forecasting introduction
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Forecasting Introduction. An essential aspect of managing any organization is planning for the future. Organizations employ forecasting techniques to determine future inventory, costs, capacities, and interest rate changes. There are two basic approaches to forecasting: -Qualitative - PowerPoint PPT PresentationTRANSCRIPT
Forecasting Introduction
An essential aspect of managing any organization is planning for the future.
Organizations employ forecasting techniques to determine future inventory, costs, capacities, and interest rate changes.
There are two basic approaches to forecasting:
-Qualitative
-Quantitative
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
few weeks cycles, seasonality, and trend may have
little effect random fluctuation is main data pattern
Qualitative Approaches to Forecasting
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.
Scenario Writing Subjective or Interactive
Approaches
Quantitative Approaches to Forecasting
Quantitative methods are based on an analysis of historical data concerning 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 series method.
If the historical data used involve other time series that are believed to be related to the time series that we are trying to forecast, the procedure is called a causal method.
Time series data-Data Patterns
Trends accounts for the gradual shifting of the time 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.
Cycle Any regular pattern of sequences of values above and below the trend line is attributable
Random fluctuation series is caused by short-term, unanticipated and non-recurring factors that affect the values of the time series.
Smoothing Methods: Moving Average
Moving Average MethodThe moving average method
consists of computing an average of the most recent n data values for the series and using this average for forecasting the value of the time series for the next period.Error in Forecasting
Measures the average error that can be expected over time.
ttt YYe ˆ
n
en
tt
1
2 )(
MSE
Moving AveragesDiamond Garden SuppliesForecasting
PeriodActual Value Three-Month Moving Averages
January 10February 12March 16April 13 10 + 12 + 16 / 3 = 12.67May 17 12 + 16 + 13 / 3 = 13.67June 19 16 + 13 + 17 / 3 = 15.33July 15 13 + 17 + 19 / 3 = 16.33August 20 17 + 19 + 15 / 3 = 17.00September 22 19 + 15 + 20 / 3 = 18.00October 19 15 + 20 + 22 / 3 = 19.00November 21 20 + 22 + 19 / 3 = 20.33December 19 22 + 19 + 21 / 3 = 20.67
Storage Shed Sales
Moving Averages ForecastDiamond Garden SupplyForecasting 3 period moving average
Input Data Forecast Error Analysis
Period Actual Value Forecast ErrorAbsolute
errorSquared
errorMonth 1 10Month 2 12Month 3 16Month 4 13 12.667 0.333 0.333 0.111Month 5 17 13.667 3.333 3.333 11.111Month 6 19 15.333 3.667 3.667 13.444Month 7 15 16.333 -1.333 1.333 1.778Month 8 20 17.000 3.000 3.000 9.000Month 9 22 18.000 4.000 4.000 16.000Month 10 19 19.000 0.000 0.000 0.000Month 11 21 20.333 0.667 0.667 0.444Month 12 19 20.667 -1.667 1.667 2.778
Average 1.333 2.000 6.074Next period 19.667 BIAS MAD MSE
Actual Value - Forecast
Weighted Moving Average This is a variation on the simple moving average where
instead of the weights used to compute the average being equal, they are not equal
This allows more recent demand data to have a greater effect on the moving average, therefore the forecast
The weights must add to 1.0 and generally decrease in value with the age of the data
The distribution of the weights determine impulse response of the forecast
1tF = w1Yt + w2Yt-1 +w3Yt-2 + …+ wnYt-n+1
wi = 1
