topic 6 - forecasting

8/8/2019 Topic 6 - Forecasting

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OperationsManagement

Forecasting

Prof. Upendra Kachru


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Operations ManagementProf. Upendra KachruProf. Upendra Kachru

Prediction Prediction

Reflects judgment after taking all

considerations into account

Involves anticipated changes in

future that may or may not happen

Based on intuition

It can be biasedNo error analysis

Based on unique representations


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Forecasting

Forecasting

Involves the projection of the pastinto the future

Estimating the demand on the basis

of factors that generated thedemand

Based on theoretical model

It is objective

Error Analysis is possible

Results are replicable


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A forecast is an estimate of

a future event achieved by

systematically combiningand casting forward , in a

predetermined way, data

about the past.

DEFININGFORECASTING


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Forecasting vs. Prediction

Forecasting Prediction

Involves the projection of the past intothe future

Reflects managements judgment aftertaking all considerations into account

Estimating the demand on the basis of

factors that generated the demand

Involves anticipated changes in future

that may or may not generate thedemand

Based on theoretical model Based on intuition

It is objective It can be biased

Error Analysis is possible No error analysis

Results are replicable Based on unique representations


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Forecasting is the start

of any planning activity.

The main purpose of

forecasting is to estimatethe occurrence, timing or

magnitude of future

events.

WHYFORECASTING?


7/77Operations ManagementProf. Upendra KachruProf. Upendra Kachru

The Decision making Cycle

Forecasts help management take into account external

factors that impact operations and reduce the uncertainty.

The decision making cycle reflects how organizations use

forecasting to reduce the impact of market forces on abusiness.



Decision Types requiring Forecasting

Forecasting horizon in years

Specific demand

Aggregate

demand

Strategies &

facilities

Types of Decision

Short term

Long term

Planning

Medium

term


9/77Operations ManagementProf. Upendra KachruProf. Upendra Kachru9

Demand Forecasting

Demand Forecasting is theactivity of estimating the quantityof a product or service that

consumers will purchase.

Demand forecasting involvestechniques including both formal

and informal methods.

Demand forecasting may be used

in making scheduling decisions, in

assessing future capacity

requirements, or in making

decisions on whether to enter

a new market.


10/77Operations ManagementProf. Upendra KachruProf. Upendra Kachru 10

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

Types of Demand

Aggregate Planning is concerned with aggregate demandi.e. the amount of a particular economic goodor service that a consumer or group of consumers

will want to purchase (at a given price).



The firm should be able toforecast ideal levels of

inventory.The relative cost of holdingeither too much or too littleinventory might be differentfrom the ideal levels because

of poor forecasts of demand. If demand were less than

expected, the firm would incurextra inventories and the cost ofholding them.

If demand were greater than

expected, the firm would incurback-order or shortage cost andthe possible opportunity costs oflost sales or a lower volume ofactivity.

Demand and Costs



Demand Management

Do I manage demand ?

Do I live with it?

Demand management describes the process ofinfluencing the volume of consumption of the

product or service through management decision

so that firms can use their resources and

production capacity more effectively.


13/77Operations ManagementProf. Upendra KachruProf. Upendra Kachru13

Can take an active role toinfluence demand. For example,air conditioner manufacturesoffer discounts for theirproducts in winter , when

demand for the products falls. Demand management is also

used to spread demand moreevenly. Telephone companies,world over, offer discounts for

calls made during late hours orat night.

Can take a passive role andsimply respond to demand

Independent Demand

What to do?


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Eight Steps toEight Steps to

ForecastingForecasting

Determining the use of theDetermining the use of theforecast--what are theforecast--what are the

objectives?objectives?

