4 – 1 psm10 © 2006 prentice hall, inc. powerpoint presentation to accompany heizer/render...

4 4 –– 11PSM10PSM10© 2006 Prentice Hall, Inc.

PowerPoint presentation to accompanyPowerPoint presentation to accompany Heizer/Render Heizer/Render Operations Management, 8e Operations Management, 8e

Chapter 4 – ForecastingChapter 4 – Forecasting

4 4 –– 22PSM10PSM10

What is Forecasting?What is Forecasting?

Process of Process of predicting a future predicting a future eventevent

Underlying basis of Underlying basis of

all business all business decisionsdecisions ProductionProduction

InventoryInventory

PersonnelPersonnel

FacilitiesFacilities

??

4 4 –– 33PSM10PSM10

Forecasting Time HorizonsForecasting Time Horizons

Short-range forecastShort-range forecast Up to 1 year, generally less than 3 monthsUp to 1 year, generally less than 3 months Purchasing, job scheduling, workforce Purchasing, job scheduling, workforce

levels, job assignments, production levelslevels, job assignments, production levels

Medium-range forecastMedium-range forecast 3 months to 3 years3 months to 3 years Sales and production planning, budgetingSales and production planning, budgeting

Long-range forecastLong-range forecast 33++ years years New product planning, facility location, New product planning, facility location,

research and developmentresearch and development

4 4 –– 44PSM10PSM10

Distinguishing DifferencesDistinguishing Differences

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

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

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

4 4 –– 55PSM10PSM10

Influence of Product Life CycleInfluence of Product Life Cycle

Introduction and growth require longer Introduction and growth require longer forecasts than maturity and declineforecasts than maturity and decline

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

Inventory levelsInventory levels

Factory capacityFactory capacity

Introduction – Growth – Maturity – Decline

4 4 –– 66PSM10PSM10

Types of ForecastsTypes of Forecasts

Economic forecastsEconomic forecasts Address business cycle – inflation rate, Address business cycle – inflation rate,

money supply, housing starts, etc.money supply, housing starts, etc.

Technological forecastsTechnological forecasts Predict rate of technological progressPredict rate of technological progress

Impacts development of new productsImpacts development of new products

Demand forecastsDemand forecasts Predict sales of existing productPredict sales of existing product

4 4 –– 77PSM10PSM10

Strategic Importance of ForecastingStrategic Importance of Forecasting

Human Resources – Hiring, training, Human Resources – Hiring, training, laying off workerslaying off workers

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

Supply-Chain Management – Good Supply-Chain Management – Good supplier relations and price advancesupplier relations and price advance

4 4 –– 88PSM10PSM10

Seven Steps in ForecastingSeven Steps in Forecasting

1.1. Determine the use of the forecastDetermine the use of the forecast

2.2. Select the items to be forecastedSelect the items to be forecasted

3.3. Determine the time horizon of the Determine the time horizon of the forecastforecast

4.4. Select the forecasting model(s)Select the forecasting model(s)

5.5. Gather the dataGather the data

6.6. Make the forecastMake the forecast

7.7. Validate and implement resultsValidate and implement results

4 4 –– 99PSM10PSM10

The Realities!The Realities!

Forecasts are seldom perfectForecasts are seldom perfect

Most techniques assume an Most techniques assume an underlying stability in the systemunderlying stability in the system

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

4 4 –– 1010PSM10PSM10

Forecasting ApproachesForecasting Approaches

Used when situation is vague Used when situation is vague and little data existand little data exist New productsNew products

New technologyNew technology

Involves intuition, experienceInvolves intuition, experience e.g., forecasting sales on Internete.g., forecasting sales on Internet

Qualitative MethodsQualitative Methods

4 4 –– 1111PSM10PSM10

Forecasting ApproachesForecasting Approaches

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

Current technologyCurrent technology

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

televisionstelevisions

Quantitative MethodsQuantitative Methods

4 4 –– 1212PSM10PSM10

Overview of Qualitative MethodsOverview of Qualitative Methods

Jury of executive opinionJury of executive opinion Pool opinions of high-level Pool opinions of high-level

executives, sometimes augment by executives, sometimes augment by statistical modelsstatistical models

