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Forecasting Introduction
An essential aspect of managing anyorganization is planning for the future.
Organizations employ forecasting techniquesto determine future inventory, costs,capacities, and interest rate changes.
There are two basic approaches toforecasting:
-Qualitative
-Quantitative
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Time Span of Forecasts
Long-range
time spans usually greater than one year
necessary to support strategic decisions about
planning products, processes, and facilities Short-range
time spans ranging from a few days to a fewweeks
cycles, seasonality, and trend may have littleeffect
random fluctuation is main data pattern
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Qualitative Approaches toForecasting
Delphi Approach A panel of experts, each of whom is physically separated from
the others and is anonymous, is asked to respond to a
sequential series of questionnaires. After each questionnaire, the responses are tabulated and the
information and opinions of the entire group are made knownto each of the other panel members so that they may revisetheir previous forecast response.
The process continues until some degree of consensus isachieved.
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Qualitative Approaches(continued)
Scenario Writing Scenario writing consists of developing a conceptual scenario of
the future based on a well defined set of assumptions.
After several different scenarios have been developed, the
decision maker determines which is most likely to occur in thefuture and makes decisions accordingly.
Subjective or Interactive Approaches These techniques are often used by committees or panels
seeking to develop new ideas or solve complex problems. They often involve "brainstorming sessions".
It is important in such sessions that any ideas or opinions bepermitted to be presented without regard to its relevancy andwithout fear of criticism.
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Qualitative Approaches(continued)
Subjective or Interactive Approaches These techniques are often used by committees or panels
seeking to develop new ideas or solve complex problems.
They often involve "brainstorming sessions". It is important in such sessions that any ideas or opinions be
permitted to be presented without regard to its relevancy andwithout fear of criticism.
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Quantitative Approaches toForecasting
Quantitative methods are based on an analysis of historical dataconcerning one or more time series.
A time series is a set of observations measured at successive
points in time or over successive periods of time. If the historical data used are restricted to past values of the series
that we are trying to forecast, the procedure is called a time seriesmethod.
If the historical data used involve other time series that are believedto be related to the time series that we are trying to forecast, theprocedure is called a causal method.
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Time Series Data
Time Series Data is usually plotted on a graphto determine the various characteristics or
components of the time series data. There are 4 Major Components: Trend,
Cyclical, Seasonal, and Irregular Components.
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Data Patterns
Trends accounts for the gradual shifting of thetime series over a long period of time.
Seasonality of the series accounts for regular
patterns of variability within certain time periods,such as over a year.
CycleAny regular pattern of sequences of valuesabove and below the trend line is attributable
Random fluctuation series is caused by short-term, unanticipated and non-recurring factors thataffect the values of the time series.
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Data Patterns
Horizontal
When there is no trend in the data pattern, wedeal with horizontal data pattern.
Mean
Time
ForecastVariable
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Data Patterns
Trend
Long-term growth movement of a time series
t t
tt
YtYt
Yt Yt
Trend Trend
Trend
Trend
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Data Patterns
Seasonal Pattern
A predictable and repetitive movement observedaround a trend line within a period of 1 year or
less.
Time
Forecas
tVariable
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Data Patterns
Cyclical
Occurs with business and economic expansionsand contractions.
Lasts longer than 1 year.
Correlated with business cycles.
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Smoothing Methods: MovingAverage
Moving Average MethodThe moving average method consists of
computing an average of the most recent n
data values for the series and using thisaverage for forecasting the value of the timeseries for the next period.