Select the items to be forecastSelect the items to be forecast

Determine the time horizon ofDetermine the time horizon ofthe forecastthe forecast

Select the forecasting model(s)Select the forecasting model(s)

Collect the dataCollect the data

Validate the forecasting modelValidate the forecasting model Make the forecastMake the forecast

Implement the resultsImplement the results

Prof. Upendra KachruProf. Upendra Kachru



15

Quantitative

Time Series Analysis Exponential Method

Regression Analysis

Simulation/ Scenario PlanningQualitative (Judgmental)

Types of Forecasts



Time Series1. Extrapolation

2. Moving average Method

Exponential Method

1. Simple Exponential Method2. Double Exponential Method

3. Triple Exponential Method

Regression Analysis

1. Simple Regression Analysis2. Multiple Regression Analysis

QuantitativeApproach



Time Series

There are five basic patterns in which demand varieswith time that have been identified:

Horizontal Trend

Seasonal Cyclical Random



Graphical Representation

Time

Demand(units)

Constant



Moving Average Method

Where:

Ft+1

is the moving average for the period t+1,

At, A

t-1, A

t-2, A

t-3etc. are actual values for the corresponding

period, and n is the total number of periods in theaverage

Or it can be written as:

F =A + A + A +...+A

nt

t-1 t-2 t-3 t-n

The general formula for moving average is:

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

+ At-n+1 ) / n


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Simple Moving Average Problem

Week Demand

1 650

2 678

3 7204 785

5 859

6 920

7 850

8 7589 892

10 920

11 789

12 844

F = A + A + A +...+An

t t-1 t-2 t-3 t-n

Question: What are the 3-week and 6-week movingaverage forecasts fordemand?

Assuming you only have 3weeks and 6 weeks of actualdemand data for therespective forecasts

Question: What are the 3-week and 6-week moving

average forecasts fordemand?

Assuming you only have 3weeks and 6 weeks of actual

demand data for therespective forecasts


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Week Demand 3-Week 6-Week

1 650

2 678

3 720

4 785 682.67

5 859 727.676 920 788.00

7 850 854.67 768.67

8 758 876.33 802.00

9 892 842.67 815.3310 920 833.33 844.00

11 789 856.67 866.50

12 844 867.00 854.83

F4=(650+678+720)/3

=682.67F7=(650+678+720

+785+859+920)/6

=768.67

Calculating the moving averages gives us:

The McGraw-Hill Companies, Inc.,


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Problem (2) Data

Week Demand1 820

2 775

3 680

4 655

5 620

6 600

7 575

Question: What is the 3week moving average

forecast for this data?Assume you only have 3weeks and 5 weeks ofactual demand data for the

respective forecasts

Question: What is the 3week moving average

forecast for this data?Assume you only have 3weeks and 5 weeks ofactual demand data for therespective forecasts


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Problem (2) Solution

Week Demand 3-Week 5-Week

1 820

2 7753 680

4 655 758.33

5 620 703.33

6 600 651.67 710.00

7 575 625.00 666.00

F4=(820+775+680)/3

=758.33F6=(820+775+680

+655+620)/5

=710.00


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Weighted Moving Average

While the moving average formula implies an equal weightbeing placed on each value that is being averaged, the

weighted moving average permits an unequal weighting on

prior time periods

While the moving average formula implies an equal weight

being placed on each value that is being averaged, the

weighted moving average permits an unequal weighting on

prior time periods

The general formula for the weighted moving average then

changes to:

Ft+1 = wtAt + wt-1 At-1 + wt-2 At-2 + wt-3 At-3 +

+ wt-n+1 At-n+1Where:

Ft+1 is the weighted moving average for the period t+1,wt is the weighing factor, and wt = 1


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Operations ManagementProf. Upendra KachruProf. Upendra Kachru25

Weights:

t-1 .5

t-2 .3

t-3 .2

Week Demand

1 650

2 678

3 720

4

Question: Given the weekly demand and weights,what is the forecast for the 4th period or Week 4?

Question: Given the weekly demand and weights,

what is the forecast for the 4th period or Week 4?

