Demand Forecasting Student 01

7/29/2019 Demand Forecasting Student 01

1/87

1

Demand Forecasting

By

Prof.Raju Gundala


2/87

2

Demand Forecasting Models

Introduction Qualitative Forecasting Methods

Quantitative Forecasting Models

How to Have a Successful Forecasting System Computer Software for Forecasting

Problem /Case Analysis


3/87

3

Introduction

Demand estimates for products and services are thestarting point for all the other planning in operations

management.

Management teams develop sales forecasts based in

part on demand estimates.

The sales forecasts become inputs to both business

strategy and production resource forecasts.


4/87

4

Forecasting is an Integral Part

of Business Planning

Forecast

Method(s)

Demand

Estimates

Sales

Forecast

Management

Team

Inputs:Market,

Economic,

Other

Business

Strategy

Production Resource

Forecasts


5/87

5

Some Reasons Why

Forecasting is Essential in OM

New Facility PlanningIt can take 5 years to designand build a new factory or design and implement a

new production process.

Production PlanningDemand for products vary

from month 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 hourand employees weekly work schedules must be

developed in advance.


6/87

6

Examples of Production Resource Forecasts

Long

Range

Medium

Range

ShortRange

Years

Months

Days,Weeks

Product Lines,

Factory Capacities

Forecast

Horizon

Time

Span

Item Being

Forecasted

Unit of

Measure

Product Groups,

Depart. Capacities

Specific Products,Machine Capacities

Dollars,

Tons

Units,

Pounds

Units,Hours


7/87

7

Forecasting Methods

Qualitative Approaches Quantitative Approaches


8/87

8

Qualitative Approaches

Usually based on judgments about causal factors thatunderlie 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

Approaches vary in sophistication from scientifically

conducted surveys to intuitive hunches about future

events

The approach/method that is appropriate depends on aproducts life cycle stage


9/87

9

Qualitative Methods

Educated guess intuitive hunches Executive committee consensus

Delphi method

Survey of sales force Survey of customers

Historical analogy

Market research scientifically conducted surveys


10/87

10

Quantitative Forecasting Approaches

Based on the assumption that the forces thatgenerated the past demand will generate the future

demand, 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 of time series analysis


11/87

11

A time series is a set of numbers where the order orsequence of the numbers is important, e.g., historical

demand

Analysis of the time series identifies patterns

Once the patterns are identified, they can be used to

develop a forecast

Time Series Analysis


12/87

12

Components of a Time Series

Trends are noted by an upward or downward slopingline.

Cycle is a data pattern that may cover several years

before it repeats itself.

Seasonality is a data pattern that repeats itself over

the period of one year or less.

Random fluctuation (noise) results from random

variation or unexplained causes.


13/87

13

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


14/87

14

Quantitative Forecasting Approaches

Linear Regression Simple Moving Average

Weighted Moving Average

Exponential Smoothing (exponentially weightedmoving average)

Exponential Smoothing with Trend (double

exponential smoothing)


15/87

15

Long-Range Forecasts

Time spans usually greater than one year Necessary to support strategic decisions about

planning products, processes, and facilities


16/87

16

Simple Linear Regression

Linear regression analysis establishes a relationshipbetween a dependent variable and one or more

independent variables.

In simple linear regression analysis there is only one

independent variable.

If the data is a time series, the independent variable is

the time period.

The dependent variable is whatever we wish toforecast.


17/87

17


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


18/87

18


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


19/87

19


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.


20/87

20

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


21/87

21



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


22/87

22



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


23/87

23



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.


24/87

24


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.


25/87

25

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.


26/87

26


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


27/87

27



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


28/87

28



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)


29/87

29



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.


30/87

30

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)


31/87

31

Coefficient of Correlation (r)

The coefficient of correlation, r, explains the relativeimportance of the relationship betweenx andy.

The sign ofrshows the direction of the relationship.

The absolute value ofrshows the strength of the

relationship.

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

rcan take on any value between1 and +1.


32/87

32


Meanings of several values ofr:-1 a perfect negative relationship (asx goes up,y

goes down by one unit, and vice versa)

+1 a perfect positive relationship (asx goes up,y

goes up by one unit, and vice versa)

0 no relationship exists betweenx andy

+0.3 a weak positive relationship

-0.8 a strong negative relationship


33/87

33


r is computed by:

2 2 2 2( ) ( )

n xy x yr

n x x n y y


34/87

34

Coefficient of Determination (r2)

The coefficient of determination, r2

, is the square ofthe coefficient of correlation.

