demand forecasting karthi

8/13/2019 Demand Forecasting Karthi

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12002 South-Western/Thomson Learning2002 South-Western/Thomson Learning TMTM

Slides preparedSlides prepared

by John Loucksby John Loucks


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Demand Forecasting


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Overview

Introduction Qualitative Forecasting Methods

Quantitative Forecasting Models

How to Have a Successful Forecasting System Computer Software for Forecasting

Forecasting in Small Businesses and Start-Up

Ventures

Wrap-Up: What World-Class Producers Do


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Introduction

ForecastingEstimating the future demand for productsand services and the resources necessary to produce these

outputs

Sales forecastsStarting point for the Operations

Management

The sales forecasts become inputs to both businessstrategy and production resource forecasts.


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Examples of Production Resource Forecasts

Long

Range

Medium

Range

ShortRange

Years

Months

Days,Weeks

New Products,

Factory Capacities,Facility needs

Forecast

Horizon

Time

Span

Item Being

ForecastedUnit of

Measure

Product groups,

Purchased materials and

Inventories

Specific Products,

Machine Capacities

Dollars,

Tons

Units,

Pounds

Units,Hours


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Some Reasons Why

Forecasting is Essential in OM

New Facility PlanningIt can take 5 years to design and

build a new factory or design and implement a new

production process.

Production PlanningDemand for products vary frommonth to month and it can take several months to change

the capacities of production processes.

Workforce SchedulingDemand for services (and the

necessary staffing) can vary from hour to hour and

employees weekly work schedules must be developed in

advance.


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Forecasting is an Integral Part

of Business Planning

Forecast

Method(s)

Out put:Demand

Estimates

Sales

Forecast

Management Team

ProcessorCapacity,

Avl.Reso, Risk, Experience

Inputs:

Market conditions

competitor actions,

customer taste

conomic Outlook - Stock

Other factors

Business

StrategyMarketing plan,

roduction plan, Finance plan

Production Resource

Forecasts

Long, medium and short range


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Forecasting Methods

Qualitative Approaches Quantitative Approaches


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Qualitative Approaches

Used to develop the sales forecasts

Usually based on judgments about factors that underlie the

demand of particular products or services

Do not require a demand history for the product or service,

therefore are useful for new products/services

The approach/method that is appropriate depends on a

products life cycle stage


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Qualitative Methods

Educated guessShort term forecasts Executive committee consensus Compromise forecasts -

Delphi method

Survey of sales force - Sales forecast to ensure realistic

estimates

Survey of customers

Historical analogyForecasting sales for new products

Market research - New products or existing products to be

introduced into new market segments


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Quantitative Forecasting Approaches

Mathematical model based on the historical data - generatethe future demand based on the past data, i.e., history will

tend to repeat itself

Analysis of the past demand pattern provides a good basis

for forecasting future demand

Majority of quantitative approaches fall in the category oftime series analysis

Forecast accuracyHigh accuracy with low forecast error


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A time series is a set of numbers where the order or

sequence of the numbers is important, e.g., historicaldemand

Time Series Analysis

Trends are noted by an upward or downward sloping line. Cycle is a data pattern that may cover several years before

it repeats itself.

Seasonality is a data pattern that repeats itself over theperiod of one year or less.

Random fluctuation (noise) results from random variation

or unexplained causes.

Components of a Time Series


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Seasonal Patterns

Length of Time Number of

Before Pattern Length of Seasons

Is Repeated Season in Pattern

Year Quarter 4

Year Month 12

Year Week 52

Month Day 28-31

Week Day 7


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Simple Linear Regression

Least square methodLong term forecasting

Linear regression analysis establishes a relationship between

a dependent variable and one or more independent variables

in the historical observations

Ex. Independent variabletime period and dependent

variable - sales forecasting in sales


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Regression EquationThis model is of the form:

Y = a + bX

Y = dependent variable

X = independent variable

a = y-axis intercept

b = slope of regression line


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Constants a and bThe constants a and b are computed using the

following equations:

2

2 2x y- x xya =n x -( x)

2 2

xy- x yb = n x -( x)

n


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Once the a and b values are computed, a future valueof X can be entered into the regression equation and a

corresponding value of Y (the forecast) can be

calculated.


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Example: College Enrollment

Simple Linear RegressionAt a small regional college enrollments have grown

steadily over the past six years, as evidenced below.

Use time series regression to forecast the student

enrollments for the next three years.