Note that the weights place more emphasis onthe most recent data, that is time period t-1

Note that the weights place more emphasis onthe most recent data, that is time period t-1

F = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t-n

w = 1ii=1

n

wt = weight given to time period toccurrence (weights must add to one)

wt = weight given to time period toccurrence (weights must add to one)

The formula for the moving average can also be written as:The formula for the moving average can also be written as:


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Problem Solution

Week Demand Forecast

1 650

2 678

3 720

4 693.4

F4 = 0.5(720)+0.3(678)+0.2(650)=693.4


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Problem (2) Data

Weights:

t-1 .7

t-2 .2t-3 .1

Week Demand

1 820

2 775

3 680

4 655

Question: Given the weekly demand informationand weights, what is the weighted movingaverage forecast of the 5th period or week?

Question: Given the weekly demand informationand weights, what is the weighted movingaverage forecast of the 5th period or week?


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Week Demand Forecast

1 820

2 7753 680

4 655

5 672

F5 = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672


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Exponential method is atechnique that is applied to time

series data, either to producesmoothed data for presentation,

or to make forecasts.

Premise: The most recent

observations might have thehighest predictive value.Therefore, we should give moreweight to the more recent timeperiods when forecasting

ExponentialMethod


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Exponential Smoothing Model

The exponential relationship be written as:

Ft+1 = Dt + (1 - ) FtWhere:

Dtis the actual value

Ftis the forecasted value

is the weighting factor, which ranges from 0 to 1

t is the current time period.

The variance is given by:

(Dt - Ft+1 )2/n = Variance


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Problem (1) Data

Week Demand

1 820

2 775

3 6804 655

5 750

6 802

7 7988 689

9 775

10

Question: Given the weeklydemand data, what are theexponential smoothing forecastsfor periods 2-10 using =0.10and =0.60?Assume F1=D1

Which is a better choice?

Question: Given the weeklydemand data, what are theexponential smoothing forecastsfor periods 2-10 using =0.10

and =0.60?Assume F1=D1

Which is a better choice?


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Week Demand 0.1 0.6

1 820 820.00 820.00

2 775 820.00 820.00

3 680 815.50 793.00

4 655 801.95 725.205 750 787.26 683.08

6 802 783.53 723.23

7 798 785.38 770.49

8 689 786.64 787.00

9 775 776.88 728.20

10 776.69 756.28

Answer: The respective alphas columns denote the forecastvalues. Note that you can only forecast one time period into thefuture.

Answer: The respective alphas columns denote the forecastvalues. Note that you can only forecast one time period into thefuture.

F3=775x0.1 + (1-0.1)x820 =815.50


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Answer: Variance0.3 = 6675.61 and Variance0.6 = 5369.39. Thereforealpha as 0.6 is a better choice

Answer: Variance0.3 = 6675.61 and Variance0.6 = 5369.39. Thereforealpha as 0.6 is a better choice

Demand 0.1 D-W (D-W)2 0.6 D-W (D-W)2

820 820.00 0.00 0.00 820.00 0.00 0775 820.00 -45.00 2025.00 820.00 -45.00 2025

680 815.50 -135.50 18360.25 793.00 -113.00 12769

655 801.95 -146.95 21594.30 725.20 -70.20 4928.04

750 787.26 -37.26 1387.94 683.08 66.92 4478.286

802 783.53 18.47 341.16 723.23 78.77 6204.398

798 785.38 12.62 159.35 770.49 27.51 756.6461

689 786.64 -97.64 9533.35 787.00 -98.00 9603.436

775 776.88 -1.88 3.52 728.20 46.80 2190.348

53404.87 42955.15

Which one?


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Plotting the Solution

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

1 2 3 4 5 6 7 8 9 1 0

W e e

Demand

D e m a

0 . 1

0 . 6

Note how that the smaller alpha results in a smootherline in this exampleNote how that the smaller alpha results in a smootherline in this example


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Problem (2) Data

Question: What are theexponential smoothingforecasts for periods 2-5using a =0.5?

Assume F1=D1

Question: What are theexponential smoothing

forecasts for periods 2-5using a =0.5?

