1. An Integrated Goods and Services Approach
OPERATIONS MANAGEMENT
An Integrated Goods and Services Approach
CHAPTER 11
Forecasting Models and Analysis
JAMES R. EVANS
AND
DAVID A. COLLIER
Operations Management/Ch. 11 Forecasting Models and Analysis
©2007 Thomson South-Western

2. Chapter 11 Learning Objectives
To understand the need for forecasts and the implications of information technology for forecasting in the value chain.
To understand the basic elements of forecasting, namely, the choice of planning horizon, different types of data patterns, and how to calculate forecasting errors.
To be aware of different forecasting approaches and methods.
To understand basic time-series forecasting methods, be aware of more advanced methods, and use spreadsheet models to make forecasts.

3. Chapter 11 Learning Objectives
To learn the basic ides and method of regression analysis.
To understand the role of human judgment in forecasting and when judgmental forecasting is most appropriate.
To know that judgment and quantitative forecast methodologies can complement one another, and therefore improve overall forecast accuracy.

4. Chapter 11 Forecasting Models and Analysis
Forecasting is the process of projecting the values of one or more variables into the future.
Poor forecasting can result in poor inventory and staffing decisions, resulting in part shortages, inadequate customer service, and many customer complaints.

5. Chapter 11 Forecasting Models and Analysis
Many firms integrate forecasting with value chain and capacity management systems to make better operational decisions. Good forecasting and demand planning systems result in
higher capacity utilization,
reduced inventories and costs,
more efficient process performance,
more flexibility,
improved customer service, and
increased profit margins.

6. Chapter 11 Forecasting Models and Analysis
Accurate forecasts are needed throughout the value chain, and are used by all functional areas of the organization, including accounting, finance, marketing, operations, and distribution.

7. Chapter 11 Forecasting Models and Analysis
One of the biggest problems with forecasting systems is that they are driven by different departmental needs and incentive systems.
Demand planning software systems integrate marketing, inventory, sales, operations planning, and financial data.

8. Exhibit 11.1
The Need for Forecasts in a Value Chain

9. Chapter 11 Forecasting Models and Analysis
SAP Demand Planning module enables companies to integrate planning information from different departments or organizations into a single demand plan. The software offers these key capabilities:
Multilevel Planning
Data Analysis
Statistical Forecasting
Trade Promotion Support
Collaborative Demand Planning
Collaborative demand planning is information-sharing across the entire value chain.

10. Exhibit 11.2
Impact of Collaborative Demand Planning

11. Chapter 11 Forecasting Models and Analysis
Basic Concepts in Forecasting
The planning horizon is the length of time on which a forecast is based. This spans from short-range forecasts with a planning horizon of under 3 months to long-range forecasts of 1 to 10 years.

12. Chapter 11 Forecasting Models and Analysis
Basic Concepts in Forecasting
A time series is a set of observations measured at successive points in time or over successive periods of time. A time series pattern may have one or more of the following five characteristics:
Trend
Seasonal
Cyclical
Random Variation
Irregular (one time) Variation

13. Exhibit 11.3
Linear Trend of Industrial Photographic Equipment
A trend is the underlying pattern of growth or decline in a time series.

14. Exhibit 11.4
Example of Linear and Nonlinear Trend Patterns

15. Exhibit 11.5
Seasonal Pattern of Home Natural Gas Usage
Seasonal patterns are characterized by repeatable periods of ups and downs over short periods of time.

16. Exhibit 11.6
Trend and Business Cycle Characteristics (each data point is 1 year apart)
Cyclical patterns are regular patterns in a data series that take place over long periods of time.

17. Chapter 11 Forecasting Models and Analysis
Basic Concepts in Forecasting
Random variation (sometimes called noise) is the unexplained deviation of a time series from a predictable pattern, such as a trend, seasonal, or cyclical pattern. Because of these random variations, forecasts are never 100 percent accurate.

18. Chapter 11 Forecasting Models and Analysis
Basic Concepts in Forecasting
Irregular variation is one-time variation that is explainable. For example, a hurricane can cause a surge in demand for building materials, food, and water.
The next example shows a time series of data representing call volumes over 24 quarters from a call center at a major financial institution. The data is plotted in Exhibit 8.

19. Exhibit 7.7
Exhibit 11.7
Call Center Volume

20. Exhibit 11.8
Chart of Call Volume
There is an increasing trend over the six years along with seasonal patterns within each year.

21. Chapter 11 Forecasting Models and Analysis
Forecast error (et) is the difference between the observed value of the time series and the forecast, or At – Ft.
Mean Square Error (MSE)
Mean Absolute Deviation Error (MAD)
Mean Absolute Percentage Error (MAPE)

22. Exhibit 11.9
Forecast Error of Example Time Series Data

23. Chapter 11 Forecasting Models and Analysis
Forecast Errors and Accuracy
A major difference between MSE and MAD is that MSE is influenced much more by large forecasts errors than by small errors (because errors are squared).
MAPE is different in that the measurement scale factor is eliminated by dividing the absolute error by the time-series value data. This makes the measure easier to interpret.
The selection of the best measure of forecast accuracy is not a simple matter; indeed, forecasting experts often disagree on which measure should be used.

24. Chapter 11 Forecasting Models and Analysis
Types of Forecasting Approaches
Judgmental forecasting relies upon opinions and expertise of people in developing forecasts.
Statistical forecasting is based on the assumption that the future will be an extrapolation of the past.
Many commercial software packages and general statistical analysis programs, such as SPSS, Minitab, and SAS, have forecasting features or modules. Various other stand-alone software packages exist that automate some of these tasks.