Delphi methodDelphi method Panel of experts, queried iterativelyPanel of experts, queried iteratively

4 4 –– 1313PSM10PSM10

Overview of Qualitative MethodsOverview of Qualitative Methods

Sales force compositeSales force composite Estimates from individual Estimates from individual

salespersons are reviewed for salespersons are reviewed for reasonableness, then aggregated reasonableness, then aggregated

Consumer Market SurveyConsumer Market Survey Ask the customerAsk the customer

4 4 –– 1414PSM10PSM10

Involves small group of high-level Involves small group of high-level managersmanagers

Group estimates demand by working Group estimates demand by working togethertogether

Combines managerial experience with Combines managerial experience with statistical modelsstatistical models

Relatively quickRelatively quick

‘‘Group-think’Group-think’disadvantagedisadvantage

Jury of Executive OpinionJury of Executive Opinion

4 4 –– 1515PSM10PSM10

Sales Force CompositeSales Force Composite

Each salesperson projects his or Each salesperson projects his or her salesher sales

Combined at district and national Combined at district and national levelslevels

Sales reps know customers’ wantsSales reps know customers’ wants

Tends to be overly optimisticTends to be overly optimistic

4 4 –– 1616PSM10PSM10

Delphi MethodDelphi Method

Iterative group Iterative group process, process, continues until continues until consensus is consensus is reachedreached

3 types of 3 types of participantsparticipants Decision makersDecision makers StaffStaff RespondentsRespondents

Staff(Administering

survey)

Decision Makers(Evaluate

responses and make decisions)

Respondents(People who can make valuable

judgments)

4 4 –– 1717PSM10PSM10

Consumer Market SurveyConsumer Market Survey

Ask customers about purchasing Ask customers about purchasing plansplans

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

Sometimes difficult to answerSometimes difficult to answer

4 4 –– 1818PSM10PSM10

Overview of Quantitative ApproachesOverview of Quantitative Approaches

1.1. Naive approachNaive approach

2.2. Moving averagesMoving averages

3.3. Exponential Exponential smoothingsmoothing

4.4. Trend projectionTrend projection

5.5. Linear regressionLinear regression

Time-Series Time-Series ModelsModels

Associative Associative ModelModel

4 4 –– 1919PSM10PSM10

Time Series ForecastingTime Series Forecasting

Set of evenly spaced numerical Set of evenly spaced numerical datadata Obtained by observing response Obtained by observing response

variable at regular time periodsvariable at regular time periods

Forecast based only on past Forecast based only on past valuesvalues Assumes that factors influencing Assumes that factors influencing

past and present will continue past and present will continue influence in futureinfluence in future

4 4 –– 2020PSM10PSM10

Trend

Seasonal

Cyclical

Random

Time Series ComponentsTime Series Components

4 4 –– 2121PSM10PSM10

Components of DemandComponents of DemandD

eman

d f

or

pro

du

ct o

r se

rvic

e

| | | |1 2 3 4

Year

Average demand over four years

Seasonal peaks

Trend component

Actual demand

Random variation

4 4 –– 2222PSM10PSM10

Trend ComponentTrend Component

Persistent, overall upward or Persistent, overall upward or downward patterndownward pattern

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

Typically several years Typically several years duration duration

4 4 –– 2323PSM10PSM10

Seasonal ComponentSeasonal Component

Regular pattern of up and Regular pattern of up and down fluctuationsdown fluctuations

Due to weather, customs, etc.Due to weather, customs, etc.

Occurs within a single year Occurs within a single year

Number ofPeriod Length Seasons

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

4 4 –– 2424PSM10PSM10

Cyclical ComponentCyclical Component

Repeating up and down movementsRepeating up and down movements

Affected by business cycle, political, Affected by business cycle, political, and economic factorsand economic factors

Multiple years durationMultiple years duration

Often causal or Often causal or associative associative relationshipsrelationships

00 55 1010 1515 2020

4 4 –– 2525PSM10PSM10

Random ComponentRandom Component

Erratic, unsystematic, ‘residual’ Erratic, unsystematic, ‘residual’ fluctuationsfluctuations