Assume F1=D1

Week Demand

1 8202 775

3 680

4 6555


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Week Demand 0.5

1 820 820.00

2 775 820.00

3 680 797.50

4 655 738.75

5 696.88

F1=820x0.5 + (1.0-0.5)x820 =

820F3=775x0.5 + (1.0-0.5)x820

=797.75


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Exponential Smoothing & SimpleMoving Average

An exponentially weighted moving average with

a smoothing constant a, corresponds roughly toa simple moving average of length (i.e., period)

n, where and n are related by:

= 2/(n+1) OR n = (2 - )/ .


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Double and Triple Smoothing

An exponential smoothing over an alreadysmoothed time series is called double-exponential smoothing. It applies the process ofexponential smoothing to a time series that is

already exponentially smoothened.This is used when trends are not stationary.

In the case of nonlinear trends it might benecessary to extend it even to a triple-exponential smoothing. Triple ExponentialSmoothing is better at handling parabola trendsand is normally used for such data.


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Operations Management

Double Exponential Smoothing

What happens when there is a definitenon-stationary trend?

A trendy clothing boutique has had the following salesover the past 6 months:

1 2 3 4 5 6510 512 528 530 542 552

48 0

49 0

50 0

51 0

52 0

53 0

54 0

55 0

56 0

1 2 3 4 5 6 7 8 9 10

Month

Demand

Actual

Forecast



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Deseasoning Demand: Seasonal Index

Seasonal index represents the extent of seasonalinfluence for a particular segment of the year. Thecalculation involves a comparison of the expectedvalues of that period to the grand mean.The formula for computing seasonal factors is:

Si = Di/D,where:

Si = the seasonal index for i th period,

Di= the average values of i th period,

D = grand average,

i = the ith seasonal period of the cycle


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Regression Analysis is a

method of predicting the value

of one variable based on the

value of other variables.

It reflects the casual

relationship underlying the

demand being forecast and an

independent variable.

RegressionAnalysis


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Regression analysis is of two

types:

(a)Simple Linear Regression: A

regression using only one predictor iscalled a simple regression, and

(b)Multiple Regressions: Where thereare two or more predictors, multiple

regression analysis is employed.

There are two types of variables,

one that is being forecasted and

one from which the forecast is

made.

The first one is known as thedependent variable, the latter asthe independent variable.

RegressionAnalysis


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Where:

yt is the dependent variable

a is the Y interceptb is the slope of the line, and

x is the time period

Simple Regression Analysis

The functional relationship between the two canbe visualized within a system of coordinates

where the dependent variable is shown on the y

and independent variable on the x-axis.

yt=f(x) or yt = a + bx


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yt = a + bx

0 1 2 3 4 5 x (Time)

Y

The simple linear regression

model seeks to fit a linethrough various data over

time

The simple linear regression

model seeks to fit a linethrough various data over

time

Is the linear regression modelIs the linear regression model

a

Yt is the regressed forecast value or dependent variable inthe model, a is the intercept value of the the regression

line, and b is similar to the slope of the regression line.However, since it is calculated with the variability of thedata in mind, its formulation is not as straight forward asour usual notion of slope.


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Operations ManagementProf. Upendra KachruProf. Upendra Kachru 46

Simple Linear Regression FormulasFor Calculating a and b

a = y - b x

b =xy- n(y)(x)

x - n(x2 2

)


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Problem

Week Sales

1 150

2 157

3 1624 166

5 177

Question: Given the data below, what is the simple linearregression model that can be used to predict sales infuture weeks?

Question: Given the data below, what is the simple linearregression model that can be used to predict sales infuture weeks?

