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Forecasting Outlines

Forecasting in Operations ManagementForecasting in Operations Management Science and Art of ForecastingScience and Art of Forecasting Seven Steps in the ForecastingSeven Steps in the Forecasting Categories and Models of Forecasting Categories and Models of Forecasting

(Focus on Time-Series Forecasting)(Focus on Time-Series Forecasting) Measure the Forecast AccuracyMeasure the Forecast Accuracy Selecting the Best Forecasting TechniquesSelecting the Best Forecasting Techniques Forecasting in service sector; forecasting Forecasting in service sector; forecasting

and ITand IT

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Learning Objectives

When you complete this chapter, you should be able to :Identify or DefineIdentify or Define::

ForecastingForecastingCategories of forecastsCategories of forecastsTime horizonsTime horizonsApproaches to measure forecastsApproaches to measure forecasts

Explain and Apply:Explain and Apply:Moving averagesMoving averagesExponential smoothingExponential smoothingTrend and seasonal projectionsTrend and seasonal projectionsMeasures of forecast accuracyMeasures of forecast accuracy

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Why Forecasting?

Forecasting lays a ground for reducing the risk in all Forecasting lays a ground for reducing the risk in all decision making because many of the decisions decision making because many of the decisions need to be made under uncertainty.need to be made under uncertainty.

In business applications, forecasting serves as a In business applications, forecasting serves as a starting point of major decisions in finance, starting point of major decisions in finance, marketing, productions, and purchasing.marketing, productions, and purchasing.

Under what condition there is no value for Under what condition there is no value for forecasting?forecasting?

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Decisions Requiring Forecasting in Operations Management

Predicting demands of new and existing Predicting demands of new and existing productsproducts

Predicting results of new product research Predicting results of new product research and developmentand development

Projecting quality improvementProjecting quality improvement Anticipating customer’s needsAnticipating customer’s needs Predicting cost of materialsPredicting cost of materials

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Decisions Relevant to Demand Forecasts Select product portfolioSelect product portfolio Predicting new facility locationPredicting new facility location Anticipating capacity needsAnticipating capacity needs Identifying labor requirementsIdentifying labor requirements Projecting material requirementsProjecting material requirements Developing production schedules Developing production schedules Creating maintenance schedulesCreating maintenance schedules

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Forecasting at Tupperware

Via forecasting, managers make important Via forecasting, managers make important decisionsdecisions

Each of 50 profit centers around the world is Each of 50 profit centers around the world is responsible for computerized monthly, quarterly, responsible for computerized monthly, quarterly, and 12-month sales projectionsand 12-month sales projections

These projections are aggregated by product These projections are aggregated by product family and region, then globally, at Tupperware’s family and region, then globally, at Tupperware’s World HeadquartersWorld Headquarters

Tupperware uses all techniques discussed in textTupperware uses all techniques discussed in text

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Successful Forecasting = Science + Art

"Science" implies that the body of the forecasting "Science" implies that the body of the forecasting knowledge lies on the solid ground of quantitative knowledge lies on the solid ground of quantitative forecasting methods and their correct utilization for forecasting methods and their correct utilization for various business situations.various business situations.

"Art" represents a combination of a decision maker's "Art" represents a combination of a decision maker's experience, logic, and intuition to supplement the experience, logic, and intuition to supplement the forecasting quantitative analysis.forecasting quantitative analysis.

Both the science and art of forecasting are essential Both the science and art of forecasting are essential in developing accurate forecasts. in developing accurate forecasts.

All managers are forecasters!All managers are forecasters!

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Forecast Categories

TYPESTYPESQualitativeQualitative Executive opinionsExecutive opinions

Sales force surveysSales force surveysDelphi methodDelphi methodConsumer surveysConsumer surveys

Quantitative Quantitative Times series methods Times series methods Associative (causal) Associative (causal) methodsmethods

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For Tupperware’s Strategic Decisions - Forecast by Consensus

Although inputs come from sales, marketing, finance, and production, final forecasts are the consensus of all participating managers.

