1. 4 Forecasting PowerPoint presentation to accompany Heizer and Render
Operations Management, 10e
Principles of Operations Management, 8e
PowerPoint slides by Jeff Heyl
© 2011 Pearson Education, Inc. publishing as Prentice Hall

2. ?? What is Forecasting? Process of predicting a future event
Underlying basis of all business decisions
Production
Inventory
Personnel
Facilities ??
© 2011 Pearson Education, Inc. publishing as Prentice Hall

3. Forecasting Time Horizons
Short-range forecast
Up to 1 year, generally less than 3 months
Purchasing, job scheduling, workforce levels, job assignments, production levels
Medium-range forecast
3 months to 3 years
Sales and production planning, budgeting
Long-range forecast
3+ years
New product planning, facility location, research and development
© 2011 Pearson Education, Inc. publishing as Prentice Hall

4. Types of Forecasts Economic forecasts Technological forecasts
Address business cycle – inflation rate, money supply, housing starts, etc.
Technological forecasts
Predict rate of technological progress
Impacts development of new products
Demand forecasts
Predict sales of existing products and services
© 2011 Pearson Education, Inc. publishing as Prentice Hall

5. Forecasting Approaches
Qualitative Methods
Used when situation is vague and little data exist
New products
New technology
Involves intuition, experience
e.g., forecasting sales on Internet
© 2011 Pearson Education, Inc. publishing as Prentice Hall

6. Forecasting Approaches
Quantitative Methods
Used when situation is ‘stable’ and historical data exist
Existing products
Current technology
Involves mathematical techniques
e.g., forecasting sales of color televisions
© 2011 Pearson Education, Inc. publishing as Prentice Hall

7. Overview of Quantitative Approaches
Naive approach
Moving averages
Exponential smoothing
Trend projection
Linear regression
time-series models
associative model
© 2011 Pearson Education, Inc. publishing as Prentice Hall

8. Time Series Forecasting
Set of evenly spaced numerical data
Obtained by observing response variable at regular time periods
Forecast based only on past values, no other variables important
Assumes that factors influencing past and present will continue influence in future
© 2011 Pearson Education, Inc. publishing as Prentice Hall

9. Time Series Components
Trend
Cyclical
Seasonal
Random
© 2011 Pearson Education, Inc. publishing as Prentice Hall

10. Average demand over 4 years
Components of Demand
Trend component
Demand for product or service
| | | |
Time (years)
Seasonal peaks
Actual demand line
Average demand over 4 years
Random variation
Figure 4.1
© 2011 Pearson Education, Inc. publishing as Prentice Hall

11. Trend Component Persistent, overall upward or downward pattern
Changes due to population, technology, age, culture, etc.
Typically several years duration
© 2011 Pearson Education, Inc. publishing as Prentice Hall

12. Seasonal Component Regular pattern of up and down fluctuations
Due to weather, customs, etc.
Occurs within a single year
Number of
Period Length Seasons
Week Day 7
Month Week 4-4.5
Month Day 28-31
Year Quarter 4
Year Month 12
Year Week 52
© 2011 Pearson Education, Inc. publishing as Prentice Hall

13. Cyclical Component Repeating up and down movements
Affected by business cycle, political, and economic factors
Multiple years duration
Often causal or associative relationships
© 2011 Pearson Education, Inc. publishing as Prentice Hall

14. Random Component Erratic, unsystematic, ‘residual’ fluctuations
Due to random variation or unforeseen events
Short duration and nonrepeating
M T W T F
© 2011 Pearson Education, Inc. publishing as Prentice Hall

15. ∑ demand in previous n periods
Moving Average Method
MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing
Provides overall impression of data over time
Moving average =
∑ demand in previous n periods n
© 2011 Pearson Education, Inc. publishing as Prentice Hall

16. Exponential Smoothing
Form of weighted moving average
Weights decline exponentially
Most recent data weighted most
Requires smoothing constant ()
Ranges from 0 to 1
Subjectively chosen
Involves little record keeping of past data
© 2011 Pearson Education, Inc. publishing as Prentice Hall

17. Exponential Smoothing
New forecast = Last period’s forecast
+ a (Last period’s actual demand
– Last period’s forecast)
Ft = Ft – 1 + a(At – 1 - Ft – 1)
where Ft = new forecast
Ft – 1 = previous forecast
a = smoothing (or weighting) constant (0 ≤ a ≤ 1)
© 2011 Pearson Education, Inc. publishing as Prentice Hall