Due to random variation or Due to random variation or unforeseen eventsunforeseen events

Short duration and Short duration and nonrepeating nonrepeating

MM TT WW TT FF

4 4 –– 2626PSM10PSM10

Naive ApproachNaive Approach

Assumes demand in next period is Assumes demand in next period is the same as demand in most the same as demand in most recent periodrecent period e.g., If May sales were 48, then June e.g., If May sales were 48, then June

sales will be 48sales will be 48

Sometimes cost effective and Sometimes cost effective and efficientefficient

4 4 –– 2727PSM10PSM10

Moving Average MethodMoving Average Method

MA is a series of arithmetic means MA is a series of arithmetic means

Used if little or no trendUsed if little or no trend

Used often for smoothingUsed often for smoothingProvides overall impression of data Provides overall impression of data

over timeover time

Moving average =Moving average =∑∑ demand in previous n periodsdemand in previous n periods

nn

4 4 –– 2828PSM10PSM10

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month3-MonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average

(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33

(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33

Moving Average ExampleMoving Average Example

101012121313

((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33

4 4 –– 2929PSM10PSM10

Graph of Moving AverageGraph of Moving Average

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

JJ FF MM AA MM JJ JJ AA SS OO NN DD

Sh

ed S

ales

Sh

ed S

ales

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

Actual Actual SalesSales

Moving Moving Average Average ForecastForecast

4 4 –– 3030PSM10PSM10

Weighted Moving AverageWeighted Moving Average

Used when trend is present Used when trend is present Older data usually less importantOlder data usually less important

Weights based on experience and Weights based on experience and intuitionintuition

WeightedWeightedmoving averagemoving average ==

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

∑∑ weightsweights

4 4 –– 3131PSM10PSM10

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month Weighted3-Month WeightedMonthMonth Shed SalesShed Sales Moving AverageMoving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 14[(3 x 16) + (2 x 13) + (12)]/6 = 1411//33

[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20[(3 x 23) + (2 x 19) + (16)]/6 = 2011//22

Weighted Moving AverageWeighted Moving Average

101012121313

[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66

Weights Applied Period

3 Last month2 Two months ago1 Three months ago6 Sum of weights

4 4 –– 3232PSM10PSM10

Potential Problems With Moving AveragePotential Problems With Moving Average

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

Do not forecast trends wellDo not forecast trends well

Require extensive historical dataRequire extensive historical data

4 4 –– 3333PSM10PSM10

Moving Average And Weighted Moving Moving Average And Weighted Moving AverageAverage

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

Sa

les

de

man

dS

ale

s d

em

and

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


Actual Actual salessales

Moving Moving averageaverage

Weighted Weighted moving moving averageaverage

4 4 –– 3434PSM10PSM10

Exponential SmoothingExponential Smoothing

Form of weighted moving averageForm of weighted moving average Weights decline exponentiallyWeights decline exponentially

Most recent data weighted mostMost recent data weighted most

Requires smoothing constant Requires smoothing constant (()) Ranges from 0 to 1Ranges from 0 to 1

Subjectively chosenSubjectively chosen

Involves little record keeping of past Involves little record keeping of past datadata

4 4 –– 3535PSM10PSM10

Exponential SmoothingExponential Smoothing

New forecast =New forecast = last period’s forecastlast period’s forecast+ + ((last period’s actual demand last period’s actual demand

– – last period’s forecastlast period’s forecast))

FFtt = F = Ft t – 1– 1 + + ((AAt t – 1– 1 - - F Ft t – 1– 1))

wherewhere FFtt == new forecastnew forecast

FFt t – 1– 1 == previous forecastprevious forecast

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

4 4 –– 3636PSM10PSM10

Exponential Smoothing ExampleExponential Smoothing Example

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

4 4 –– 3737PSM10PSM10



New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)

4 4 –– 3838PSM10PSM10



New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)

= 142 + 2.2= 142 + 2.2

= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars

4 4 –– 3939PSM10PSM10

Effect ofEffect of Smoothing Constants Smoothing Constants

Weight Assigned toWeight Assigned to

MostMost 2nd Most2nd Most 3rd Most3rd Most 4th Most4th Most 5th Most5th MostRecentRecent RecentRecent RecentRecent RecentRecent RecentRecent

