ch03- s3 - forecasting.pdf

7/23/2019 CH03- S3 - Forecasting.pdf

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Operations ManagementOperations Management

Chapter 3Chapter 3

Demand ForecastingDemand Forecasting


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OutlineOutline

Where do we use forecasts

Operations Management : Why do we need forecasts Forecastsdefinition

Forecasting process Forecasting needs identification

Horizon, period, aggregation level

Data selection

Forecasting method choice

Make the forecast

Forecasts errors analysis

2 Dr. Ali Cheaitou - 2013


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OutlineOutline





Data selection


Make the forecast




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ForecastForecast

Forecast a statement about the future value

of a variable of interest Forecasts are an important element in making

informed decisions

e ma e orecas s a ou suc ngs as wea er,demand, and resource availability



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Where do we use Forecasts?Where do we use Forecasts?

Weather

Bettin on Racin

Stock Market

Operations Management and SC



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Two Important Aspects of ForecastsTwo Important Aspects of Forecasts

Expected level of demand

The level of demand may be a function of somestructural variation such as trend or seasonalvariation

Related to the potential size of forecast error



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OutlineOutline





Data selection Forecasting method choice

Make the forecast




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Operations Management: Why do weOperations Management: Why do we

need forecastsneed forecasts

DistributionDecisions

Distribution

Decisions

Assembling

DecisionsManufacturing

Decisions

AssemblingDecisions

TransportDecision

Replenishment

Decisions

ManufacturingDecisions

Man 6

Ass 2

Ass 3

Ass 1Man 1

Man 2 Man 4

Man 3 Man 5

Transp

TranspSuppliers

Demand

Lead times



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Why to Forecast in Operations?Why to Forecast in Operations?

Supply Chain is in continuous change:

Customers habits change Introduction of a new product

Need to anticipate and to make decisions inadvance in order to optimize the supply chain

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Customer DemandCustomer Demand

Forecasting demand for finished goods or services isthe starting point for all operating activities in a

Logistics System



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Example 1

Strategic selection of raw material supplier and of a3PL (third-party logistics provider) associated withthe production and distribution of a finished goodover several years

e s ou ave, over t s p ann ng or zon an eaabout the demand:

To ensure that the suppliers have adequatecapacities

To be able to negotiate prices



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Example 2

Materials flow management of FMCG (Fast Moving Consumer

Goods) Customers need to be delivered with very short lead times

Retailer (supermarket) needs to:

The manufacturer needs to:

have raw material supplies

produce a part or the totality of its production

before receiving the customers orders.

A need to have an idea about future demand



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Production plans

Personnel needs: full time, part time, contractual

Capacity levels: equipment, machines, buildings

urc ase requ remen s: raw ma er a s, componen s,services;

Plans for subcontractor requirements

Transport requirements: raw materials, finished

goods and/or personnel



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OutlineOutline






Make the forecast




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Optimistic ForecastOptimistic Forecast

Company estimates sales of

6 million product unitsfor a particular year, but only sells

4.5 million.

What effect may this have on the business ? Excessive inventory of finished product

Associated high storage costs

Inventory becomes obsolescent Finished product must be sold at a loss

Plant capacity is used unnecessarily



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Pessimistic ForecastPessimistic Forecast

Company estimates that it will sell

6 million of its product units

for a particular year

Orders are received for 7.5 million.

Results in inadequate stock (finsihed products) and lostorders poor customer relationships Insufficient raw material stops production

Excessive costs due to subcontracting Excessive costs due to overtime/ to hiring of part time labour



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Is it better to be Optimistic or Pessimistic?

Pessimistic versus OptimisticPessimistic versus Optimistic



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Pessimistic versus OptimisticPessimistic versus Optimistic

It is considered better to be Optimistic rather than

Pessimistic when forecasting.

