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What is Forecasting?What is Forecasting?

Process of predicting aProcess of predicting afuture eventfuture event

Underlying basis ofUnderlying basis ofall business decisionsall business decisions ProductionProduction

InventoryInventory

PersonnelPersonnel

FacilitiesFacilities

??

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Demand Management

A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand:

Raw Materials,

Component parts,Sub-assemblies, etc.

Independent Demand:Finished Goods

15-2

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Independent Demand:

What a firm can do to manage it?

Can take an active role to influence

demand

Can take a passive role and simply

respond to demand

15-3

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

Purchasing, job scheduling, workforce levels, jobassignments, production levels

Medium-range forecast 3 months to 3 years

Sales and production planning, budgeting

Long-range forecast

3+ years New product planning, facility location, research and

development

Forecasting Time HorizonsForecasting Time Horizons

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Distinguishing DifferencesDistinguishing Differences

Medium/long range forecasts deal with more

comprehensive issues and support management

decisions regarding planning and products, plants

and processes

Short-term forecasting usually employs different

methodologies than longer-term forecasting

Short-term forecasts tend to be more accuratethan longer-term forecasts

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Types of ForecastsTypes of Forecasts

Economic forecasts

Address business cycle inflation rate, money

supply, housing starts, etc.

Technological forecasts

Predict rate of technological progress

Impacts development of new products

Demand forecasts Predict sales of existing products and services

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The RealitiesThe Realities

Forecasts are seldom perfectForecasts are seldom perfect

Most techniques assume an underlying stabilityMost techniques assume an underlying stabilityin the systemin the system

Product family and aggregated forecasts areProduct family and aggregated forecasts aremore accurate than individual product forecastsmore accurate than individual product forecasts

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Simple Moving Average

Ft = At 1 +At 2 +At 3+..Atn

n

Ft= Forecast for the coming period At 1 = Actual value in period t 1

n = Number of periods to be averaged

At 2,At 3 ,Atn Actual occurrences two periods ago ,three

periods ago and so on up to n periods ago

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JanuaryJanuary 1010

FebruaryFebruary 1212MarchMarch 1313

AprilApril 1616

MayMay 1919

JuneJune 2323

JulyJuly 2626

ActualActual 33--MonthMonthMonthMonth 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

1010

12121313

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

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Three period Moving Average

If actual demand in period 6 turns out tobe 38, the moving average forecast for

period 7 would be

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Three Period Moving Average

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Weighted Moving Average

The formula for a weighted moving average

Ft = w At 1 + w At 2+.. + wnAt n

w= weight to be given to actual occurrence for the periodt-1

w= weight to be given to actual occurrence for the

period t-2wn = weight to be given to actual occurrence for theperiod t-n

n =Total Number of Periods in the forecast .

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Weighted Moving Average

Although many periods may be ignored (that is theirweights are zero ) and the weighting scheme may be inany order (for e.g. more distant data may have greater

weights than more recent data) the sum of all theweights must be equal to 1.

Choosing Weights ---Experience and trial and error arethe simplest ways to choose weights .As a general rule,the most recent past is the most important indicator ofwhat to expect in the future and therefore it should get ahigher weighting .

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Illustration

Given the following demand data, a) Computeaweighted

averageforecastusingaweight of .40 forthemostrecent

period, .30 forthenextmostrecent, .20 forthenext,and .10

forthenext. b)If theactual demand forperiod 6 is 39,

forecast demand forperiod 7using thesameweightsasin

parta.

Period 1 2 3 4 5

Demand 42 40 43 40 41

Solution: ---

F6 =.10(40) +.20(43) +.30(40) +.40(41) = 41.0

F7 =.10(43) +.20(40) +.30(41) +.40(39) = 40.2

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Moving Average AndMoving Average AndWeighted Moving AverageWeighted Moving Average

3030

2525

2020

1515

1010

55

Salesdemand

Salesdemand

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

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

ActualActualsalessales

MovingMovingaverageaverage

WeightedWeightedmovingmovingaverageaverage

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Form of weighted moving average

Weights decline exponentially

Most recent data weighted most Requires smoothing constant (E)

Ranges from 0 to 1

Subjectively chosen

Involves little record keeping of past data

Exponential SmoothingExponential Smoothing

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Illustration

A department store may find that in a four month period the

best forecast is derived using 40percent of the actual sales

for the most recent month ,30 percent of two months ago

,20 percent of three month ago and 10 percent of four

month ago .If actual sales experience was

Month 1 Month2 Month3 Month4

100 90 105 95 ?