SmoothingSmoothing PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriodConstantConstant (()) (1 - (1 - )) (1 - (1 - ))22 (1 - (1 - ))33 (1 - (1 - ))44

= .1= .1 .1.1 .09.09 .081.081 .073.073 .066.066

= .5= .5 .5.5 .25.25 .125.125 .063.063 .031.031

4 4 –– 4040PSM10PSM10

Impact of Different Impact of Different

225 225 –

200 200 –

175 175 –

150 150 –| | | | | | | | |

11 22 33 44 55 66 77 88 99

QuarterQuarter

De

ma

nd

De

ma

nd

= .1= .1

Actual Actual demanddemand

= .5= .5

4 4 –– 4141PSM10PSM10

Choosing Choosing

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

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 errorForecast error = Actual demand - Forecast value= Actual demand - Forecast value

= A= Att - F - Ftt

4 4 –– 4242PSM10PSM10

Other interpretationOther interpretation

FFtt = F = Ft t – 1– 1 + + ((AAt t - - F Ft t – 1– 1) – ) – forecast for the t+1st period, Aforecast for the t+1st period, At t – demand – demand

of the t-th period of the t-th period

11 ttt F)(AF 21 11 ttt F)(A)(A

22

1 11 ttt F)(A)(A

322

1 111 tttt F)(Ar)(A)(A

...F)(A)(A)(A tttt 33

22

1 111

iti

iAαα

01

Exponential smoothing is the weighted average of the Exponential smoothing is the weighted average of the complete historic demand. The weights are decreasing complete historic demand. The weights are decreasing exponentially from period to period.exponentially from period to period.

4 4 –– 4343PSM10PSM10

Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation Mean Absolute Deviation ((MADMAD))

MAD =MAD =∑∑ |actual - forecast||actual - forecast|

nn

Mean Squared Error Mean Squared Error ((MSEMSE))

MSE =MSE =∑∑ ((forecast errorsforecast errors))22

nn

4 4 –– 4444PSM10PSM10

Common Measures of ErrorCommon Measures of Error

Mean Absolute Percent Error Mean Absolute Percent Error ((MAPEMAPE))

MAPE =MAPE =100 100 ∑∑ |actual |actualii - forecast - forecastii|/actual|/actualii

nn

nn

i i = 1= 1

4 4 –– 4545PSM10PSM10

Comparison of Forecast Error Comparison of Forecast Error

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100

4 4 –– 4646PSM10PSM10


RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviationTonageTonage withwith forfor withwith forfor

QuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100

MAD =∑ |deviations|

n

= 84/8 = 10.50

For = .10

= 100/8 = 12.50

For = .50

4 4 –– 4747PSM10PSM10




11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 10.5010.50 12.5012.50

= 1,558/8 = 194.75

For = .10

= 1,612/8 = 201.50

For = .50

MSE =∑ (forecast errors)2

n

4 4 –– 4848PSM10PSM10




11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 10.5010.50 12.5012.50MSEMSE 194.75194.75 201.50201.50

= 45.62/8 = 5.70%

For = .10

= 54.8/8 = 6.85%

For = .50

MAPE =100 ∑ |deviationi|/actuali

n

n

i = 1

4 4 –– 4949PSM10PSM10


RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded = .10 = .10 = .10 = .10 = .50 = .50 = .50 = .50

11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 10.5010.50 12.5012.50MSEMSE 194.75194.75 201.50201.50

MAPEMAPE 5.70%5.70% 6.85%6.85%

4 4 –– 5050PSM10PSM10

Exponential Smoothing with Trend Exponential Smoothing with Trend AdjustmentAdjustment

When a trend is present, exponential When a trend is present, exponential smoothing must be modifiedsmoothing must be modified

Forecast Forecast including including ((FITFITtt)) = = trendtrend

exponentiallyexponentially exponentiallyexponentiallysmoothed smoothed ((FFtt)) + + ((TTtt)) smoothedsmoothedforecastforecast trendtrend

4 4 –– 5151PSM10PSM10

Exponential Smoothing with Trend Exponential Smoothing with Trend AdjustmentAdjustment