Pessimistic forecasts result in:

oss o cus omers ue o na y o or ers

demotivating effects on the staff (stress / moreproductive)

high costs idle production line/labor due to

insufficient raw material



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Features Common to All ForecastsFeatures Common to All Forecasts

1. Techniques assume some underlying causal systemthat existed in the past will persist into the future

2. Forecasts are not perfect

3. Forecasts for groups of items are more accurate thanthose for individual items

4. Forecast accuracy decreases as the forecastinghorizon increases



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Elements of a Good ForecastElements of a Good Forecast

The forecast

should be timely should be accurate

should be reliable

s ou e expresse n mean ng u un s

should be in writing

technique should be simple to understand and use

should be cost effective



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Forecast Accuracy and ControlForecast Accuracy and Control

Forecasters want to minimize forecast errors

It is nearly impossible to correctly forecast real-worldvariable values on a regular basis

So, it is important to provide an indication of the

value of the variable that actually occurs

Forecast accuracy should be an importantforecasting technique selection criterion

Error = Actual Forecast

If errors fall beyond acceptable bounds, correctiveaction may be necessary



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Forecast Accuracy MetricsForecast Accuracy Metrics

n = tt ForecastActualMAD MAD weights all errors evenly

n

=

100Actual

ForecastActual

MAPE t

tt

( )2tt1

ForecastActualMSE

=

n

MSE weights errors according to theirsquared values

MAPE weights errors according to

relative error

23

Dr. Ali Cheaitou - 2013


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PeriodActual

(A)

Forecast

(F)

(A-F)Error |Error| Error2 [|Error|/Actual]x100

1 107 110 -3 3 9 2.80%

2 125 121 4 4 16 3.20%

3 115 112 3 3 9 2.61%

Forecast Error CalculationForecast Error Calculation

4 118 120 -2 2 4 1.69%

5 108 109 1 1 1 0.93%

Sum 13 39 11.23%

n = 5 n-1 = 4 n = 5

MAD MSE MAPE

= 2.6 = 9.75 = 2.25%



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OutlineOutline






Make the forecast




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Forecasting ProcessForecasting Process

The forecasting process objective is to determine:

Future average value of a variable (demand, )

Forecast accuracy (variability, measure of the difference between the average

value and the different possible real values)

Forecasting errors (high standard deviation) deteriorate theSupply Chain performance

xamp e : sa es o

with heat wave during summer

without heat wave during summer

Forecasting process should be improved in order to reduce theforecasts errors

In the decision process, one must take into account the averagevalue and the error estimation

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Forecasting Process: Forecasts definitionForecasting Process: Forecasts definition

Three possible configurations:

Forecasts users :salesman, producer, distributer,

Forecasts experts (statistician)

Forecasts committee: Users (marketing, sales): information collection, forecasts use

Experts : models, statistical methods,

Marketing Forecasts Sales Forecasts

Statistical forecasts

Forecasts Committee

Final forecasts

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Six steps forecasting process:

Forecasting needs identification

Horizon, period, aggregation level Data selection

Demand history (not sales history)

romot ona campa gn,

Information Systems

Collaborative forecasts


Make the forecast


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Horizon, period, aggregation level Data selection


romot ona campa gn,

Information Systems



Make the forecast


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Forecasting Process:Forecasting Process:Forecasting MethodsForecasting Methods

Qualitative methods

Based on experience, judgment, knowledge

E.g. Expert Judgement, Data gathering methods, etc..

Quantitative methods

Based on data, statistics

E.g. Causal methods, Extrapolative methods (timeseries)

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F i PF i P


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Qualitative methods




Based on data, statistics

E.g. Causal methods, Extrapolative methods

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F ti PF ti P


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Qualitative methods

When do we use Judgemental Methods

When little information about sales history is available.

