2. Chapter 3
Demand Forecasting

3. 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

4. Introduction
Demand estimates for products and services are the starting point for all the other planning in operations management.
Management teams develop sales forecasts based in part on demand estimates.
The sales forecasts become inputs to both business strategy and production resource forecasts.

5. Forecasting is an Integral Part of Business Planning
Inputs:
Market,
Economic,
Other
Demand
Estimates
Forecast
Method(s)
Sales
Forecast
Management
Team
Business
Strategy
Production Resource
Forecasts

6. Some Reasons Why Forecasting is Essential in OM
New Facility Planning – It can take 5 years to design and build a new factory or design and implement a new production process.
Production Planning – Demand for products vary from month to month and it can take several months to change the capacities of production processes.
Workforce Scheduling – Demand for services (and the necessary staffing) can vary from hour to hour and employees weekly work schedules must be developed in advance.

7. Examples of Production Resource Forecasts
Horizon
Time
Span
Item Being
Forecasted
Unit of
Measure
Long
Range
Years
Product Lines,
Factory Capacities
Dollars,
Tons
Medium
Range
Months
Product Groups,
Depart. Capacities
Units,
Pounds
Short
Range
Days,
Weeks
Specific Products,
Machine Capacities
Units,
Hours

8. Qualitative Approaches Quantitative Approaches
Forecasting Methods
Qualitative Approaches
Quantitative Approaches

9. Qualitative Approaches
Usually based on judgments about causal 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
Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events
The approach/method that is appropriate depends on a product’s life cycle stage

10. Qualitative Methods Educated guess intuitive hunches
Executive committee consensus
Delphi method
Survey of sales force
Survey of customers
Historical analogy
Market research scientifically conducted surveys

11. Quantitative Forecasting Approaches
Based on the assumption that the “forces” that generated the past demand will generate the future demand, 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 of time series analysis

12. Time Series Analysis
A time series is a set of numbers where the order or sequence of the numbers is important, e.g., historical demand
Analysis of the time series identifies patterns
Once the patterns are identified, they can be used to develop a forecast

13. Components of a Time Series
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 the period of one year or less.
Random fluctuation (noise) results from random variation or unexplained causes.

14. 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
Week Day 7

15. Quantitative Forecasting Approaches
Linear Regression
Simple Moving Average
Weighted Moving Average
Exponential Smoothing (exponentially weighted moving average)
Exponential Smoothing with Trend (double exponential smoothing)

16. Long-Range Forecasts Time spans usually greater than one year
Necessary to support strategic decisions about planning products, processes, and facilities

17. Simple Linear Regression
Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables.
In simple linear regression analysis there is only one independent variable.
If the data is a time series, the independent variable is the time period.
The dependent variable is whatever we wish to forecast.

18. Simple Linear Regression
Regression Equation
This model is of the form:
Y = a + bX
Y = dependent variable
X = independent variable
a = y-axis intercept
b = slope of regression line

19. Simple Linear Regression
Constants a and b
The constants a and b are computed using the following equations:

20. Simple Linear Regression
Once the a and b values are computed, a future value of X can be entered into the regression equation and a corresponding value of Y (the forecast) can be calculated.

21. Example: College Enrollment
Simple Linear Regression
At 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)

22. Example: College Enrollment
Simple Linear Regression
x y x2 xy
Sx=21 Sy= Sx2=91 Sxy=66.5

23. Example: College Enrollment
Simple Linear Regression
Y = X

24. Example: College Enrollment
Simple Linear Regression
Y7 = (7) = 3.65 or 3,650 students
Y8 = (8) = 3.83 or 3,830 students
Y9 = (9) = 4.01 or 4,010 students
Note: Enrollment is expected to increase by 180
students per year.

25. Simple Linear Regression
Simple linear regression can also be used when the independent variable X represents a variable other than time.
In this case, linear regression is representative of a class of forecasting models called causal forecasting models.

26. Example: Railroad Products Co.
Simple Linear Regression – Causal Model
The manager of RPC wants to project the firm’s sales for the next 3 years. He knows that RPC’s long-range sales are tied very closely to national freight car loadings. On the next slide are 7 years of relevant historical 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.