Step 1: Compute FStep 1: Compute Ftt

Step 2: Compute TStep 2: Compute Ttt

Step 3: Calculate the forecast FITStep 3: Calculate the forecast FITtt == F Ftt + + TTtt

11

111

1

1

tttt

tttt

TFFT

TFAF

4 4 –– 5252PSM10PSM10

Exponential Smoothing with Trend Exponential Smoothing with Trend Adjustment ExampleAdjustment Example

ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding

MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt

11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636

1010

4 4 –– 5353PSM10PSM10




11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636

1010

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

4 4 –– 5454PSM10PSM10




11 1212 1111 22 13.0013.0022 1717 12.8012.8033 202044 191955 242466 212177 313188 282899 3636

1010

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

4 4 –– 5555PSM10PSM10




11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.9233 202044 191955 242466 212177 313188 282899 3636

1010

FIT2 = F2 + T1

FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2

4 4 –– 5656PSM10PSM10




11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.92 14.7214.7233 202044 191955 242466 212177 313188 282899 3636

1010

15.1815.18 2.102.10 17.2817.2817.8217.82 2.322.32 20.1420.1419.9119.91 2.232.23 22.1422.1422.5122.51 2.382.38 24.8924.8924.1124.11 2.072.07 26.1826.1827.1427.14 2.452.45 29.5929.5929.2829.28 2.322.32 31.6031.6032.4832.48 2.682.68 35.1635.16

4 4 –– 5757PSM10PSM10


| | | | | | | | |

11 22 33 44 55 66 77 88 99

Time (month)Time (month)

Pro

du

ct d

eman

dP

rod

uct

dem

and

35 35 –

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

0 0 –

Actual demand Actual demand ((AAtt))

Forecast including trend Forecast including trend ((FITFITtt))

4 4 –– 5858PSM10PSM10

Trend ProjectionsTrend Projections

Fitting a trend line to historical data points Fitting a trend line to historical data points to project into the medium-to-long-rangeto project into the medium-to-long-range

Linear trends can be found using the least Linear trends can be found using the least squares technique (regression analysis)squares technique (regression analysis)

y y = = a a + + bxbx^̂

where ywhere y= computed value of the = computed value of the variable to be predicted (dependent variable to be predicted (dependent variable)variable)aa= y-axis intercept= y-axis interceptbb= slope of the regression line= slope of the regression linexx= the independent variable= the independent variable

^̂

4 4 –– 5959PSM10PSM10

Least Squares MethodLeast Squares Method

Time periodTime period

Va

lue

s o

f D

ep

end

en

t V

ari

able

DeviationDeviation11







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

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

4 4 –– 6060PSM10PSM10


Time periodTime period

Va

lue

s o

f D

ep

end

en

t V

ari

able








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

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

Least squares method minimizes the sum of the

squared errors (deviations)

4 4 –– 6161PSM10PSM10


Equations to calculate the regression variablesEquations to calculate the regression variables

b =b =xy - nxyxy - nxy

xx22 - nx - nx22

y y = = a a + + bxbx^̂

a = y - bxa = y - bx

4 4 –– 6262PSM10PSM10

Least Squares ExampleLeast Squares Example

b b = = = 10.54= = = 10.54∑∑xy - nxyxy - nxy

∑∑xx22 - nx - nx22

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

140 - (7)(4140 - (7)(422))

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

∑∑xx = 28 = 28 ∑∑yy = 692 = 692 ∑∑xx22 = 140 = 140 ∑∑xyxy = 3,063 = 3,063xx = 4 = 4 yy = 98.86 = 98.86

4 4 –– 6363PSM10PSM10


b b = = = 10.54= = = 10.54xy - nxyxy - nxy

xx22 - nx - nx22

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

140 - (7)(4140 - (7)(422))

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

xx = 28 = 28 yy = 692 = 692 xx22 = 140 = 140 xyxy = 3,063 = 3,063xx = 4 = 4 yy = 98.86 = 98.86