This ha ens for exam le when the com an is launchin

a new product, and needs to know the likely demand

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F ti PF ti P


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Qualitative methods

Expert Judgement

It is normal to start by asking someone who is an expert in thearea to make an estimation which may be subjective not based on a quantitative models


33


F ti PF ti P


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Qualitative methods

Help can be provided to the expert as additional information, this canbe done using different Data Gathering methods

Market Research:

Assess the demand for a new product by survey


Historical Comparisons:

Review available information about similar products or processes

Scenario Analysis:

In case of judgemental forecasting associated with uncertainty:

consider and analyse the range of all possible outcomes

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Forecasting Process:Forecasting Process:


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Qualitative methods

Disadvantages

Very numerous demands to be forecast very high workload

Many factors could disrupt the forecaster (being in a bad or good

Difficulty in determining the forecast errors (due to the difficulty indetermining the knowledge degree of the expert)

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Qualitative methods

Improvement : Delphi method

Ask experts their opinion by anonymous forms and separately (inorder to avoid the inter-influence between experts)

First statistical results (based on first answers) are sent to newexper s

The new experts formulate their own forecasts:

knowing the first results

must justify their choice if it is very different from the first one

By iteration

either Consensus

or General Opinion + Some Divergence

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Qualitative methods




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Based on data, statistics E.g. Causal methods, Extrapolative methods



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Explicit mathematical models + historical data

Can be automated by computer programs Can be analyzed and improved more simply than the qualitative methods

Two sub-families

a s ca ex rapo a ve me o s : s or ca a a ynam ca evo u ons a

are extrapolated for the future periods

Causal methods (statistical regressions): historical data relationshipbetween the forecast variables(demand) and one (or different ) parameter(s).

Example: sales of mineral water and the external temperature

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Qualitative - Quantitative methods

The quantitative and qualitative methods are not exclusive of eachother.

Use a combination of different methods based on:

The existence of historical data with different natures

rs y, use e s or ca eman a a w an ex rapo a ve me o orecas

software) secondly, include in this first model the subjective opinion of the experts

concerning for example a promotional campaign




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Extrapolative methods (Time series) Long lifecycle products averaging methods (arithmetic average, movingaverage, exponential smoothing)

Long lifecycle products - Trend

-

Short lifecycle products

Causal methods (regressions)




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Extrapolative methods (Time series) Long lifecycle products averaging methods (arithmetic average, movingaverage, exponential smoothing)


-




Forecasting Approaches and MethodsForecasting Approaches and Methods


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g ppg ppTime SeriesTime Series

Time Series : series of time-ordered sequence of observations with aconstant frequency (periodicity)

Dt: demand in period t, t=1,2,, T

DT

D

(mean of D)

D(standard deviation)

Time Series Forecasts: Forecasts that project patterns identified inrecent time-series observations, by assuming that future values of thetime-series can be estimated from past values of the time-series

T

t

D

=

=

1

T

DT

t

Dt

D

=

=1

2)(




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g ppg ppTime SeriesTime Series

D

= 5229.25

D= 3215.94

Low D data quasi constant simple forecasting process

High D (20% of D) fluctuating data difficult forecasting process



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TimeTime--SeriesSeries BehaviorsBehaviors

Trend: long term upward or downward movement in the data (related topopulation shift, changing income)

Seasonality: short term, fairly regular variations (related to calendar,events, time of the day)

economic or political changes)

Irregular variations: due to unusual circumstances (weather conditions,strikes,). Their inclusion in the series may distort overall picture. Shouldbe identified and removed.

Random variation: residual variations that remain after all otherbehaviors have been accounted for.



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TimeTime--Series BehaviorsSeries Behaviors




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ggForecasting MethodsForecasting Methods


Extrapolative methods (Time series) Long lifecycle products averaging methods (arithmetic average, moving

average, exponential smoothing)


-






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Ft: demand forecast value in period t, t=1,,T,

for 1t T Ft: simulation of the realized demand

using the forecasting modelfor T


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They do not take account of external factors but

they look at a series of past values to predictwhat will happen in the future

Extrapolative MethodsExtrapolative Methods

There are many different kinds of extrapolativemethods: Nave method (Arithmetic average) Simple Moving average

Weighted moving average Exponential smoothing




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Forecasting Approaches and MethodsForecasting Approaches and MethodsNave methodNave method

This approach assumes that:

data from the immediately preceding past can be used

to forecast needs for the next period

DT

t

Can be used with

a stable time series (historical data from period to periodshowing changes are insignificant )

Trend

TF tt

==




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Example

Given the following sales history for 5 weeks, Calculatethe forecasts sales value for week 6, using the simpleavera e method?