The forecast for month 5 would be

F5=0.40 (95)+0.30(105)+0.20(90)+.10(100)=

=38+31.5+18+10

=97.5

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Exponential dependencies.

Many processes in nature have exponential

dependencies .The decay with time of the amplitudeof a pendulum swinging in air ,the decrease in time

of the temperature of an object that is initially

warmer than its surroundings and the growth in time

of an initially small bacterial colony are all processesthat are well modelled exponential relationships .

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Y=exp(x)

.

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Exponential Smoothing -1

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

Ft =Exponentially smoothed forecast for Period t

Ft 1 =Exponentially smoothed forecast for Period t-1

= Smoothing constant ,

At 1 = Actual demand in the prior period

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Exponential Smoothing -2

The smoothing constant represents a percentage of the

forecast error.Each newforecastisequal to theprevious

forecastplusapercentage of thepreviouserror.

For example, suppose the previous forecast was 42 units,actual demand was 40 units, and =.10. The new forecast

would be computed as follows:

Ft=42+0.10(40-42)=41.8

Then,if theactual demand turns out to be 43, thenext

forecastwould be

Ft= 41.8 +0.10(43-41.8)=41.92

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Illustration

The long run demand for the product under study isrelatively stable and a smoothing constant (alpha) of 0.05 isconsidered appropriate .If the exponential method wereused as a continuing policy a forecast would have been

made for last month .Assume that last months forecast Ft 1was 1050 units .If1000 actually were demanded rather than1050 ,what would be the the forecast for this month ?

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

=1050+0.05(1000-1050)

=1050+0.05(-50)

=1047.5 units

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Exponential Smoothing -3

Higher the value of alpha ,the more closely the forecast

follows the actual .

Single exponential smoothing has the shortcoming of lagging

changes in demand .

To more closely track actual demand ,a trend factor may beadded .Adjusting the value of alpha also helps .

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Impact ofDifferent Alpha

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Forecast Accuracy

Three commonly used measures for summarizing historical

errors are;

1. The mean absolute deviation (MAD)2. The mean squared error (MSE)

3. The mean absolute percent error (MAPE).

The formulas used to compute MAD, MSE, and MAPE are asfollows:

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Common Measures ofErrorCommon Measures ofError

Mean Absolute DeviationMean Absolute Deviation ((MADMAD))

MAD =MAD = |Actual|Actual -- Forecast|Forecast|

nn

Mean Squared ErrorMean Squared Error ((MSEMSE))

MSE =MSE = ((Forecast ErrorsForecast Errors))22

nn

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Common Measures ofErrorCommon Measures ofError

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

MAPE =MAPE =100100|Actual|Actualii -- ForecastForecastii|/Actual|/Actualii

nn

nn

ii = 1= 1

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Measuring Forecast Accuracy

Mean Squared Error (MSE)

represents the variance of errors in a forecast. This criterion is

most useful if you want to minimize the occurrence of a major

error(s).

n

e

=n

)2Ft-At(n

1=t

=MSE

2t

n

1=t

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Measuring Forecast Accuracy

Mean Absolute Deviation (MAD)

measures the average absolute error of a forecast. A signof an error, which represents over- or underestimation, isreally not important in most cases; we are rather

concerned with the value of deviation.

where:

At = actual value in period t,

Ft = forecasted value in period t,

et = forecast error in period t,

n = number of periods.

n

|e|

=n

|F-A|

=MAD

t

n

1=t

tt

n

1=t

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Accuracy and Control of Forecasts

Forecast error: is the difference between the value that

occurs and the value that was predicted for a given time

period.

Error = Actual Forecast

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Illustration

Compute MAD, MSE, and MAPE for the following data,showing actual and predicted numbers of accountsserviced.

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MAD/MAPE/MSE

MSE= (e) = 76/8=9.5

n

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