The final step is Tupperware’s version of the “jury of executive opinion”

Use quantitative models to examine data and use qualitative methods to converge results

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Forecast Categories

TIME HORIZONTIME HORIZONLong-termLong-term For duration of 3-5 For duration of 3-5

years or more (on years or more (on annual basis)annual basis)

Medium-termMedium-term For duration of up to three For duration of up to three years (usually on quarterly years (usually on quarterly or monthly basis)or monthly basis)

Short-termShort-term Up to one year, usually less Up to one year, usually less than three months (on than three months (on daily, weekly)daily, weekly)

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Facts in Forecasting

Main assumption: Past pattern repeats itself into the future.

Forecasts are rarely perfect: Don't expect forecasts to be exactly equal to the actual data.

The science and art of forecasting try to minimize, but not to eliminate, forecast errors. Forecast errors mean the difference between actual and forecasted values.

Forecasts for a group of products are usually more accurate than these for individual products; a shorter period tend to be more accurate.

Computer and IT are critical parts of the modern forecasting in large corporations.

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Seven Steps in Forecasting (Demands)

Determine the use of the forecastDetermine the use of the forecast Select the items to be forecastSelect the items to be forecast Determine the time horizon of the forecastDetermine the time horizon of the forecast Select the forecasting model(s)Select the forecasting model(s) Gather the dataGather the data Make the forecastMake the forecast Validate and implement resultsValidate and implement results

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Quantitative Methods

A time series is an uninterrupted set of data A time series is an uninterrupted set of data observations that have been ordered in observations that have been ordered in equally spaced intervals (units of time).equally spaced intervals (units of time).

Associative (causal) forecasting is based on Associative (causal) forecasting is based on identification of variables (factors) that can identification of variables (factors) that can predict values of the variable in question.predict values of the variable in question.

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Quantitative Forecasting Models

·· Time Series ModelsTime Series Models

Naive ForecastNaive Forecast

Simple Moving AveragesSimple Moving Averages

Weighted Moving AveragesWeighted Moving Averages

Simple Exponential SmoothingSimple Exponential Smoothing

Exponential Smoothing with Exponential Smoothing with TrendTrend

Linear Trend ProjectionLinear Trend Projection

Time Series DecompositionTime Series Decomposition

·· Associative (Causal) Associative (Causal) ModelsModels

Simple Linear RegressionSimple Linear Regression

Multiple Linear Regression Multiple Linear Regression

Nonlinear Regression Nonlinear Regression

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Time Series Pattern: Stationary

The result of many The result of many influences that act influences that act independently so as to independently so as to yield nonsystematic yield nonsystematic and non-repeating and non-repeating patterns about some patterns about some average value. average value.

Forecasting methods: Forecasting methods: naive, moving average, naive, moving average, exponential smoothingexponential smoothing

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Time Series Pattern: Trend

It represents a general It represents a general increase or decrease in increase or decrease in a time series over a time series over several consecutive several consecutive periods (some sources periods (some sources present six-seven or present six-seven or more periods). more periods).

Forecasting methods: Forecasting methods: linear trend projection, linear trend projection, exponential smoothing exponential smoothing with trend, etc.with trend, etc.

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Time Series Pattern: Seasonal

Seasonal Patterns Seasonal Patterns represent patterns that represent patterns that are periodic and are periodic and recurrent (usually on a recurrent (usually on a quarterly, monthly, or quarterly, monthly, or annual basis).annual basis).

Forecasting methods: Forecasting methods: exponential smoothing exponential smoothing with trend and with trend and seasonality, time series seasonality, time series decomposition, etc.decomposition, etc.

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Time Series Pattern: Cyclical

The result of economic and The result of economic and business expansions (increasing business expansions (increasing demand) and contractions demand) and contractions (recessions and depressions) (recessions and depressions) and usually repeat every two-and usually repeat every two-five years. Cyclical influences five years. Cyclical influences are difficult to forecast because are difficult to forecast because cyclical demands are recurrent cyclical demands are recurrent but not periodic (they happen in but not periodic (they happen in different intervals of time with different intervals of time with great variability of demands).great variability of demands).