The trend line is

y = 56.70 + 10.54x^

4 4 –– 6464PSM10PSM10


| | | | | | | | |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

Po

wer

dem

and

Po

wer

dem

and

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

141=141=56.7+8*10.5456.7+8*10.54

4 4 –– 6666PSM10PSM10

Seasonal Variations In DataSeasonal Variations In Data

The multiplicative seasonal model can The multiplicative seasonal model can modify trend data to accommodate modify trend data to accommodate seasonal variations in demandseasonal variations in demand

1.1. Find average historical demand for each season Find average historical demand for each season

2.2. Compute the average demand over all seasons Compute the average demand over all seasons

3.3. Compute a seasonal index for each season Compute a seasonal index for each season

4.4. Estimate next year’s total demandEstimate next year’s total demand

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

4 4 –– 6767PSM10PSM10

Seasonal Index ExampleSeasonal Index Example

JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494

DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 2003-20052003-2005 MonthlyMonthly IndexIndex

4 4 –– 6868PSM10PSM10


JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494


0.9570.957

Seasonal index = average 2003-2005 monthly demand

average monthly demand

= 90/94 = .957

4 4 –– 6969PSM10PSM10


JanJan 8080 8585 105105 9090 9494 0.9570.957

FebFeb 7070 8585 8585 8080 9494 0.8510.851

MarMar 8080 9393 8282 8585 9494 0.9040.904

AprApr 9090 9595 115115 100100 9494 1.0641.064

MayMay 113113 125125 131131 123123 9494 1.3091.309

JunJun 110110 115115 120120 115115 9494 1.2231.223

JulJul 100100 102102 113113 105105 9494 1.1171.117

AugAug 8888 102102 110110 100100 9494 1.0641.064

SeptSept 8585 9090 9595 9090 9494 0.9570.957

OctOct 7777 7878 8585 8080 9494 0.8510.851

NovNov 7575 7272 8383 8080 9494 0.8510.851

DecDec 8282 7878 8080 8080 9494 0.8510.851


1,1281,128

4 4 –– 7070PSM10PSM10


JanJan 8080 8585 105105 9090 9494 0.9570.957

FebFeb 7070 8585 8585 8080 9494 0.8510.851

MarMar 8080 9393 8282 8585 9494 0.9040.904

AprApr 9090 9595 115115 100100 9494 1.0641.064

MayMay 113113 125125 131131 123123 9494 1.3091.309

JunJun 110110 115115 120120 115115 9494 1.2231.223

JulJul 100100 102102 113113 105105 9494 1.1171.117

AugAug 8888 102102 110110 100100 9494 1.0641.064

SeptSept 8585 9090 9595 9090 9494 0.9570.957

OctOct 7777 7878 8585 8080 9494 0.8510.851

NovNov 7575 7272 8383 8080 9494 0.8510.851

DecDec 8282 7878 8080 8080 9494 0.8510.851


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12

Forecast for 2006

4 4 –– 7171PSM10PSM10


JanJan 95,70

FebFeb 85,10

MarMar 90,40

AprApr 106,40

MayMay 130,90

JunJun 122,30

JulJul 111,70

AugAug 106,40

SeptSept 95,70

OctOct 85,10

NovNov 85,10

DecDec 85,10

60,00

80,00

100,00

120,00

140,00

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

4 4 –– 7272PSM10PSM10


140 140 –

130 130 –

120 120 –

110 110 –

100 100 –

90 90 –

80 80 –

70 70 –| | | | | | | | | | | |


TimeTime

Dem

and

Dem

and

2006 Forecast2006 Forecast

2005 Demand 2005 Demand

2004 Demand2004 Demand

2003 Demand2003 Demand

4 4 –– 7373PSM10PSM10

Monitoring and Controlling ForecastsMonitoring and Controlling Forecasts

Measures how well the forecast is Measures how well the forecast is predicting actual valuespredicting actual values

Ratio of running sum of forecast errors Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)(RSFE) to mean absolute deviation (MAD) Good tracking signal has low valuesGood tracking signal has low values

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

Tracking SignalTracking Signal

4 4 –– 7474PSM10PSM10

Monitoring and Controlling ForecastsMonitoring and Controlling Forecasts

Tracking Tracking signalsignal

RSFERSFEMADMAD==

Tracking Tracking signalsignal ==

∑∑(actual demand in (actual demand in period i - period i -

forecast demand forecast demand in period i)in period i)