Weighted Moving AverageDiamond Garden SupplyForecasting
PeriodActual Value Weights Three-Month Weighted Moving Averages
January 10 0.222February 12 0.593March 16 0.185April 13 2.2 + 7.1 + 3 / 1 = 12.298May 17 2.7 + 9.5 + 2.4 / 1 = 14.556June 19 3.5 + 7.7 + 3.2 / 1 = 14.407July 15 2.9 + 10 + 3.5 / 1 = 16.484August 20 3.8 + 11 + 2.8 / 1 = 17.814September 22 4.2 + 8.9 + 3.7 / 1 = 16.815October 19 3.3 + 12 + 4.1 / 1 = 19.262November 21 4.4 + 13 + 3.5 / 1 = 21.000December 19 4.9 + 11 + 3.9 / 1 = 20.036
Next period 20.185
Sum of weights = 1.000
Storage Shed Sales
Weighted Moving Average
Diamond Garden Supply Forecasting 3 period weighted moving average
Input Data Forecast Error Analysis
Period Actual value Weights Forecast ErrorAbsolute
errorSquared
errorMonth 1 10 0.222Month 2 12 0.593Month 3 16 0.185Month 4 13 12.298 0.702 0.702 0.492Month 5 17 14.556 2.444 2.444 5.971Month 6 19 14.407 4.593 4.593 21.093Month 7 15 16.484 -1.484 1.484 2.202Month 8 20 17.814 2.186 2.186 4.776Month 9 22 16.815 5.185 5.185 26.889Month 10 19 19.262 -0.262 0.262 0.069Month 11 21 21.000 0.000 0.000 0.000Month 12 19 20.036 -1.036 1.036 1.074
Average 1.988 6.952 6.952Next period 20.185 BIAS MAD MSE
Sum of weights = 1.000
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 13Sales
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 “three years” moving averages. Which of the two forecasts is more reliable on
the basis of Mean Squared Error (MSE) criterion ?
Moving Average - Example
Weighted Moving Average Vacuum cleaner sales for 12 months is given below.
The owner of the supermarket decides to forecast sales by weighting 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
Actual sales (units)
10 12 13 16 19 23 26 30 28 18 16 14
Exponential Smoothing The weights used to compute the forecast (moving
average) are exponentially distributed The forecast is the sum of the old forecast and a portion
of the forecast error
Ft = Ft-1 + (At-1-Ft-1) The smoothing constant, , must be between 0.0 and
1.0 A large provides a high impulse response forecast A small provides a low impulse response forecast
New Forecast = (Actual Demand) + (1-)(Old Forecast)
Exponential Smoothing Data
PeriodActual
Value(Yt) Ŷt-1 α Yt-1 Ŷt-1 Ŷt
January 10 = 10 0.1February 12 10 + 0.1 *( 10 - 10 ) = 10.000March 16 10 + 0.1 *( 12 - 10 ) = 10.200April 13 10.2 + 0.1 *( 16 - 10.2 ) = 10.780May 17 10.78 + 0.1 *( 13 - 10.78 ) = 11.002June 19 11.002 + 0.1 *( 17 - 11.002 ) = 11.602July 15 11.602 + 0.1 *( 19 - 11.602 ) = 12.342August 20 12.342 + 0.1 *( 15 - 12.342 ) = 12.607September 22 12.607 + 0.1 *( 20 - 12.607 ) = 13.347October 19 13.347 + 0.1 *( 22 - 13.347 ) = 14.212November 21 14.212 + 0.1 *( 19 - 14.212 ) = 14.691December 19 14.691 + 0.1 *( 21 - 14.691 ) = 15.322
Storage Shed Sales
Exponential Smoothing (Alpha = .42)
Input Data Forecast Error Analysis
Period Actual value Forecast ErrorAbsolute
errorSquared
errorMonth 1 10 10.000Month 2 12 10.000 2.000 2.000 4.000Month 3 16 10.838 5.162 5.162 26.649Month 4 13 13.000 0.000 0.000 0.000Month 5 17 13.000 4.000 4.000 16.000Month 6 19 14.675 4.325 4.325 18.702Month 7 15 16.487 -1.487 1.487 2.211Month 8 20 15.864 4.136 4.136 17.106Month 9 22 17.596 4.404 4.404 19.391Month 10 19 19.441 -0.441 0.441 0.194Month 11 21 19.256 1.744 1.744 3.041Month 12 19 19.987 -0.987 0.987 0.973
Average 2.608 9.842Alpha 0.419 MAD MSE
Next period 19.573
Exponential Smoothing - example
Estimate the trend values using the data given by taking a 4 yr moving average. In January a city hotel predicted a February demand for 142 room occupancy. Actual February demand was 153 rooms. Using
α= .20 forecast the march demand using exponential smoothing method