Forecasting Approaches and MethodsForecasting Approaches and MethodsNave methodNave method

Answer : 5230

Week 1 2 3 4 5 6

ProductSales

8996 4531 2362 4249 6012




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g ppg ppTimeTime--Series ForecastingSeries Forecasting -- AveragingAveraging

These Techniques work best when a seriestends to vary about an average Averaging techniques smooth variations in the data

They can handle step changes or gradual changesin the level of a series

Techniques1. Straight moving average2. Weighted moving average

3. Exponential smoothing



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Technique that averages a number of the mostrecent actual values in generating a forecast

Moving AverageMoving Average

1==

=

An

i

it

averagemovingin theperiodsofNumber

1periodinvalueActualaveragemovingperiodMA

periodfor timeForecast

where

1

=

=

=

=

n

tAn

tF

n

t

n

t

nt

Straight Moving AveragesStraight Moving Averages


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Historical data from the npast time periods are used to forecast futureactivity

Assume that past sales of a particular product were January12500, February 16000, March 13500, April 11500, May

14000. If n =3, then for June the forecast will be

13500 + 11500 + 14000= 13000

When June sales results are available July forecast can becalculated, based on April, May and June sales.

The choice of n should be optimized by : Calculating the error between Dt and Ft for all tT

Choosing n that minimizes this error

M value influences the forecasts values: Low n values keeps the deterministic fluctuations

High n values eliminates the random fluctuations


St i ht M i ASt i ht M i A


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Example

Using the same data as for the previous example,

calculate the forecasts sales value for week 6, usingthe moving average method, with n=4?

Answer : 4289

Week 1 2 3 4 5 6

ProductSales

8996 4531 2362 4249 6012



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Weighted Moving AveragesWeighted Moving Averages

Weighted moving average models apply

Weighting to period data.

and considers

Some periods more important than others.

with

and

TnDFt

nti

iit =

=

,1

10 i 11

=

=

n

nti

i


ExampleExample


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Assume figures for past sales of a product are as shownin the following table

From experience the following weights are applied 1=0.5 on April 2= 0.3 on March 3= 0.2 on February

a s e orecas or ay =

Sales over four month period

January 10000

February 13500

March 11500

April 14000

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ExampleExample


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The forecast for May is

(0.2 x 13500 + 0.3 x 11500 + 0.5 x 14000) = 13150

the greater is the smoothing effect.


Exponential SmoothingExponential Smoothing


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Models are developed using a single weighting or

smoothing factor, named

is between 0 and 1 but never achieves values of 0or 1

The mathematical model is Ft+1 = Dt + (1- ) Ft

F = Estimated sales (Forecast)D = Actual sales (realized Demand)

= smoothing factor



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Why is it called Exponential Smoothing ?Why is it called Exponential Smoothing ?

weight

10


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Why is it called Exponential Smoothing ?Why is it called Exponential Smoothing ?

Ft+1 = Dt + (1- ) Dt-1+ (1- )2 Dt-2 ++ (1- )

t D0

When 1 : the model increases the importance of the more

more reactive in case of change

is optimized by:

Performing a simulation over the historical data (t=1T)

Taking the value of that minimizes the difference between Dt and Ftfor all t=1T




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ExampleExample

Motor car dealer predicted sales of 23000 vehicles in

March

Actual sales were 22150

factor is 0.40

Calculate forecast sales for April


Exponential SmoothingExponential SmoothingE l C l l tiE l C l l ti


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Example CalculationExample Calculation

Forecast sales for April is

FApril = DMarch + (1- )FMarch

= 0.4x22150 + 1-0.4 x23000

= 22660 vehicles




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Forecasting MethodsForecasting Methods





-




Techniques for TrendTechniques for Trend


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Techniques for TrendTechniques for Trend

