demand forecasting karthi
TRANSCRIPT
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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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Simple Linear Regression
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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Simple Linear Regression
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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Simple Linear Regression
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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Example: College Enrollment
Simple Linear Regression
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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Example: College Enrollment
Simple Linear Regression
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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Example: College Enrollment
Simple Linear Regression
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
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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Example: Railroad Products Co.
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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Example: Railroad Products Co.
Simple Linear RegressionCausal Model
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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Example: Railroad Products Co.
Simple Linear RegressionCausal Model
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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Example: Railroad Products Co.
Simple Linear RegressionCausal Model
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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Coefficient of Correlation (r)
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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Coefficient of Correlation (r)
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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Example: Railroad Products Co.
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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Example: Railroad Products Co.
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 proba- bility 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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Example: Railroad Products Co.
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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Example: Railroad Products Co.
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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Evaluating Forecast-Model Performance
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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Evaluating Forecast-Model Performance
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