Forecasting methods: time Forecasting methods: time series decomposition, multiple series decomposition, multiple regressionregression

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Product Demand Charted over 4 Years with Trend and Seasonality

Year1

Year2

Year3

Year4

Seasonal peaks Trend component

Actual demand line

Average demand over four years

Dem

and

for p

rodu

ct o

r ser

vice

Random variation

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Overview of Quantitative Approaches

Naïve approachNaïve approach Moving averagesMoving averages Exponential smoothingExponential smoothing Trend projectionTrend projection

Linear regressionLinear regression

Time-series Models

Associative models

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Set of evenly spaced numerical dataSet of evenly spaced numerical data Obtained by observing response variable at Obtained by observing response variable at

regular time periodsregular time periods Forecast based only on past valuesForecast based only on past values

Assumes that factors influencing past and Assumes that factors influencing past and present will continue influence in futurepresent will continue influence in future

ExampleExampleYear:Year: 19931993 19941994 19951995 19961996 19971997Sales:Sales: 78.778.7 63.563.5 89.789.7 93.293.2 92.192.1

What is a Time Series?

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Naïve Approach

Assumes demand in next period is the same as Assumes demand in next period is the same as demand in most recent perioddemand in most recent period

e.g., If May sales were 48, then June sales will be e.g., If May sales were 48, then June sales will be around 48around 48

Sometimes it is effective & cost efficientSometimes it is effective & cost efficient

e.g. when the demand is steady or changes slowlye.g. when the demand is steady or changes slowly

when inventory cost is low when inventory cost is low

when unmet demand will not losewhen unmet demand will not lose

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

Used if little or no trend, seasonal, and cyclical Used if little or no trend, seasonal, and cyclical patternspatterns

Used oftenUsed often for smoothingfor smoothing Provides overall impression of data over timeProvides overall impression of data over time

EquationEquation

MAMAnn

nn Demand inDemand in PreviousPrevious PeriodsPeriods

Moving Average Method

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You’re manager of a museum store that sells You’re manager of a museum store that sells historical replicas. You want to forecast sales of historical replicas. You want to forecast sales of item (123) for item (123) for 20002000 using a using a 33-period moving -period moving average.average.

19951995 441996 1996 6619971997 5519981998 3319991999 77

© 1995 Corel Corp.

Moving Average Example

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Moving Average Solution

Time ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1995 4 NA NA1996 6 NA NA1997 5 NA NA1998 3 4+6+5=15 15/3 = 51999 72000 NA

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Moving Average Solution

Time ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1995 4 NA NA1996 6 NA NA1997 5 NA NA1998 3 4+6+5=15 15/3 = 51999 7 6+5+3=14 14/3=4 2/32000 NA

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Moving Average Solution

Time ResponseYi

MovingTotal(n=3)

MovingAverage

(n=3)1995 4 NA NA1996 6 NA NA1997 5 NA NA1998 3 4+6+5=15 15/3=5.01999 7 6+5+3=14 14/3=4.72000 NA 5+3+7=15 15/3=5.0

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95 96 97 98 99 00Year

Sales

2

4

6

8 Actual

Forecast

Moving Average Graph

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

Weights based on intuitionWeights based on intuitionOften lay between 0 & 1, & sum to 1.0Often lay between 0 & 1, & sum to 1.0

EquationEquation

WMA =WMA =ΣΣ(Weight for period (Weight for period nn) (Demand in period ) (Demand in period nn))

ΣΣWeightsWeights

Weighted Moving Average Method

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Actual Demand, Moving Average, Weighted Moving Average

0

5

10

15

20

25

30

35

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

Sal

es D

eman

d

Actual sales

Moving average

Weighted moving average

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Increasing Increasing nn makes forecast less sensitive makes forecast less sensitive to changesto changes

Do not forecast trend well due to the delay Do not forecast trend well due to the delay between actual outcome and forecastbetween actual outcome and forecast

Difficult to trace seasonal and cyclical Difficult to trace seasonal and cyclical patternspatterns

Require much historical dataRequire much historical data Weighted MA may perform betterWeighted MA may perform better

Disadvantages of Moving Average Methods

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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 dataInvolves little record keeping of past data

Exponential Smoothing Method

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FFtt = = FFtt-1-1 + + ((AAtt-1-1 - - FFtt-1-1))

= = AAtt-1-1 + (1 - + (1 - ) ) FFtt-1-1

FFtt = Forecast value = Forecast value AAtt = Actual value = Actual value = Smoothing constant= Smoothing constant