Error in Forecasting
Measures the average error that can be expected over time.ttt
YYe
n
e
n
t
t
1
2)(
MSE
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Moving Averages
Diamond Garden SuppliesForecasting
Period ActualValue Three-Month Moving Averages
January 10
February 12
March 16
April 13 10 + 12 + 16 / 3 = 12.67
May 17 12 + 16 + 13 / 3 = 13.67
June 19 16 + 13 + 17 / 3 = 15.33July 15 13 + 17 + 19 / 3 = 16.33
August 20 17 + 19 + 15 / 3 = 17.00
September 22 19 + 15 + 20 / 3 = 18.00
October 19 15 + 20 + 22 / 3 = 19.00
November 21 20 + 22 + 19 / 3 = 20.33
December 19 22 + 19 + 21 / 3 = 20.67
Storage Shed Sales
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Moving Averages Forecast
Diamond Garden SupplyForecasting 3 period moving average
Input Data Forecast Error Analysis
Period Actual Value Forecast Error
Absolute
error
Squared
errorMonth 1 10
Month 2 12
Month 3 16
Month 4 13 12.667 0.333 0.333 0.111
Month 5 17 13.667 3.333 3.333 11.111
Month 6 19 15.333 3.667 3.667 13.444
Month 7 15 16.333 -1.333 1.333 1.778
Month 8 20 17.000 3.000 3.000 9.000
Month 9 22 18.000 4.000 4.000 16.000
Month 10 19 19.000 0.000 0.000 0.000
Month 11 21 20.333 0.667 0.667 0.444
Month 12 19 20.667 -1.667 1.667 2.778
Average 1.333 2.000 6.074
Next period 19.667 BIAS MAD MSE
Actual Value - Forecast
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Weighted Moving Average
This is a variation on the simple moving average where insteadof the weights used to compute the average being equal, theyare not equal
This allows more recent demand data to have a greater effecton the moving average, therefore the forecast
The weights must add to 1.0 and generally decrease in valuewith the age of the data
The distribution of the weights determine impulse response ofthe forecast
1tF
= w1Y
t+ w
2Y
t-1+w
3Y
t-2+ + w
nY
t-n+1
Swi= 1
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Weighted Moving AverageDiamond Garden SupplyForecasting
Period
Actual
Value Weights Three-Month Weighted Moving Averages
January 10 0.222February 12 0.593
March 16 0.185
April 13 2.2 + 7.1 + 3 / 1 = 12.298
May 17 2.7 + 9.5 + 2.4 / 1 = 14.556
June 19 3.5 + 7.7 + 3.2 / 1 = 14.407
July 15 2.9 + 10 + 3.5 / 1 = 16.484
August 20 3.8 + 11 + 2.8 / 1 = 17.814
September 22 4.2 + 8.9 + 3.7 / 1 = 16.815
October 19 3.3 + 12 + 4.1 / 1 = 19.262
November 21 4.4 + 13 + 3.5 / 1 = 21.000
December 19 4.9 + 11 + 3.9 / 1 = 20.036
Next period 20.185
Sum of weights = 1.000
Storage Shed Sales
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Weighted Moving Average
Diamond Garden Supply Forecasting 3 period weighted moving average
Input Data Forecast Error Analysis
Period Actual value Weights Forecast Error
Absolute
error
Squared
errorMonth 1 10 0.222
Month 2 12 0.593
Month 3 16 0.185
Month 4 13 12.298 0.702 0.702 0.492
Month 5 17 14.556 2.444 2.444 5.971
Month 6 19 14.407 4.593 4.593 21.093
Month 7 15 16.484 -1.484 1.484 2.202
Month 8 20 17.814 2.186 2.186 4.776Month 9 22 16.815 5.185 5.185 26.889
Month 10 19 19.262 -0.262 0.262 0.069
Month 11 21 21.000 0.000 0.000 0.000
Month 12 19 20.036 -1.036 1.036 1.074
Average 1.988 6.952 6.952
Next period 20.185 BIAS MAD MSE
Sum of weights = 1.000
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Following data is available about actual sales for the past 13 years.
YR 1 2 3 4 5 6 7 8 9 10 11 12 13
Sales 2.3 2.2 2 2.25 2.6 3 4.1 3.8 4 4.3 4.2 4.8 5.2
Find the Forecast for the yr 14 using Two Years as well as threeyears moving averages. Which of the two forecasts is more reliable on
the basis of Mean Squared Error (MSE) criterion ?
Moving Average - Example
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Weighted Moving Average
Vacuum cleaner sales for 12 months is given below. Theowner of the supermarket decides to forecast sales byweighting the past 3 months as follows
Wt Applied Month
3 Last month
2 Two months ago
1 Three months ago
Months 1 2 3 4 5 6 7 8 9 10 11 12
Actualsales(units)
10 12 13 16 19 23 26 30 28 18 16 14
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