Linear trend equation

Non-linear trends


Methods for Historical DataMethods for Historical DataPresenting a Linear TrendPresenting a Linear Trend


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Presenting a Linear TrendPresenting a Linear Trend

The trend is in general a long term effect of certain parameters

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Methods for Historical DataMethods for Historical DataPresenting a Linear TrendPresenting a Linear Trend


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Presenting a Linear TrendPresenting a Linear Trend

The trend is in general a long term effect of certain parameters

Ft=a+bt

where tis the timevariable

and

aand barecalculated byminimizing the error

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Methods for Historical DataMethods for Historical DataPresenting a TrendPresenting a Trend


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To forecast future values of the demand (Ft), values of aand bareestimated based on previously acquired data Dt, t=1,T

They are calculated , such as to minimize the error

where Dt is the given historical data and Ft=a + btT

FDT

t

tt=

1

2)(

Presenting a TrendPresenting a Trend

The obtained values are given by:

and2

11

2

1 1 1

=

==

= = =

T

t

T

t

T

t

T

t

T

t

tt

ttT

DttDT

b

T

tbD

a

T

t

T

t

t = =

=1 1

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Methods for Historical DataMethods for Historical DataPresenting a TrendPresenting a Trend


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Presenting a TrendPresenting a Trend

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gg





-



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Techniques for SeasonalityTechniques for Seasonality


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Techniques for SeasonalityTechniques for Seasonality

Seasonality regularly repeating movements in seriesvalues that can be tied to recurring events

Expressed in terms of the amount that actual valuesdeviate from the average value of a series

Models of seasonality

- Seasonality is expressed as a quantity that gets added to orsubtracted from the time-series average in order toincorporate seasonality

Multiplicative

- Seasonality is expressed as a percentage of the average (ortrend) amount which is then used to multiply the value of a

series in order to incorporate seasonality

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Models of SeasonalityModels of Seasonality


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Models of SeasonalityModels of Seasonality

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Multiplicative Method for Historical DataMultiplicative Method for Historical DataPresenting a Trend and a SeasonalityPresenting a Trend and a Seasonality


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ese t g a e d a d a Seaso a tyese t g a e d a d a Seaso a ty

If the data present a seasonality, then the seasonality factor should becalculated and taken into consideration for the different seasons (highseason/low season for example).

Cycle (high + low seasons) = T periods High season = from period i to period j, then the seasonality factor Ch(high season) and Cl (low season) are given by:

The forecasts from the linear regression (trend) are then adjusted usingthese coefficient.

=

==

T

t

t

itt

h

D

DC

1

=

= +=

+

=T

t

t

t jttt

l

D

DD

C

1

1 1

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-



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Extrapolative Methods: Short LifeExtrapolative Methods: Short LifeCycle ProductsCycle Products


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Example: fashion products, PCs, CDs, books,

Innovative products

Manufacturer (retailer) must decide about the quantities to beproduced (ordered) before knowing the exact future demand

The need a realistic estimation of the forecasts error

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Short life-cycle products have an important demand variability

In general, for short life cycle products we do not have an importanthistorical data (demand)

Time series models are suitable for long life-cycle products

Solution: a combination between a good production and inventorymanagement with a partial anticipation & a short term forecasts

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Forecasting methods

A qualitative A priori forecast realized by experts, long time before the sellingseason

Error: in general around 50-100%

After observation of the first periods realized demand quantitative (extrapolative)estimation

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Extrapolative methods (Time series)

Long lifecycle products averaging methods (arithmetic average, movingaverage, exponential smoothing)


-



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Causal MethodsCausal Methods


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Causal methods are based on a known or perceived relationship betweenthe factor to be forecast and other external or internal factors

Knowledge of variables used in forecast development:

Quantity to be forecast is the dependant variable Other variables are independent

Define t, =

Ft, t>T : estimated (forecast) of the demand

Simple linear regression assumes a linear relationship exists between thedependent variable Ft, and a single independent variable zt. Therelationship may be expressed as


Ft = a + bzt

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where Dt is the given historical data and Ft=a + bztT