The modification ofrto r2 allows us to shift from

subjective measures of relationship to a more specific

measure.

r2 is determined by the ratio of explained variation to

total variation:2

2

2( )( )Y yry y


35/87

35


Coefficient of Correlation

x y x2 xy y2

120 9.5 14,400 1,140 90.25

135 11.0 18,225 1,485 121.00130 12.0 16,900 1,560 144.00

150 12.5 22,500 1,875 156.25

170 14.0 28,900 2,380 196.00

190 16.0 36,100 3,040 256.00220 18.0 48,400 3,960 324.00

1,115 93.0 185,425 15,440 1,287.50


36/87

36


Coefficient of Correlation

r = .9829

2 2

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

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


37/87

37


Coefficient of Determination

r2 = (.9829)2 = .966

96.6% of the variation in RPC sales is explained by

national freight car loadings.


38/87

38

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.


39/87

39

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 proba-bility of exceeding the limits through chance

syx = standard error of the forecast


40/87

40

Ranging Forecasts

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

2

yx

y - a y - b xy

s = n - 2


41/87

41


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.


42/87

42


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 = .025

Appendix B, Table 2 shows t = 2.571.

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

yxs


43/87

43


Ranging Forecasts Step 3: Compute upper and lower limits.

Upper limit = 20.55 + 2.571(.5748)

= 20.55 + 1.478= 22.028

Lower limit = 20.55 - 2.571(.5748)

= 20.55 - 1.478

= 19.072

We are 95% confident the actual sales for year 8will be between $19.072 and $22.028 million.


44/87

44

Seasonalized Time Series Regression Analysis

Select a representative historical data set. Develop a seasonal index for each season.

Use the seasonal indexes to deseasonalize the data.

Perform lin. regr. analysis on the deseasonalized data. Use the regression equation to compute the forecasts.

Use the seas. indexes to reapply the seasonal patterns

to the forecasts.


45/87

45

Example: Computer Products Corp.

Seasonalized Times Series Regression AnalysisAn analyst at CPC wants to develop next years

quarterly forecasts of sales revenue for CPCs line of

Epsilon Computers. She believes that the most recent

8 quarters of sales (shown on the next slide) arerepresentative of next years sales.


46/87

46


Seasonalized Times Series Regression Analysis Representative Historical Data Set

Year Qtr. ($mil.) Year Qtr. ($mil.)

1 1 7.4 2 1 8.3

1 2 6.5 2 2 7.4

1 3 4.9 2 3 5.4

1 4 16.1 2 4 18.0


47/87

47


Seasonalized Times Series Regression Analysis Compute the Seasonal Indexes

Quarterly Sales

Year Q1 Q2 Q3 Q4 Total1 7.4 6.5 4.9 16.1 34.9

2 8.3 7.4 5.4 18.0 39.1

Totals 15.7 13.9 10.3 34.1 74.0

Qtr. Avg. 7.85 6.95 5.15 17.05 9.25

Seas.Ind. .849 .751 .557 1.843 4.000


48/87

48


Seasonalized Times Series Regression Analysis Deseasonalize the Data

Quarterly Sales

Year Q1 Q2 Q3 Q41 8.72 8.66 8.80 8.74

2 9.78 9.85 9.69 9.77


49/87

49


Seasonalized Times Series Regression Analysis Perform Regression on Deseasonalized Data

Yr. Qtr. x y x2 xy

1 1 1 8.72 1 8.721 2 2 8.66 4 17.321 3 3 8.80 9 26.401 4 4 8.74 16 34.962 1 5 9.78 25 48.90

2 2 6 9.85 36 59.102 3 7 9.69 49 67.832 4 8 9.77 64 78.16

Totals 36 74.01 204 341.39


50/87

50


Seasonalized Times Series Regression Analysis Perform Regression on Deseasonalized Data

Y = 8.357 + 0.199X

2

204(74.01) 36(341.39)a 8.357

8(204) (36)

2

8(341.39) 36(74.01)b 0.199

8(204) (36)


51/87

51


Seasonalized Times Series Regression Analysis Compute the Deseasonalized Forecasts

Y9 = 8.357 + 0.199(9) = 10.148

Y10 = 8.357 + 0.199(10) = 10.347Y11 = 8.357 + 0.199(11) = 10.546

Y12 = 8.357 + 0.199(12) = 10.745

Note: Average sales are expected to increase by

.199 million (about $200,000) per quarter.