FFtt = = AAt t - 1 - 1 + + (1-(1-))AAt t - 2- 2 + + (1- (1- ))22·A·At t - 3- 3

+ + (1- (1- ))33AAt t - 4- 4 + ... + + ... + (1- (1- ))t-t-11·A·A00

Use for computing forecastUse for computing forecast

Exponential Smoothing Equations

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You’re organizing a Kwanza meeting. You You’re organizing a Kwanza meeting. You want to forecast attendance for want to forecast attendance for 20002000 using using

exponential smoothing (exponential smoothing ( = .10 = .10). The 1995 ). The 1995 (made in 1994) forecast was (made in 1994) forecast was 175175..Actual data:Actual data:

19951995 1801801996 1996 16816819971997 15915919981998 17517519991999 190190 © 1995 Corel Corp.

Exponential Smoothing Example

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Ft = Ft-1 + ·( At-1 - Ft-1)

TimeTime ActualForecast, F t

(αα = = .10.10))

19951995 180 175.00 (Given)

19961996 168168

19971997 159159

19981998 175175

19991999 190190

20002000 NANA

175.00 +175.00 +

Exponential Smoothing Solution

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Exponential Smoothing Solution

TimeTime ActualForecast, F t

(αα = = .10.10))

19951995 180180 175.00 (Given)175.00 (Given)

19961996 168168 175.00 + 175.00 + .10.10((

19971997 159159

19981998 175175

19991999 190190

20002000 NANA

Ft = Ft-1 + ·( At-1 - Ft-1)

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Exponential Smoothing Solution

TimeTime ActualActualForecast, Forecast, FFtt

((αα = = .10.10))

19951995 180180 175.00 (Given)175.00 (Given)

19961996 168168 175.00 + 175.00 + .10.10(180(180 - -

19971997 159159

19981998 175175

19991999 190190

20002000 NANA

Ft = Ft-1 + ·( At-1 - Ft-1)

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Exponential Smoothing Solution

Time ActualForecast, Ft

(αα = = .10.10))

19951995 180180 175.00 (Given)175.00 (Given)

19961996 168168 175.00 + 175.00 + .10.10(180(180 - 175.00 - 175.00))

19971997 159159

19981998 175175

19991999 190190

20002000 NANA

Ft = Ft-1 + ·( At-1 - Ft-1)

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Exponential Smoothing Solution

TimeTime ActualActualForecast, Forecast, FFtt

((αα = = .10.10))

19951995 180180 175.00 (Given)175.00 (Given)

19961996 168168 175.00 +175.00 + .10.10(180 (180 - 175.00- 175.00)) = 175.50 = 175.50

19971997 159159

19981998 175175

19991999 190190

20002000 NANA

Ft = Ft-1 + ·( At-1 - Ft-1)

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Exponential Smoothing Solution

Time ActualForecast, F t

(αα = = .10.10))

1995 180 175.00 (Given)

19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50

19971997 159159 175.50175.50 ++ .10.10(168 -(168 - 175.50175.50)) = 174.75= 174.75

19981998 175175

19991999 190190

20002000 NANA

Ft = Ft-1 + ·( At-1 - Ft-1)

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Exponential Smoothing Solution

Time ActualForecast, F t

(α = .10)

19951995 180180 175.00 (Given)175.00 (Given)

1996 168 175.00 + .10(180 - 175.00) = 175.50

19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75

19981998 175175

19991999 190190

20002000 NANA

174.75174.75 ++ .10.10(159(159 - - 174.75174.75))= 173.18= 173.18

Ft = Ft-1 + ·( At-1 - Ft-1)

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Exponential Smoothing Solution

Time ActualForecast, F t

(α = .10)

1995 180 175.00 (Given)

19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50

19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75

19981998 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18

19991999 190190 173.18 +173.18 + .10.10(175(175 - 173.18- 173.18)) = 173.36= 173.36

20002000 NANA

Ft = Ft-1 + ·( At-1 - Ft-1)

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Exponential Smoothing Solution

Time ActualForecast, F t

(α = .10)

19951995 180180 175.00 (Given)175.00 (Given)

19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50

19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75

19981998 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18

19991999 190190 173.18 + .10(175 - 173.18) = 173.36173.18 + .10(175 - 173.18) = 173.36

20002000 NANA 173.36173.36 + + .10.10(190(190 - 173.36- 173.36) = 175.02) = 175.02

Ft = Ft-1 + ·( At-1 - Ft-1)

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Year

Sales

140150160170180190

93 94 95 96 97 98

Actual

Forecast

Exponential Smoothing Graph

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Ft = At - 1 + (1- )At - 2 + (1- )2At - 3 + ...