A Fi t i th li i f l48


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Week Week*Week Sales Week*Sales

1 1 150 1502 4 157 314

3 9 162 486

4 16 166 664

5 25 177 885

3 55 162.4 2499

Average Sum Average Sum

b = xy - n( y)(x)x - n(x

= 2499 - 5(162.4)(3 ) =

a = y - bx =162.4 - (6.3)(3) =

2 2 =

) ( )55 5 96310

6.3

143.5

Answer: First, using the linear regression formulas, wecan compute a and b

Answer: First, using the linear regression formulas, wecan compute a and b

49


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yt = 143.5 + 6.3x

180

Period

135140145

150

155

160

165

170

175

1 2 3 4 5

Sa

les Sales

Forecast

The resulting regressionmodel is:

Now if we plot the regression generated forecasts

against the actual sales we obtain the following chart:


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r = 1 -S

S

xy

2

2

y

Correlation Analysis

Mathematically, correlation coefficient is defined by:

Where:Syx

2 is the standard error of the estimated regression

equation of the y values on x, and

Sy2 is the standard error for the y values

Correlation analysis measures the degree of relationshipbetween normally distributed dependent and

independent variables and is signified by the correlation

coefficient r.


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Multiple Regression

With multiple regressions, we can use more than onepredictor.

The forecast takes the form:

Y = 0 + 1X1 + 2X2 + . . .+ nXn,

Where:

0 is the intercept, and

1, 2, . . . n are coefficients

representing the contributionof the independent variables

X1, X2,..., Xn.


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All forecasts have errors.

However, the error in a

forecast should be within

confidence limits.

The error can be measured

by or described by the

standard error, the meanabsolute deviation, or the

variance.

ForecastingErrors


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Forecast AccuracySource of forecast errors:

Model may be inadequate

Irregular variations Incorrect use of forecasting

technique

Random variation

Key to validity is randomness Accurate models: random

errors

Invalid models: nonrandom

errors

Key question: How to determine if

forecasting errors are random?


Forecasting

Errors


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Error measuresError - difference between actual

value and predicted value

Mean Absolute Deviation(MAD) - Average absolute

error Mean Squared Error (MSE) -Average of squared error

Mean Absolute PercentError (MAPE) - Averageabsolute percent error


ErrorMeasurements


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MAD =Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

Actual Forecast 100Actual

MAPEn

=


Forecasting Error Formulae

MAD Ch t i ti


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1 M A D 0.8 standard deviation

1 standarddeviation 1.25 M AD

The ideal MAD is zero which would mean there is no

forecasting error

When the error is less than three standard deviations, itis considered as an acceptable forecast.

= (/2) x MAD 1.25 MAD

Where is the standard deviation

The larger the MAD, the less the accurate the resultingmodel

MAD Characteristics


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MAD Problem (1)

Month Sales Forecast

1 220 n/a

2 250 255

3 210 205

4 300 320

5 325 315

Question: What is the MAD value given theforecast values in the table below?Question: What is the MAD value given theforecast values in the table below?


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Solution

MAD =

A - F

n=

40

4= 10

t tt=1

n

Month Sales Forecast Abs Error 1 220 n/a

2 250 255 5

3 210 205 5

4 300 320 20

5 325 315 10

40

Note that by itself, the MADonly lets us know the meanerror in a set of forecasts

Note that by itself, the MADonly lets us know the meanerror in a set of forecasts

= 1.25 MAD = 12.5; 3 =37.5

All readings are within limits


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Example (2)

P erio d Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual )*1

1 217 215 2 2 4 0.

2 213 216 -3 3 9 1.

3 216 215 1 1 1 0.

4 210 214 -4 4 16 1.

5 213 211 2 2 4 0.

6 219 214 5 5 25 2.

7 216 217 -1 1 1 0.

8 212 216 -4 4 16 1.

-2 22 76 10.

MAD= 2.75

MSE= 10.86

MAPE= 1.28

MAD = 22/8 = 2.75

MSE = 76/7 = 10.86

MAPE = 10.26/8 =10.86


T ki Si l


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Tracking Signals

Depending on the number of MADs selected, the TS can be used like a quality control chartindicating when the model is generating too much error in its forecasts.