27. Example: Railroad Products Co.
Simple Linear Regression – Causal Model
RPC Sales Car Loadings
Year ($millions) (millions)

28. Example: Railroad Products Co.
Simple Linear Regression – Causal Model
x y x2 xy
,400 1,140
,225 1,485
,900 1,560
,500 1,875
,900 2,380
,100 3,040
,400 3,960
1, ,425 15,440

29. Example: Railroad Products Co.
Simple Linear Regression – Causal Model
Y = X

30. Example: Railroad Products Co.
Simple Linear Regression – Causal Model
Y8 = (250) = $20.55 million
Y9 = (270) = $22.16 million
Y10 = (300) = $24.56 million
Note: RPC sales are expected to increase by $80,100 for each additional million national freight car loadings.

31. Multiple Regression Analysis
Multiple regression analysis is used when there are two or more independent variables.
An example of a multiple regression equation is:
Y = X X2 – 0.03X3
where: Y = firm’s annual sales ($millions)
X1 = industry sales ($millions)
X2 = regional per capita income ($thousands)
X3 = regional per capita debt ($thousands)

32. Coefficient of Correlation (r)
The coefficient of correlation, r, explains the relative importance of the relationship between x and y.
The sign of r shows the direction of the relationship.
The absolute value of r shows the strength of the relationship.
The sign of r is always the same as the sign of b.
r can take on any value between –1 and +1.

33. Coefficient of Correlation (r)
Meanings of several values of r:
-1 a perfect negative relationship (as x goes up, y goes down by one unit, and vice versa)
+1 a perfect positive relationship (as x goes up, y goes up by one unit, and vice versa)
0 no relationship exists between x and y
a weak positive relationship
a strong negative relationship

34. Coefficient of Correlation (r)
r is computed by:

35. Coefficient of Determination (r2)
The coefficient of determination, r2, is the square of the coefficient of correlation.
The modification of r to r2 allows us to shift from subjective measures of relationship to a more specific measure.
r2 is determined by the ratio of explained variation to total variation:

36. Example: Railroad Products Co.
Coefficient of Correlation
x y x2 xy y2
,400 1,
,225 1,
,900 1,
,500 1,
,900 2,
,100 3,
,400 3,
1, ,425 15,440 1,287.50

37. Example: Railroad Products Co.
Coefficient of Correlation
r = .9829

38. 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.

39. Ranging Forecasts
Forecasts for future periods are only estimates and are subject 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.

40. 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

41. Ranging Forecasts
The standard error (deviation) of the forecast is computed as:

42. Example: Railroad Products Co.
Ranging Forecasts
Recall 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.

43. 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 = n – 2 = 5.
Area in upper tail = .05/2 = .025
Appendix B, Table 2 shows t =

44. Example: Railroad Products Co.
Ranging Forecasts
Step 3: Compute upper and lower limits.
Upper limit = (.5748) = =
Lower limit = (.5748) = =
We are 95% confident the actual sales for year 8 will be between $ and $ million.

45. Seasonalized Time Series Regression Analysis
Select a representative historical data set.
Develop a seasonal index for each season.
Use the seasonal indexes to deseasonalize the data.
Perform lin. regr. analysis on the deseasonalized data.
Use the regression equation to compute the forecasts.
Use the seas. indexes to reapply the seasonal patterns to the forecasts.

46. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales.

47. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
Representative Historical Data Set
Year Qtr. ($mil.) Year Qtr. ($mil.)

48. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
Compute the Seasonal Indexes
Quarterly Sales
Year Q1 Q2 Q3 Q4 Total
Totals
Qtr. Avg
Seas.Ind

49. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
Deseasonalize the Data
Quarterly Sales
Year Q1 Q2 Q3 Q4

50. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
Perform Regression on Deseasonalized Data
Yr. Qtr. x y x2 xy
Totals

51. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
Perform Regression on Deseasonalized Data
Y = X

52. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
Compute the Deseasonalized Forecasts
Y9 = (9) =
Y10 = (10) =
Y11 = (11) =
Y12 = (12) =
Note: Average sales are expected to increase by
.199 million (about $200,000) per quarter.