C C


52/87

52


Seasonalized Times Series Regression Analysis Seasonalize the Forecasts

Seas. Deseas. Seas.

Yr. Qtr. Index Forecast Forecast3 1 .849 10.148 8.62

3 2 .751 10.347 7.77

3 3 .557 10.546 5.873 4 1.843 10.745 19.80

Sh R F


53/87

53

Short-Range Forecasts

Time spans ranging from a few days to a few weeks Cycles, seasonality, and trend may have little effect

Random fluctuation is main data component

E l i F M d l P f


54/87

54

Evaluating Forecast-Model Performance

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

Impulse response

Noise-dampening ability

Accuracy

E l ti F t M d l P f


55/87

55


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 data

are said to have a high impulse response.

A forecast system that responds quickly to data

changes necessarily picks up a great deal of

random fluctuation (noise). Hence, there is a trade-off between high impulse

response and high noise dampening.

E l ti F t M d l P f


56/87

56


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

M it i A


57/87

57

Monitoring Accuracy

Accuracy of a forecasting approach needs to bemonitored to assess the confidence you can have in its

forecasts and changes in the market may require

reevaluation of the approach

Accuracy can be measured in several ways Standard error of the forecast (covered earlier)

Mean absolute deviation (MAD)

Mean squared error (MSE)

M it i A


58/87

58

Monitoring Accuracy

Mean Absolute Deviation (MAD)

n

periodsnfordeviationabsoluteofSum=MAD

n

i i

i=1

Actual demand -Forecast demand

MAD =n

M it i A


59/87

59

Mean Squared Error (MSE)

MSE = (Syx)2

A small value for Syx means data points are

tightly grouped around the line and error range issmall.

When the forecast errors are normally

distributed, the values of MAD and syx are related:

MSE = 1.25(MAD)

Monitoring Accuracy

Sh t R F ti M th d


60/87

60

Short-Range Forecasting Methods

(Simple) Moving Average Weighted Moving Average

Exponential Smoothing

Exponential Smoothing with Trend

Si l M i A


61/87

61

Simple Moving Average

An averaging period (AP) is given or selected The forecast for the next period is the arithmetic

average of the AP most recent actual demands

It is called a simple average because each period

used to compute the average is equally weighted

. . . more

Simple Mo ing A erage


62/87

62

Simple Moving Average

It is called moving because as new demand databecomes available, the oldest data is not used

By increasing the AP, the forecast is less responsive

to fluctuations in demand (low impulse response and

high noise dampening) By decreasing the AP, the forecast is more responsive

to fluctuations in demand (high impulse response and

low noise dampening)



63/87

63


This is a variation on the simple moving averagewhere the weights used to compute the average are

not equal.

This allows more recent demand data to have a

greater effect on the moving average, therefore theforecast.

. . . more



64/87

64


The weights must add to 1.0 and generally decreasein value with the age of the data.

The distribution of the weights determine the impulse

response of the forecast.



65/87

65

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 (A t-1-Ft-1).

Ft = Ft-1 + a(A t-1-Ft-1)

. . . more




66/87

66


The smoothing constant,a

, must be between 0.0 and1.0.

A large a provides a high impulse response forecast.

A small a provides a low impulse response forecast.

Example: Central Call Center


67/87

67


Moving AverageCCC wishes to forecast the number of incoming

calls it receives in a day from the customers of one of

its clients, BMI. CCC schedules the appropriate

number of telephone operators based on projected callvolumes.

CCC believes that the most recent 12 days of call

volumes (shown on the next slide) are representative

of the near future call volumes.



68/87

68


Moving Average Representative Historical Data

Day Calls Day Calls

1 159 7 2032 217 8 195

3 186 9 188

4 161 10 168

5 173 11 1986 157 12 159



69/87

69


Moving AverageUse the moving average method with an AP = 3

days to develop a forecast of the call volume in Day

13.

F13 = (168 + 198 + 159)/3 = 175.0 calls



70/87

70


Weighted Moving AverageUse the weighted moving average method with an

AP = 3 days and weights of .1 (for oldest datum), .3,

and .6 to develop a forecast of the call volume in Day

13.

F13 = .1(168) + .3(198) + .6(159) = 171.6 calls

Note: The WMA forecast is lower than the MA

forecast because Day 13s relatively low call volumecarries almost twice as much weight in the WMA

(.60) as it does in the MA (.33).



71/87

71


Exponential SmoothingIf a smoothing constant value of .25 is used and

the exponential smoothing forecast for Day 11 was

180.76 calls, what is the exponential smoothing

forecast for Day 13?

