ISEN 220 Introduction to Production and Manufacturing Systems

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ISEN 220Introduction to Production and
Manufacturing Systems
12/31/2009
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Texas AM Industrial Engineering
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Trend Projections
Fitting a trend line to historical data points to
project into the medium-to-long-range
Linear trends can be found using the least
squares technique
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Least Squares Method
Figure 4.4
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Least Squares Method
Least squares method minimizes the sum of the
squared errors (deviations)
Figure 4.4
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Least Squares Method
Equations to calculate the regression variables
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Least Squares Example
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Least Squares Example
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Least Squares Example
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Least Squares Requirements

• We always plot the data to insure a linear
  relationship
• We do not predict time periods far beyond the
  database
• Deviations around the least squares line are
  assumed to be random

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The Difficulty with Long-Term Forecasts
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Seasonal Variations In Data
The multiplicative seasonal model can modify
trend data to accommodate seasonal variations in
demand

• Find average historical demand for each season
• Compute the average demand over all seasons
• Compute a seasonal index for each season
• Estimate next years total demand
• Divide this estimate of total demand by the
  number of seasons, then multiply it by the
  seasonal index for that season

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Seasonal Index Example
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Seasonal Index Example
0.957
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Seasonal Index Example
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Seasonal Index Example
Expected annual demand 1,200
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Seasonal Index Example
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San Diego Hospital
Trend Data
Figure 4.6
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San Diego Hospital
Seasonal Indices
Figure 4.7
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San Diego Hospital
Combined Trend and Seasonal Forecast
Figure 4.8
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Associative Forecasting
Used when changes in one or more independent
variables can be used to predict the changes in
the dependent variable
Most common technique is linear regression
analysis
We apply this technique just as we did in the
time series example
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Associative Forecasting
Forecasting an outcome based on predictor
variables using the least squares technique
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Associative Forecasting Example
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Associative Forecasting Example
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Associative Forecasting Example
Sales 1.75 .25(payroll)
If payroll next year is estimated to be 600
million, then
Sales 1.75 .25(6) Sales 325,000
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Standard Error of the Estimate

• A forecast is just a point estimate of a future
  value
• This point is actually the mean of a
  probability distribution

Figure 4.9
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Standard Error of the Estimate
where y y-value of each data point yc compute
d value of the dependent variable, from the
regression equation n number of data points
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Standard Error of the Estimate
Computationally, this equation is considerably
easier to use
We use the standard error to set up prediction
intervals around the point estimate
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Standard Error of the Estimate
Sy,x .306
The standard error of the estimate is 30,600 in
sales
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How to Use Standard Error