Forecast Effects of Smoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10%

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Ft = At - 1 + (1- ) At - 2 + (1- )2At - 3 + ...

Forecast Effects of Smoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9%

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Ft = At - 1 + (1- )At - 2 + (1- )2At - 3 + ...

Forecast Effects of Smoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9% 8.1%

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Ft = At - 1 + (1- )At - 2 + (1- )2At - 3 + ...

Forecast Effects of Smoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9% 8.1%

90%

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Ft = At - 1 + (1- ) At - 2 + (1- )2At - 3 + ...

Forecast Effects of Smoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9% 8.1%

90% 9%

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Ft = At - 1 + (1- ) At - 2 + (1- )2At - 3 + ...

Forecast Effects of Smoothing Constant

Weights

Prior Period

2 periods ago

(1 - )

3 periods ago

(1 - )2

=

= 0.10

= 0.90

10% 9% 8.1%

90% 9% 0.9%

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You want to achieve:You want to achieve: Smallest forecast errorSmallest forecast error

Mean square error (MSE)Mean square error (MSE) Mean absolute deviation (MAD)Mean absolute deviation (MAD)

No pattern or direction in forecast No pattern or direction in forecast errorerror Error = (Error = (YYii - - YYii) = (Actual - Forecast)) = (Actual - Forecast)

Seen in plots of errors over timeSeen in plots of errors over time

Guidelines for Selecting Forecasting Model

^

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How to Choose

Seek to minimize the Mean Absolute Deviation (MAD)

If: Forecast error = demand - forecast

Then:n

errorsforecast MAD

Note that the sum of all weights in exponential smoothing equals to 1. It is popular because of the simplicity of data keeping.

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Measuring Forecast Accuracy

Mean Squared Error (MSE) Mean Squared Error (MSE)

represents the variance of errors in a forecast. This criterion represents the variance of errors in a forecast. This criterion is most useful if you want to minimize the occurrence of a is most useful if you want to minimize the occurrence of a major error(s).major error(s).

n

e =

n

)2Ft - At(n

1=t = MSE

2t

n

1=t

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Exponential Smoothing with Trend Adjustment

Forecast including trend (FITt)

= exponentially smoothed forecast (Ft)

+ exponentially smoothed trend (Tt)

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Ft = (Actual demand this period)

+ (1- )(Forecast last period+Trend estimate last period)

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

or

Tt = (Forecast this period - Forecast last period)

+ (1-)(Trend estimate last period

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

Exponential Smoothing with Trend Adjustment - continued

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FFtt = exponentially smoothed forecast of the = exponentially smoothed forecast of the data series in period data series in period tt

TTtt = exponentially smoothed trend in period = exponentially smoothed trend in period tt

AAtt = actual demand in period = actual demand in period tt

= smoothing constant for the average= smoothing constant for the average = smoothing constant for the trend= smoothing constant for the trend

Exponential Smoothing with Trend Adjustment - continued

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Comparison of Forecasts

0

5

10

15

20

25

30

35

40

Jan Feb Mar Apr May Jun Jul Aug Sep

Month

Pro

du

ct D

eman

d

Actual Demand

Exponential smoothing

Exponential smoothing + Trend

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Used for forecasting linear trend lineUsed for forecasting linear trend line Assumes relationship between response Assumes relationship between response

variable, variable, Y, Y, and time, and time, X, X, is a linear is a linear functionfunction

Estimated by least squares methodEstimated by least squares method Minimizes sum of squared errorsMinimizes sum of squared errors

iY a bX i

Linear Trend Projection

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Y a bXi i b > 0

b < 0

a

a

Y

Time, X

Linear Trend Projection Model

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Slope (Slope (bb)) Estimated Estimated YY changes by changes by bb for each 1 unit increase for each 1 unit increase

in in XX If If bb = 2, then sales ( = 2, then sales (YY) is expected to increase ) is expected to increase

by 2 for each 1 unit increase in advertising (by 2 for each 1 unit increase in advertising (XX)) Y-intercept (Y-intercept (aa))