Students Students

Year Enrolled (1000s) Year Enrolled (1000s)

1 2.5 4 3.22 2.8 5 3.3

3 2.9 6 3.4


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x y x2 xy

1 2.5 1 2.5

2 2.8 4 5.63 2.9 9 8.7

4 3.2 16 12.8

5 3.3 25 16.5

6 3.4 36 20.4Sx=21 Sy=18.1 Sx2=91 Sxy=66.5


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Y = 2.387 + 0.180X

2

91(18.1) 21(66.5)2.387

6(91) (21)a

6(66.5) 21(18.1)0.180

105b


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Y7= 2.387 + 0.180(7) = 3.65 or 3,650 students

Y8= 2.387 + 0.180(8) = 3.83 or 3,830 students

Y9= 2.387 + 0.180(9) = 4.01 or 4,010 students

Note: Enrollment is expected to increase by 180

students per year.


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Simple linear regression can also be used when theindependent variable X represents a variable other

than time.

In this case, linear regression is representative of a

class of forecasting models called causal forecastingmodels.


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Example: Railroad Products Co.

Simple Linear RegressionCausal ModelThe manager of RPC wants to project the firms

sales for the next 3 years. He knows that RPCs long-

range sales are tied very closely to national freight car

loadings. On the next slide are 7 years of relevanthistorical data.

Develop a simple linear regression model

between RPC sales and national freight car loadings.Forecast RPC sales for the next 3 years, given that the

rail industry estimates car loadings of 250, 270, and

300 million.


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Simple Linear RegressionCausal Model

RPC Sales Car Loadings

Year ($millions) (millions)

1 9.5 1202 11.0 1353 12.0 1304 12.5 150

5 14.0 1706 16.0 1907 18.0 220


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x y x2 xy

120 9.5 14,400 1,140

135 11.0 18,225 1,485130 12.0 16,900 1,560

150 12.5 22,500 1,875

170 14.0 28,900 2,380

190 16.0 36,100 3,040220 18.0 48,400 3,960

1,115 93.0 185,425 15,440


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Y = 0.528 + 0.0801X

2

185, 425(93) 1,115(15, 440)a 0.528

7(185, 425) (1,115)

2

7(15,440) 1,115(93)b 0.0801

7(185,425) (1,115)


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Y8 = 0.528 + 0.0801(250) = $20.55 million

Y9 = 0.528 + 0.0801(270) = $22.16 million

Y10= 0.528 + 0.0801(300) = $24.56 million

Note: RPC sales are expected to increase by$80,100 for each additional million national freight

car loadings.


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Multiple Regression Analysis

Multiple regression analysis is used when there aretwo or more independent variables.

An example of a multiple regression equation is:

Y = 50.0 + 0.05X1+ 0.10X20.03X3

where: Y = firms annual sales ($millions)

X1= industry sales ($millions)

X2= regional per capita income ($thousands)X3= regional per capita debt ($thousands)


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Coefficient of Correlation (r)

The coefficient of correlation, r, explains the relativeimportance of the relationship betweenxandy.

The sign of rshows the direction of the relationship.

The absolute value of rshows the strength of the

relationship.

The sign of ris always the same as the sign of b.

rcan take on any value between1 and +1.


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Meanings of several values of r:-1 a perfect negative relationship (asxgoes up,y

goes down by one unit, and vice versa)

+1 a perfect positive relationship (asxgoes up,y

goes up by one unit, and vice versa)

0 no relationship exists betweenxandy

+0.3 a weak positive relationship

-0.8 a strong negative relationship


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r is computed by:

2 2 2 2( ) ( )

n xy x yr

n x x n y y


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Coefficient of Determination (r2)

The coefficient of determination, r2

, is the square ofthe coefficient of correlation.

The modification of rto r2allows us to shift from

subjective measures of relationship to a more specific

measure.

r2is determined by the ratio of explained variation to

total variation:2

2

2( )( )Y yry y


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Coefficient of Correlation

r = .9829

2 2

7(15,440) 1,115(93)

7(185,425) (1,115) 7(1,287.5) (93)r


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Coefficient of Determination

r2 = (.9829)2 = .966

96.6% of the variation in RPC sales is explained by

national freight car loadings.


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Ranging Forecasts

Forecasts for future periods are only estimates and aresubject to error.

One way to deal with uncertainty is to develop best-

estimate forecasts and the ranges within which the

actual data are likely to fall.

The ranges of a forecast are defined by the upper and

lower limits of a confidence interval.


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Ranging Forecasts

The ranges or limits of a forecast are estimated by:Upper limit = Y + t(syx)

Lower limit = Y - t(syx)

where:Y = best-estimate forecast

t = number of standard deviations from the mean

of the distribution to provide a given probability of exceeding the limits through chance

syx = standard error of the forecast


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Ranging Forecasts

The standard error (deviation) of the forecast iscomputed as:

2

yx

y - a y - b xy

s = n - 2


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Ranging ForecastsRecall that linear regression analysis provided a

forecast of annual sales for RPC in year 8 equal to

$20.55 million.