The TS formula is:

The Tracking Signal or TS is a measure

that indicates whether the forecastaverage is keeping pace with anygenuine upward or downward changesin demand.

MAD

demand)Forecast-demand(Actualn

1

i=i


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Control Charts

A control chart is: A visual tool for monitoring forecast errors

Used to detect non-randomness in errors

Forecasting errors are in control if All errors are within the control limits

No patterns, such as trends or cycles, are present



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Controlling the forecast



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Control charts

Control charts are based on the following assumptions: when errors are random, they are Normally distributed

around a mean of zero.

Standard deviation of error is

95.5% of data in a normal distribution is within 2 standard

deviation of the mean

99.7% of data in a normal distribution is within 3 standard

deviation of the mean

Upper and lower control limits are often determine via

MSE

0 2 0 3MSE or MSE


E l


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Example

Compute 2s control limits forforecast errors to determine ifthe forecast is accurate.

-6.59

-4.59

-2.59

-0.59

1.41

3.41

5.41

0 10

3.295

2 6.59

s MSE

s

= =

=


Errors are all

between -6.59 and

+6.59No pattern is

observed

Therefore,

according to

control chartcriterion, forecast

is reliable

(Refer Slide 42)


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CPFR is forecasting based on

the concept of supply chain

management. It is a business

model that takes a holistic

approach to supply chain

management and information

exchange among tradingpartners.

It uses common metrics,

standard language, and firm

agreements to improve supplychain efficiencies for all

participants.

CollaborativePlanning

Forecasting andReplenishment(CPFR)


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In other words, CPFR isbased on considering the

entire supply chain orpartnerships as a single unitand the sharing of informationbetween the links in the chain.

The objective is to

collectively, as members ofthe supply chain, meet theneeds of the final consumer.

This is accomplished bysupplying the right product atthe right place, right time andright price to the customer.




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CPFR usually begins with identifying a forecasting

champion. The forecasting champion can be it a single

person, a department, or a firm.

A forecast collaboration group is formed with each organization

choosing its member in this group. Group members shouldrepresent a variety of functional areas including sales,

marketing, logistics/operations, finance, and information

systems.


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The driving premise of CPFR is

that all supply chain participants

develop a synchronized forecast.A company can collaborate with

numerous other supply network

members both upstream and

downstream in the supply

network.

Every participant in a CPFR

process supplier,

manufacturer, distributor, retailer

can view and amend forecastdata to optimize the process from

end to end.




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Special Long-Term ForecastMethodologies

1. Identify and analyze the

organizational issues that

will provide the decisionfocus

2. Specify the key decision

factors

3. Identify and analyze the keyenvironmental forces

4. Establish the scenario logics

5. Select and elaborate the

scenario6. Interpret the scenario for

their decision implications

ScenarioPlanning


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Qualitativeapproach

(Judgmental)

Historical Analogy

Method

Executive Opinion

Method

Survey Methods

The Delphi Method


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Usually based on judgmentsUsually based on judgmentsabout causal factors thatabout causal factors that

underlie the demand ofunderlie the demand of

particular products or servicesparticular products or services

Do not require a demandDo not require a demand

history for the product orhistory for the product orservice, therefore are usefulservice, therefore are useful

for new products/servicesfor new products/services

Approaches vary inApproaches vary in

sophistication fromsophistication from

scientifically conductedscientifically conducted

surveys to intuitive hunchessurveys to intuitive hunches

about future eventsabout future events

Qualitative ApproachesQualitative Approaches


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Executive Opinion MethodExecutive Opinion Method

TechniqueTechnique Low SalesLow Sales High SalesHigh Sales

ManagersManagersOpinionOpinion

40.7%40.7% 39.6%39.6%

ExecutivesExecutivesOpinionOpinion

40.7%40.7% 41.6%41.6%

Sales ForceSales ForceCompositeComposite

29.6%29.6% 35.4%35.4%

Number inNumber in

SampleSample

2727 4848



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How to choose the right Tool



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Operations

Management

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topic 6 - forecasting

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