Average value of Average value of YY when when XX = 0 = 0 If If aa = 4, then average sales ( = 4, then average sales (YY) is expected to ) is expected to

be 4 when advertising (be 4 when advertising (XX) is 0) is 0

Interpretation of Coefficients

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How to Find a and b: Least Squares Equations

Equation:ii bxaY

Slope:

xnx

yxnyxb

i

n

i

ii

n

i

Y-Intercept: xbya

Criteria of finding a and b:

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Defining Forecast Accuracy

Accuracy is usually measured in forecasting by the Accuracy is usually measured in forecasting by the value of its adverse characteristic--forecast error.value of its adverse characteristic--forecast error.

Forecast error or residual is the difference between Forecast error or residual is the difference between actual and forecasted values in the same period. actual and forecasted values in the same period.

The smaller the forecast error, the closer the The smaller the forecast error, the closer the forecasted value to the actual value and the more forecasted value to the actual value and the more accurate the forecast.accurate the forecast.

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Measuring Forecast Accuracy

Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)measures the average absolute error of a forecast. A sign of measures the average absolute error of a forecast. A sign of an error, which represents over- or underestimation, is really an error, which represents over- or underestimation, is really not important in most cases; we are rather concerned with not important in most cases; we are rather concerned with the value of deviation.the value of deviation.

where:where:AAt t = actual value in period t,= actual value in period t,

FFt t = forecasted value in period t,= forecasted value in period t,

eett = forecast error in period t, = forecast error in period t,

n = number of periods.n = number of periods.

n

|e| =

n

|F - A| = MAD

t

n

1=ttt

n

1=t

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Measuring Forecast Accuracy

Mean Squared Error (MSE) Mean Squared Error (MSE)

represents the variance of errors in a forecast. This criterion represents the variance of errors in a forecast. This criterion is most useful if you want to minimize the occurrence of a is most useful if you want to minimize the occurrence of a major error(s).major error(s).

n

e =

n

)2Ft - At(n

1=t = MSE

2t

n

1=t

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Include seasonal and cyclical patternsInclude seasonal and cyclical patterns In decomposition, a time series is described as a function of In decomposition, a time series is described as a function of

four components:four components:Y = T*C*S*I Y = T*C*S*I multiplicative model (commonly used)multiplicative model (commonly used)Y = T+C+S+IY = T+C+S+I additive modeladditive modelwhere: where: Y =Y = actual value of time seriesactual value of time seriesT =T = trend componenttrend componentC =C = cyclical component cyclical component S =S = seasonal componentseasonal componentI = I = irregular (random) component irregular (random) component

General Description of TS Models: Time Series Decomposition

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General Description of TS Models: Time Series Decomposition

The goal of the time series decomposition method is The goal of the time series decomposition method is to identify the values of components of a time series to identify the values of components of a time series (trend, cyclical, seasonal, irregular), and use these (trend, cyclical, seasonal, irregular), and use these components for forecasting–re-composition of the components for forecasting–re-composition of the model.model.

In multiplicative model, the trend component is In multiplicative model, the trend component is measured in the same units as these for the relevant measured in the same units as these for the relevant time series. The cyclical, seasonal, and irregular time series. The cyclical, seasonal, and irregular components are represented by respective indexescomponents are represented by respective indexes

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Multiplicative Seasonal Model

Find Find average historical demandaverage historical demand for each for each “season”“season” by summing the demand for by summing the demand for that season in each year, and dividing by that season in each year, and dividing by the number of years for which you have the number of years for which you have data.data.

Compute the Compute the average demand over all average demand over all seasonsseasons by dividing the total average by dividing the total average annual demand by the number of seasons.annual demand by the number of seasons.

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Multiplicative Seasonal Model

Compute a Compute a seasonal indexseasonal index by dividing by dividing that season’s historical demand (from that season’s historical demand (from step 1) by the average demand over all step 1) by the average demand over all seasons.seasons.

