –

0% –

Hour of dayA.M. P.M.

2 4 6 8 10 12 2 4 6 8 10 12


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Heizer Ch04 Forecasting