FDT

t

tt=

1

2)(


and2

11

2

1 1 1

=

==

= = =

T

t

t

T

t

t

T

t

T

t

T

t

tttt

zzT

DzDzT

b

T

zbD

a

T

t

T

t

tt = =

=1 1

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Data selection


romot ona campa gn,

Information Systems



Make the forecast


80


Forecasting Process:Forecasting Process:Forecasts errors analysisForecasts errors analysis


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Forecasting models :

Should fit the real world scenario as closely as possible

Do not provide perfect predictions

A model with wide discrepancies is invalid and should be revised orcompletely rebuilt from start

An error analysis permits to measure the forecasting process performance

improve (if necessary) the whole (or a part) of the forecasting process

To test model accuracy apply

Mean Absolute Deviation (MAD)

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Mean Absolute DeviationMean Absolute Deviation(MAD)(MAD)


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MAD is derived from the absolute deviation

This is the absolute (positive) value of the forecast error

Forecast error: the difference between actual value Dtand forecast value Ft in the same time period

Absolute deviation = |Dt-Ft|

Mean absolute deviation (MAD) =

For each developed model MAD is calculated. The modelwith lowest MAD value should be the preferred model.

T

FDT

t

tt=

1

82


Forecasting Approaches and MethodsForecasting Approaches and MethodsError measurementError measurement


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Other measurements can be used to estimate the forecast error:

Simple difference: et=Dt-Ft

Mean (algebraic) error

( )FDT

t

tt=

1

Mean squared error (deviation)

T

FDT

t

tt=

1

2)(

83



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Numerical Application

84



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Causal methods are based on a known or perceived relationshipbetween the factor to be forecast and other external or internal factors

Knowledge of variables used in forecast development:

Quantity to be forecast is the dependant variable Other variables are independent

Define Dt, t=1 T : realized value of the demand

Ft, t>T : estimated (forecast) of the demand

Simple linear regression assumes a linear relationship exists between thedependent variable Ft, and a single independent variable zt. Therelationship may be expressed as

Ft = a + bzt

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where Dt is the given historical data and Ft=a + bztT

FDT

t

tt=

1

2)(


and2

11

2

1 1 1

=

==

= = =

T

t

t

T

t

t

T

t

T

t

T

t

tttt

zzT

DzDzT

b

T

zbD

a

T

t

T

t

tt = =

=1 1

87


Example of Causal MethodExample of Causal Method


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A company manufactures a successful range of products,

it wants to:

Forecast product demand for the next year, knowing that :

- Product sales are affected by the advertising budget.

- Sales and advertising budgets for 8 quarters (2 years) areshown in the following table. Product advertising/salesrelationships is shown in the following chart.

88


T bl f E l F tT bl f E l F t


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Table for Example ForecastTable for Example Forecast

Quarter Advertising

budget

Sales

1 15.0 153

2 17.5 198

Product Sales

200

250

3 12.0 147

4 8.5 104

5 9.5 131

6 12.5 159

7 14.5 1608 11.0 124

0

50

100

150

0 5 10 15 20Advertising

S

ales

89


Calculate the Sales ForecastCalculate the Sales Forecast


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The budget for advertising in quarters 9, 10,

11 and 12 is 12.0, 17.0. 20.0 and 14.0 respectively.

9,10,11 and 12 ?

90


Calculate the values forCalculate the values for

Quarters 9 10 11 & 12Quarters 9 10 11 & 12


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Quarters 9, 10, 11 & 12Quarters 9, 10, 11 & 12Quarter Advertising

budget

Sales

1 15.0 153

2 17.5 198

3 12.0 147

.

5 9.5 131

6 12.5 159

7 14.5 160

8 11.0 124

9 12.0

10 17.0

11 20.0

12 14.091


RegressionRegression


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Straight line in chart is the regression line calculated tominimise the sum of squares of the error terms, that is to

minimise

8

((Predicted sales in uarter i) (actual sales in uarter i))2

If Dt is the sales in quarter tand zt is the advertising budgetin quarter t, regression equations are used to calculate the

best fit line. The values obtained are displayed on equationin the chart.

i = 1

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Forecast: Example ChartForecast: Example Chart


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Forecast: Example ChartForecast: Example Chart

Product Sales

200

250

t= . t .