53. Example: Computer Products Corp.
Seasonalized Times Series Regression Analysis
Seasonalize the Forecasts
Seas. Deseas. Seas.
Yr. Qtr. Index Forecast Forecast

54. Short-Range Forecasts
Time spans ranging from a few days to a few weeks
Cycles, seasonality, and trend may have little effect
Random fluctuation is main data component

55. Evaluating Forecast-Model Performance
Short-range forecasting models are evaluated on the basis of three characteristics:
Impulse response
Noise-dampening ability
Accuracy

56. 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 data are said to have a high impulse response.
A forecast system that responds quickly to data changes necessarily picks up a great deal of random fluctuation (noise).
Hence, there is a trade-off between high impulse response and high noise dampening.

57. 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

58. Monitoring Accuracy
Accuracy of a forecasting approach needs to be monitored to assess the confidence you can have in its forecasts and changes in the market may require reevaluation of the approach
Accuracy can be measured in several ways
Standard error of the forecast (covered earlier)
Mean absolute deviation (MAD)
Mean squared error (MSE)

59. Monitoring Accuracy
Mean Absolute Deviation (MAD)

60. Monitoring Accuracy Mean Squared Error (MSE) MSE = (Syx)2
A small value for Syx means data points are tightly grouped around the line and error range is small.
When the forecast errors are normally distributed, the values of MAD and syx are related:
MSE = 1.25(MAD)

61. Short-Range Forecasting Methods
(Simple) Moving Average
Weighted Moving Average
Exponential Smoothing
Exponential Smoothing with Trend

62. Simple Moving Average An averaging period (AP) is given or selected
The forecast for the next period is the arithmetic average of the AP most recent actual demands
It is called a “simple” average because each period used to compute the average is equally weighted
. . . more

63. Simple Moving Average
It is called “moving” because as new demand data becomes available, the oldest data is not used
By increasing the AP, the forecast is less responsive to fluctuations in demand (low impulse response and high noise dampening)
By decreasing the AP, the forecast is more responsive to fluctuations in demand (high impulse response and low noise dampening)

64. Weighted Moving Average
This is a variation on the simple moving average where the weights used to compute the average are not equal.
This allows more recent demand data to have a greater effect on the moving average, therefore the forecast.
. . . more

65. Weighted 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.

66. 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 (a) of the forecast error (A t-1 - Ft-1).
Ft = Ft-1 + a(A t-1 - Ft-1)
. . . more

67. Exponential Smoothing
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.

68. Example: Central Call Center
Moving Average
CCC wishes to forecast the number of incoming calls it receives in a day from the customers of one of its clients, BMI. CCC schedules the appropriate number of telephone operators based on projected call volumes.
CCC believes that the most recent 12 days of call volumes (shown on the next slide) are representative of the near future call volumes.

69. Example: Central Call Center
Moving Average
Representative Historical Data
Day Calls Day Calls

70. Example: Central Call Center
Moving Average
Use the moving average method with an AP = 3 days to develop a forecast of the call volume in Day 13.
F13 = ( )/3 = calls

71. Example: Central Call Center
Weighted Moving Average
Use the weighted moving average method with an AP = 3 days and weights of .1 (for oldest datum), .3, and .6 to develop a forecast of the call volume in Day 13.
F13 = .1(168) + .3(198) + .6(159) = calls
Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).

72. Example: Central Call Center
Exponential Smoothing
If a smoothing constant value of .25 is used and the exponential smoothing forecast for Day 11 was calls, what is the exponential smoothing forecast for Day 13?
F12 = (198 – ) =
F13 = (159 – ) =

73. Example: Central Call Center
Forecast Accuracy - MAD
Which forecasting method (the AP = 3 moving average or the a = .25 exponential smoothing) is preferred, based on the MAD over the most recent 9 days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call volume.)

74. Example: Central Call Center
AP = a = .25
Day Calls Forec. |Error| Forec. |Error|
MAD

75. Exponential Smoothing with Trend
As we move toward medium-range forecasts, trend becomes more important.
Incorporating a trend component into exponentially smoothed forecasts is called double exponential smoothing.
The estimate for the average and the estimate for the trend are both smoothed.