F12 = 180.76 + .25(198180.76) = 185.07

F13 = 185.07 + .25(159185.07) = 178.55



72/87

72


Forecast Accuracy - MADWhich forecasting method (the AP = 3 moving

average or the a= .25 exponential smoothing) is

preferred, based on the MAD over the most recent 9

days? (Assume that the exponential smoothingforecast for Day 3 is the same as the actual call

volume.)



73/87

73


AP = 3 a= .25

Day Calls Forec. |Error| Forec. |Error|

4 161 187.3 26.3 186.0 25.05 173 188.0 15.0 179.8 6.8

6 157 173.3 16.3 178.1 21.17 203 163.7 39.3 172.8 30.28 195 177.7 17.3 180.4 14.69 188 185.0 3.0 184.0 4.010 168 195.3 27.3 185.0 17.011 198 183.7 14.3 180.8 17.212 159 184.7 25.7 185.1 26.1

MAD 20.5 18.0



74/87

74


As we move toward medium-range forecasts, trendbecomes more important.

Incorporating a trend component into exponentially

smoothed forecasts is called double exponential

smoothing. The estimate for the average and the estimate for the

trend are both smoothed.



75/87

75


Model FormFTt = St-1 + Tt-1

where:

FTt = forecast with trend in period tSt-1 = smoothed forecast (average) in period t-1

Tt-1 = smoothed trend estimate in period t-1



76/87

76


Smoothing the AverageSt = FTt + a(AtFTt)

Smoothing the Trend

Tt = Tt-1 +b(FTtFTt-1 - Tt-1)

where: a = smoothing constant for the average

b = smoothing constant for the trend

Criteria for Selecting


77/87

77

a Forecasting Method

Cost Accuracy

Data available

Time span

Nature of products and services

Impulse response and noise dampening



78/87

78


Cost and Accuracy There is a trade-off between cost and accuracy;

generally, more forecast accuracy can be obtained

at a cost.

High-accuracy approaches have disadvantages: Use more data

Data are ordinarily more difficult to obtain

The models are more costly to design,implement, and operate

Take longer to use



79/87

79


Cost and Accuracy

Low/Moderate-Cost Approachesstatistical

models, historical analogies, executive-committee

consensus

High-Cost Approachescomplex econometricmodels, Delphi, and market research


i


80/87

80


Data Available

Is the necessary data available or can it be

economically obtained?

If the need is to forecast sales of a new product,

then a customer survey may not be practical;instead, historical analogy or market research may

have to be used.


F i M h d


81/87

81


Time Span

What operations resource is being forecast and for

what purpose?

Short-term staffing needs might best be forecast

with moving average or exponential smoothingmodels.

Long-term factory capacity needs might best be

predicted with regression or executive-committeeconsensus methods.


F i M h d


82/87

82


Nature of Products and Services

Is the product/service high cost or high volume?

Where is the product/service in its life cycle?

Does the product/service have seasonal demand

fluctuations?


F ti M th d


83/87

83


Impulse Response and Noise Dampening

An appropriate balance must be achieved between:

How responsive we want the forecasting model

to be to changes in the actual demand data

Our desire to suppress undesirable chance

variation or noise in the demand data

Reasons for Ineffective Forecasting


84/87

84

easo s o e ect ve o ecast g

Not involving a broad cross section of people

Not recognizing that forecasting is integral to

business planning

Not recognizing that forecasts will always be wrong

Not forecasting the right things

Not selecting an appropriate forecasting method

Not tracking the accuracy of the forecasting models

Monitoring and Controlling

F ti M d l


85/87

85

a Forecasting Model

Tracking Signal (TS)

The TS measures the cumulative forecast errorover n periods in terms of MAD

If the forecasting model is performing well, the TSshould be around zero

The TS indicates the direction of the forecastingerror; if the TS is positive -- increase the forecasts,if the TS is negative -- decrease the forecasts.

n

i i

1

(Actual demand - Forecast demand )

TS =MAD

i

Monitoring and Controlling

F ti M d l


86/87

86

a Forecasting Model

Tracking Signal

The value of the TS can be used to automatically

trigger new parameter values of a model, thereby

correcting model performance.

If the limits are set too narrow, the parametervalues will be changed too often.

If the limits are set too wide, the parameter values

will not be changed often enough and accuracywill suffer.


87/87

Demand Forecasting Student 01

Documents

Transcript of Demand Forecasting Student 01