∑∑|actual - forecast|/n|actual - forecast|/n))

4 4 –– 7575PSM10PSM10

Tracking SignalTracking Signal

Tracking signalTracking signal

++

00 MADs MADs

––

Upper control limitUpper control limit

Lower control limitLower control limit

TimeTime

Signal exceeding limitSignal exceeding limit

Acceptable Acceptable rangerange

4 4 –– 7676PSM10PSM10

Tracking Signal ExampleTracking Signal Example

CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute

ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD

11 9090 100100 -10-10 -10-10 1010 1010 10.010.022 9595 100100 -5-5 -15-15 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 -10-10 -10-10 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2

4 4 –– 7777PSM10PSM10

CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute

ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD

11 9090 100100 -10-10 -10-10 1010 1010 10.010.022 9595 100100 -5-5 -15-15 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 -10-10 -10-10 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2

Tracking Signal ExampleTracking Signal Example

TrackingSignal

(RSFE/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 The variation of the tracking signal between between -2.0-2.0 and and +2.5+2.5 is within acceptable is within acceptable limitslimits

4 4 –– 7878PSM10PSM10

Forecasting in the Service SectorForecasting in the Service Sector

Presents unusual challengesPresents unusual challenges Special need for short term recordsSpecial need for short term records

Needs differ greatly as function of Needs differ greatly as function of industry and productindustry and product

Holidays and other calendar eventsHolidays and other calendar events

Unusual eventsUnusual events

4 4 –– 7979PSM10PSM10

QuestionsQuestions

Answer the following questionsAnswer the following questions

How would you rate the time horizon for long range forecast in the field of How would you rate the time horizon for long range forecast in the field of mobile information technologies? mobile information technologies?

Which of the Seven Steps in Forecasting is the most interesting for you?Which of the Seven Steps in Forecasting is the most interesting for you?

Did you ever use the method of “Jury of Executive Opinion” when Did you ever use the method of “Jury of Executive Opinion” when discussing family affairs at home?discussing family affairs at home?

Which week sides if the Delphi method would you identify?Which week sides if the Delphi method would you identify?

Under which circumstances do the Weighted Moving Average method and Under which circumstances do the Weighted Moving Average method and the method of exponential smoothing coincide?the method of exponential smoothing coincide?

Can the two methods of exponential smoothing ever coincide?Can the two methods of exponential smoothing ever coincide?

Look for the various opportunities of using forecast methods by Excel.Look for the various opportunities of using forecast methods by Excel.

Let the demand follow the function d(t) = 10 + 2t and apply the simple Let the demand follow the function d(t) = 10 + 2t and apply the simple weighted average forecast method with n = 2. What can you say about the weighted average forecast method with n = 2. What can you say about the tracking signal?tracking signal?

4 4 –– 8080PSM10PSM10

QuestionsQuestions

Homework No. 3:Homework No. 3:

Create an Excel Spreadsheet to solve the following problem! Sales of music Create an Excel Spreadsheet to solve the following problem! Sales of music stands at Johnny Ho’s music store, in Columbus, Ohio, over the past 10 weeks stands at Johnny Ho’s music store, in Columbus, Ohio, over the past 10 weeks are shown in the table below. are shown in the table below.

WeekWeek DemandDemand WeekWeek DemandDemand

11 2020 66 2929

22 2121 77 3636

33 2828 88 2222

44 3737 99 2525

55 2525 1010 2?2?

a)a) Forecast demand for each week, including week 10, using exponential Forecast demand for each week, including week 10, using exponential smoothing with smoothing with αα = 0.3 (initial forecast F = 0.3 (initial forecast F11 = 20) = 20)

b)b) Compute the MADCompute the MAD..

c)c) Compute the tracking signal. Compute the tracking signal. Submit your solution file via E-Mail to Submit your solution file via E-Mail to [email protected] (term: 29.04.2010). (term: 29.04.2010).

Don’t forget to indicate your university ID card number. Don’t forget to indicate your university ID card number.

Put here the last digit of your Put here the last digit of your university ID card number. university ID card number.

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