76. Exponential Smoothing with Trend
Model Form
FTt = St-1 + Tt-1
where:
FTt = forecast with trend in period t
St-1 = smoothed forecast (average) in period t-1
Tt-1 = smoothed trend estimate in period t-1

77. Exponential Smoothing with Trend
Smoothing the Average
St = FTt + a (At – FTt)
Smoothing the Trend
Tt = Tt-1 + b (FTt – FTt-1 - Tt-1)
where: a = smoothing constant for the average
b = smoothing constant for the trend

78. Criteria for Selecting a Forecasting Method
Cost
Accuracy
Data available
Time span
Nature of products and services
Impulse response and noise dampening

79. Criteria for Selecting a Forecasting Method
Cost and Accuracy
There is a trade-off between cost and accuracy; generally, more forecast accuracy can be obtained at a cost.
High-accuracy approaches have disadvantages:
Use more data
Data are ordinarily more difficult to obtain
The models are more costly to design, implement, and operate
Take longer to use

80. Criteria for Selecting a Forecasting Method
Cost and Accuracy
Low/Moderate-Cost Approaches – statistical models, historical analogies, executive-committee consensus
High-Cost Approaches – complex econometric models, Delphi, and market research

81. Criteria for Selecting a Forecasting Method
Data Available
Is the necessary data available or can it be economically obtained?
If the need is to forecast sales of a new product, then a customer survey may not be practical; instead, historical analogy or market research may have to be used.

82. Criteria for Selecting a Forecasting Method
Time Span
What operations resource is being forecast and for what purpose?
Short-term staffing needs might best be forecast with moving average or exponential smoothing models.
Long-term factory capacity needs might best be predicted with regression or executive-committee consensus methods.

83. Criteria for Selecting a Forecasting Method
Nature of Products and Services
Is the product/service high cost or high volume?
Where is the product/service in its life cycle?
Does the product/service have seasonal demand fluctuations?

84. Criteria for Selecting a Forecasting Method
Impulse Response and Noise Dampening
An appropriate balance must be achieved between:
How responsive we want the forecasting model to be to changes in the actual demand data
Our desire to suppress undesirable chance variation or noise in the demand data

85. Reasons for Ineffective Forecasting
Not involving a broad cross section of people
Not recognizing that forecasting is integral to business planning
Not recognizing that forecasts will always be wrong
Not forecasting the right things
Not selecting an appropriate forecasting method
Not tracking the accuracy of the forecasting models

86. Monitoring and Controlling a Forecasting Model
Tracking Signal (TS)
The TS measures the cumulative forecast error over n periods in terms of MAD
If the forecasting model is performing well, the TS should be around zero
The TS indicates the direction of the forecasting error; if the TS is positive -- increase the forecasts, if the TS is negative -- decrease the forecasts.

87. Monitoring and Controlling a Forecasting Model
Tracking Signal
The value of the TS can be used to automatically trigger new parameter values of a model, thereby correcting model performance.
If the limits are set too narrow, the parameter values will be changed too often.
If the limits are set too wide, the parameter values will not be changed often enough and accuracy will suffer.

88. Computer Software for Forecasting
Examples of computer software with forecasting capabilities
Forecast Pro
Autobox
SmartForecasts for Windows
SAS
SPSS
SAP
POM Software Libary
Primarily for
forecasting
Have
Forecasting
modules

89. Forecasting in Small Businesses and Start-Up Ventures
Forecasting for these businesses can be difficult for the following reasons:
Not enough personnel with the time to forecast
Personnel lack the necessary skills to develop good forecasts
Such businesses are not data-rich environments
Forecasting for new products/services is always difficult, even for the experienced forecaster

90. Sources of Forecasting Data and Help
Government agencies at the local, regional, state, and federal levels
Industry associations
Consulting companies

91. Some Specific Forecasting Data
Consumer Confidence Index
Consumer Price Index (CPI)
Gross Domestic Product (GDP)
Housing Starts
Index of Leading Economic Indicators
Personal Income and Consumption
Producer Price Index (PPI)
Purchasing Manager’s Index
Retail Sales

92. Wrap-Up: World-Class Practice
Predisposed to have effective methods of forecasting because they have exceptional long-range business planning
Formal forecasting effort
Develop methods to monitor the performance of their forecasting models
Do not overlook the short run.... excellent short range forecasts as well