Set the limits (ranges) of the forecast so that there

is only a 5 percent probability of exceeding the limits

by chance.


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Ranging Forecasts Step 1: Compute the standard error of the

forecasts, syx.

Step 2: Determine the appropriate value for t.

n = 7, so degrees of freedom = n2 = 5.Area in upper tail = .05/2=0.025

Area in lower tail = .05/2=0.025

Appendix B, Table 2 shows t = 2.571.

1287.5 .528(93) .0801(15,440) .57487 2

yxs


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Evaluating Forecast-Model Performance

Short-range forecasting models are evaluated on thebasis of three characteristics:

Impulse response

Noise-dampening ability

Accuracy


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Impulse Response and Noise-Dampening Ability If forecasts have little period-to-period fluctuation, they

are said to be noise dampening.

Forecasts that respond quickly to changes in historical

data are said to have a high impulse response. Similarly,

it has little impact on the historical data than its low

impulse response.

A forecast system that responds quickly to data changesnecessarily picks up a great deal of random fluctuation

(noise).

Hence, there is a trade-off between high impulse

response and high noise dampening.


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Accuracy Accuracy is the typical criterion for judging the

performance of a forecasting approach

Accuracy is how well the forecasted values match

the actual values

Accuracy can be measured in several ways

Standard error of the forecast (Syx) (discussed earlier)

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


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Monitoring Accuracy

Mean Absolute Deviation (MAD)

n

periodsnfordeviationabsoluteofSum=MAD

n

i ii=1

Actual demand -Forecast demand

MAD =n


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Short-Range Forecasting Methods

(Simple) Moving Average Weighted Moving Average

Exponential Smoothing

Exponential Smoothing with Trend


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Simple Moving Average

Average the data from a few recent periods, andthis average becomes the forecast for the next

period

An averaging period (AP) is given or selected

It is called a simple average because each period

used to compute the average is equally weighted

It is called moving because as new demand data

becomes available, the oldest data is not used . . . more


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Weighted Moving Average

This is a variation on the simple moving average where theweights used to compute the average are not equal.

This allows more recent demand data to have a greater

effect on the moving average

The weights must add to 1.0 and generally decrease in value

with the age of the data.

The distribution of the weights determine the impulse

response of the forecast. . . . more

S i


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Example: Short term Forecasting

Moving Average

Representative Historical Data

Week Act.Inven.Demand

1 100 10 902 125 11 105

3 90 12 95

4 110 13 115

5 105 14 1206 130 15 80

7 85 16 95

8 102 17 100

9 110

Moving Average Short-Range Forecastingk


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Week Forecasts

AP = 3 weeks 5 weeks 7 weeks

8 106.7 104.0 106.4

9 105.7 106.4 106.7

10 99 106.4 104.6

11 100.7 103.4 104.6

12 101.7 98.4 103.9

13 96.7 100.4 102.4

14 105 103 100.3

15 110 105 105.3

16 105 103 102.1

17 98.3 101 100

M i A


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Moving Average

Sample computations

Considering a 10thweek

F3 = 85+102+110/3=99

F5 = 85+102+110+130+85/5=106.4

F7 = 90+110+105+130+85+102+110/7=104.6


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M i A F t A t l C h D d


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Moving Average Forecast vs Actual Cash Demand

Forecast for 18th

week = 115+120+80+95+100/5 = 102

E ti l S thi


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The weights used to compute the forecast (movingaverage) are exponentially distributed.

The forecast is the sum of the old forecast and a portion

(a) of the forecast error (At-1-Ft-1).

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

. . . More

Smoothing constant (a), must be between 0.0 and 1.0. A large aprovides a high impulse response forecast.

A small aprovides a low impulse response forecast.

Exponential Smoothing


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Mean Absolute Deviation


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Week Actual Forecasts

Demand = 0.1 = 0.2 = 0.3

8 102 85 (17) 85 (17) 85 (17)

9 110 86.7 (23.3) 88.4 (21.6) 90.1 (19.9)

10 90 89 (1) 92.7 (2.7) 96.1 (6.1)

11 105

12 95

13 11514 120

15 80

16 95

17 100 94.6 (5.4) 97.7 (2.3) 98 (2.0)

MAD 133.9/10 = 13.9 12.44 12.60

Exponential Smoothing Forecast


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Exponential Smoothing Forecast

vs Actual Cash Demand


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Forecast for 18th

week (= 0.2 ) = Ft= Ft-1+ (At-1- Ft-1) = F17+ (A17F17)

F18= 97.7 + 0.2 (100- 97.7) = 98.2

End of Chapter 3


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End of Chapter 3

demand forecasting karthi

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