18. Common Measures of Error
Mean Absolute Deviation (MAD)
MAD =
∑ |Actual - Forecast| n
Mean Squared Error (MSE)
MSE =
∑ (Forecast Errors)2 n
© 2011 Pearson Education, Inc. publishing as Prentice Hall

19. Common Measures of Error
Mean Absolute Percent Error (MAPE)
MAPE =
∑100|Actuali - Forecasti|/Actuali n
i = 1
© 2011 Pearson Education, Inc. publishing as Prentice Hall

20. 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
y = a + bx ^
where y = computed value of the variable to be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable ^
© 2011 Pearson Education, Inc. publishing as Prentice Hall

21. Seasonal Variations In Data
The multiplicative seasonal model can adjust trend data for seasonal variations in demand
© 2011 Pearson Education, Inc. publishing as Prentice Hall

22. 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
© 2011 Pearson Education, Inc. publishing as Prentice Hall

23. Associative Forecasting
Forecasting an outcome based on predictor variables using the least squares technique
y = a + bx ^
where y = computed value of the variable to be predicted (dependent variable)
a = y-axis intercept
b = slope of the regression line
x = the independent variable though to predict the value of the dependent variable ^
© 2011 Pearson Education, Inc. publishing as Prentice Hall

24. Associative Forecasting Example
Sales Area Payroll
($ millions), y ($ billions), x
2.0 1
3.0 3
2.5 4
2.0 2
3.5 7
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Sales
Area payroll
© 2011 Pearson Education, Inc. publishing as Prentice Hall

25. Associative Forecasting Example
Sales, y Payroll, x x2 xy
∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5
b = = = .25
∑xy - nxy
∑x2 - nx2
(6)(3)(2.5)
80 - (6)(32)
x = ∑x/6 = 18/6 = 3
y = ∑y/6 = 15/6 = 2.5
a = y - bx = (.25)(3) = 1.75
© 2011 Pearson Education, Inc. publishing as Prentice Hall

26. Associative Forecasting Example
y = x ^
Sales = (payroll)
If payroll next year is estimated to be $6 billion, then:
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Nodel’s sales
Area payroll
3.25
Sales = (6)
Sales = $3,250,000
© 2011 Pearson Education, Inc. publishing as Prentice Hall

27. 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
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Nodel’s sales
Area payroll
3.25
Figure 4.9
© 2011 Pearson Education, Inc. publishing as Prentice Hall

28. Standard Error of the Estimate
Sy,x =
∑(y - yc)2
n - 2
where y = y-value of each data point
yc = computed value of the dependent variable, from the regression equation
n = number of data points
© 2011 Pearson Education, Inc. publishing as Prentice Hall

29. Correlation
How strong is the linear relationship between the variables?
Correlation does not necessarily imply causality!
Coefficient of correlation, r, measures degree of association
Values range from -1 to +1
© 2011 Pearson Education, Inc. publishing as Prentice Hall

30. Correlation Coefficient
nSxy - SxSy
[nSx2 - (Sx)2][nSy2 - (Sy)2]
© 2011 Pearson Education, Inc. publishing as Prentice Hall

31. Correlation Coefficienty x
(a) Perfect positive correlation: r = +1 y x
(b) Positive correlation: 0 < r < 1
Correlation Coefficient
r =
nSxy - SxSy
[nSx2 - (Sx)2][nSy2 - (Sy)2] y x
(c) No correlation: r = 0 y x
(d) Perfect negative correlation: r = -1
© 2011 Pearson Education, Inc. publishing as Prentice Hall

32. For the Nodel Construction example:
Correlation
Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x
Values range from 0 to 1
Easy to interpret
For the Nodel Construction example:
r = .901
r2 = .81
© 2011 Pearson Education, Inc. publishing as Prentice Hall

33. Multiple Regression Analysis
If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables
y = a + b1x1 + b2x2 … ^
Computationally, this is quite complex and generally done on the computer
© 2011 Pearson Education, Inc. publishing as Prentice Hall

34. Multiple Regression Analysis
In the Nodel example, including interest rates in the model gives the new equation:
y = x x2 ^
An improved correlation coefficient of r = .96 means this model does a better job of predicting the change in construction sales
Sales = (6) - 5.0(.12) = 3.00
Sales = $3,000,000
© 2011 Pearson Education, Inc. publishing as Prentice Hall