Estimate next year’s total demand by Estimate next year’s total demand by using smoothed linear trend projection using smoothed linear trend projection modelmodel

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

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Example of Multiplicative Seasonal ModelThe following trend projection is used to predict quarterly demand: Y = 350 - 2.5t, where t = 1 in the first quarter of 1998. Seasonal (quarterly) relatives are Quarter 1 = 1.5; Quarter 2 = 0.8; Quarter 3 = 1.1; and Quarter 4 = 0.6. What is the seasonally adjusted forecast for the four quarters of 2000? (10%)

Period Projection Adjusted

9 327.5 491.25

10 325 260

11 322.5 354.75

12 320 192

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Seven Steps in Forecasting (Demands)

Determine the use of the forecastDetermine the use of the forecast Select the items to be forecastSelect the items to be forecast Determine the time horizon of the forecastDetermine the time horizon of the forecast Select the forecasting model(s)Select the forecasting model(s) Gather the dataGather the data Make the forecastMake the forecast Validate and implement resultsValidate and implement results

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Past Data of Nurse Demand: What patterns can be observed?

0

5

10

15

20

1 3 5 7 9

11Time Period

Nu

mb

er o

f Nu

rses

Number ofNurses

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Forecasting Issues During a Product’s Life

Introduction Growth Maturity Decline

Standardization

Less rapid product changes - more minor changes

Optimum capacity

Increasing stability of process

Long production runs

Product improvement and cost cutting

Little product differentiation

Cost minimization

Over capacity in the industry

Prune line to eliminate items not returning good margin

Reduce capacity

Forecasting critical

Product and process reliability

Competitive product improvements and options

Increase capacity

Shift toward product focused

Enhance distribution

Product design and development critical

Frequent product and process design changes

Short production runs

High production costs

Limited models

Attention to quality

Best period to increase market share

R&D product engineering critical

Practical to change price or quality image

Strengthen niche

Cost control critical

Poor time to change image, price, or qualityCompetitive costs become critical

Defend market position

OM

Str

ateg

y/Is

sues

Com

pany

Str

ateg

y/Is

sues

HDTV

CD-ROM

Color copiers

Drive-thru restaurants Fax machines

Station wagons

Sales

3 1/2” Floppy disks

Internet

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Measures how well the forecast is predicting Measures how well the forecast is predicting actual valuesactual 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

Should be within upper and lower control Should be within upper and lower control limitslimits

Tracking Signal

MAD

errorforecast ˆ

1

MAD

yy

MAD

RSFETS

n

iii

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Plot of a Tracking Signal

Time

Lower control limit

Upper control limit

Signal exceeded limit

Tracking signal

Acceptable range

MAD

+

0

-

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Time (Years)

Error

0

Desired Pattern

Time (Years)

Error

0

Trend Not Fully Accounted for

Pattern of Forecast Error: Identified Only by Observation

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Predicting Cyclical Factors

Leading indicators Leading indicators Investment (public/private)Investment (public/private) ExportExport Business purchasingBusiness purchasing Consumer confidenceConsumer confidence Government expendingGovernment expending

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Advanced Forecasting Methods

To improve the accuracy, more complicated models To improve the accuracy, more complicated models might be required. For example, might be required. For example, Adaptive smoothingAdaptive smoothing Focus forecastingFocus forecasting

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Application in Wholesale/Retail Sectors

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Applications in Marketing

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Applications in Finance and Accounting

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Seven Steps in Forecasting

Determine the use of the forecastDetermine the use of the forecast Select the items to be forecast (e.g. type of nurse)Select the items to be forecast (e.g. type of nurse) Determine the time horizon of the forecast (why Determine the time horizon of the forecast (why

quarterly)quarterly) Select the forecasting models (among both Select the forecasting models (among both

qualitative and quantitative)qualitative and quantitative) Gather the dataGather the data Make the forecastMake the forecast Validate and implement resultsValidate and implement results

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Assignment: Forecasting inventory and Warehouse Expansion

May apply any material you have learned May apply any material you have learned about forecastingabout forecasting

Please answer ALL questions in a clear Please answer ALL questions in a clear formatformat

It is not necessary to print out the detailed It is not necessary to print out the detailed result form POMresult form POM

It is desirable to describe and justify your It is desirable to describe and justify your decisions in a precise and concise way (e.g. decisions in a precise and concise way (e.g. using charts or figures)using charts or figures)