0

50

100

150

0 5 10 15 20

Advertising

Sa

les

Sales

Linear (Sales)

93


Calculation ExampleCalculation Example

Values obtained are displayed in the equation on the chart


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Values obtained are displayed in the equation, on the chart,

a = 36.74and

b = 8.78,

so that yt , the forecast sales quarter is given by

Ft = 8.7773z + 36.735.

This relationship can be used to forecast the sales in the next

four quarters on the basis of the budgeted advertising in thesequarters as follows

Quarter 9 = 8.78 x 12.0 + 36.74 = 142

Quarter 10 = 8.78 x 17.0+ 36.74 = 186 Quarter 11 = 8.78 x 20.0+ 36.74 = 211.94 Quarter 12 = 8.78 x 14.0+ 36.74 = 159.66

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Example: fashion products, PCs, CDs, books,

Innovative products

Manufacturer (retailer) must decide about the quantities to beproduced (ordered) before knowing the exact future demand

The need a realistic estimation of the forecasts error

96



Short life-cycle products have an important demand variability


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S o t e cyc e p oducts a e a po ta t de a d a ab ty

In general, for short life cycle products we do not have an importanthistorical data (demand)

Time series models are suitable for long life-cycle products

Solution: a combination between a good production and inventorymanagement with a partial anticipation & a short term forecasts

97



Forecasting methods


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g

A qualitative A priori forecast realized by experts, long time before the sellingseason

Error: in general around 50-100%

After observation of the first periods realized demand quantitative (extrapolative)estimation

98



N : number of products of the same products family


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p p y

T: periods of the product (family) life cycle

Di,t: demand of product i at period t

All products have the same demand shape

Tobs: observation horizon length (number of time periods)Tobs

: ratio of the demand during Tobs over thewhole demand of product i

: in order to get a standard criteria (valid for

all products)

=

==

T

1t

ti,

1t

ti,

obsci

D)(TF

N

Tobs==

N

1i

ci

obsc

)(F

)(TF

99



The forecast for product i over all the life cycle:


100/103

)(

D

F

Tobs

1t

ti,

1ti,

obsc

T

t TF

=

=

=

For any product of the same family: if we observe a total demand of

then the whole demand forecast (for all the life cycle) will be

)(

DobsT

1t

ti,

1

,

obsc

T

t

tiTF

F =

=

=

=

obs

T

1t

ti,D

100



Numerical application


101/103

pp

N = 3 products

Observation horizon Tobs = 2 periods

Life cycle of all the products T = 8 periods

Period Product A Product B Product C

For a product D, of the same products family as products A, B and C, if ademand of 5200 products is observed over 2 periods, what will be the totaldemand forecast over the entire life cycle (8 periods)?

2 1850 1800 1850

3 2300 2800 1950

4 2500 2250 2250

5 1200 2100 2450

6 1000 1700 2500

7 900 1300 2000

8 700 1000 1300

101





102/103

0.26811750

3150

D

D

)(TF:AProductT

1ttA,

Tobs

1t

tA,

obscA ===

=

=

DTobs

0.241

14700D

)(TF:BProductT

1t

tB,

1t

,

obscB ===

=

=

0.22416050

3600

D

D

)(TF:CProduct T

1t

tC,

Tobs

1t

tC,

obscC ===

=

=

102





103/103

244.00.2240.2410.268

3

)(F)(F)(F)(F

)(TFcCcBcA

3

1i

ci

obsc

=++

=

++

==

= obsobsobs

obs TTT

N

T

For product D, the estimated demand over the 8-period selling season is:

21311244.0

5200)(

D2

1t

tD,8

1

, ===

=

= obsct

tDTF

F

103


ch03- s3 - forecasting.pdf

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