25. Exhibit 11.10
Classification of Basic Forecasting Methods

26. Chapter 11 Forecasting Models and Analysis
Statistical Forecasting Models
The following list explains some of the basic and more popular statistical forecasting models.
Single Moving Average
Weighed Moving Average
Single Exponential Smoothing
When trend or seasonal factors exist, several other methods are used. These models include:
Double Moving Average
Double Exponential Smoothing
Season Additive or Multiplicative
Holt-Winters Additive
Holt-Winters Multiplicative

27. Chapter 11 Forecasting Models and Analysis
Single Moving Average
A moving average (MA) forecast is an average of the most recent “k” observations in a time series.
MA methods work best for short planning horizons when there is no major trend, seasonal, or business cycle patterns.
As the value of “k” increases, the forecast reacts slowly to recent changes in the time series data.
A weighted moving average allows a forecaster to put more weight on recent observations than older observations.

28. Exhibit 11.11
Gas-Mart Milk Sales Time-Series Data

29. Exhibit 11.12
Summary of 3-Month Moving-Average Forecasts

30. Exhibit 11.13
Milk-Sales Forecast Error Analysis

31. Exhibit 11.14
Results of Excel Moving Average Tool (note misalignment of forecasts with the time series)

32. Exhibit 11.15
Comparison of 3-Month Moving Average and Weighted Moving Average Models

33. Chapter 11 Forecasting Models and Analysis
Single Exponential Smoothing
This is a forecast technique that uses a weighted average of past time-series values to forecast the value of the time series in the next period.
The forecast “smoothes out” the irregular fluctuations in the time series.

34. Chapter 11 Forecasting Models and Analysis
Single Exponential Smoothing
As the number of data points increases, the weights associated with older data get progressively smaller.
CBPredictor is an Excel add-on for forecasting. CBPredictor will run each forecasting method you select and will recommend the one that best forecasts your data.

35. Exhibit 11.16
Summary of Single Exponential Smoothing Milk-Sales Forecasts with α = 0.2

36. Exhibit 11.17
Graph of Single Exponential Smoothing Milk-Sales Forecasts with α = 0.2

37. Exhibit 11.18
CBPredictor Input Data Dialog

38. Exhibit 11.19
CBPredictor Methods Gallery Dialog

39. Exhibit 11.20
Portions of CBPredictor Report Worksheet

40. Exhibit 11.21
Data Attributes Tab of CBPredictor Dialog

41. Exhibit 11.22
CBPredictor Results

42. Chapter 11 Forecasting Models and Analysis
Regression analysis is a method for building a statistical model that defines a relationship between a single dependent variable and one or more independent variables, all of which are numerical.
Yt = a + bt
Simple linear regression finds the best values of a and b using the method of least squares.
Excel provides a very simple tool to find the best-fitting regression model for a time series by selecting the Add Trendline option from the Chart menu.

43. Exhibit 11.23
Call Center Volume Forecasts for Year 7

44. Exhibit 11.24
Factory Energy Costs

45. Exhibit 11.25
Add Trendline Dialog

46. Exhibit 11.26
Add Trendline Options Tab

47. Exhibit 11.27
Least-Squares Regression Model for Energy Cost Forecasting

48. Exhibit 11.28
Gasoline Sales Data

49. Exhibit 11.29
Chart of Sales Versus Time

50. Exhibit 11.30
Multiple Regression Results

51. Chapter 11 Forecasting Models and Analysis
Judgmental Forecasting
When no historical data is available, only judgmental forecasting is possible.
The Delphi approach consists of forecasting by expert opinion by gathering judgments and opinions of key personnel based on their experience and knowledge of the situation.

52. Chapter 11 Forecasting Models and Analysis
Judgmental Forecasting
Another common approach to gathering data is a survey. Sample sizes are usually much larger than with Delphi; however, the cost of such surveys can be high.
The major reasons for using judgmental methods are:
Greater accuracy,
Ability to incorporate unusual or one-time events, and
The difficultly of obtaining the data necessary for quantitative techniques.

53. Chapter 11 Forecasting Models and Analysis
Forecasting in Practice
Managers use a variety of judgmental and quantitative forecasting techniques.
Statistical methods alone cannot account for such factors as sales promotions, competitive strategies, unusual economic disturbances, new products, large one time orders, natural disasters or labor complications.

54. Chapter 11 Forecasting Models and Analysis
Forecasting in Practice
The first step in developing a practical forecast is to understand the purpose, time horizon, and level of aggregation.
Different forecasting methods require different levels of technical ability and understanding of mathematical principles and assumptions.

55. Chapter 11 Solved Problem #1
Develop a three-period and four-period moving-average forecasts and single exponential smoothing forecasts. Compute the MAD, MAPE, and MSE for each. Which method provides a better forecast?
Period
Demand 1 86 7 91 2 93 8 3 88 9 96 4 89 10 97 5 92 11 6 94 12 95

56. Chapter 11 Solved Problem #1
Based on the three error metrics (MAD, MSE, MAPE) the 3-month moving average is the best method among these three.

57. Chapter 11 Solved Problem #2
Average attendance figures at a major university's home football games have generally been increasing as the team’s performance and popularity has been improving:
Year Attendance
1 26,000
2 30,000
3 31,500
4 40,000
5 33,000
6 32,200
7 35,000

58. Chapter 11 Solved Problem #2
Solution
The forecast for the next year (Year 8) would be
Attendance = 1175(8) = 37,229
However, Year 4 appears to be an unusual value, or “outlier.” Outliers can significantly change the results. If we delete this value, we obtain the model Y = 1175x with R2 = 0.82.
The forecast would be 1175(8) = 35,983.
Checking for outliers is an important preliminary step before doing regression. However, you should only delete outliers for logical reasons. Here, if the large attendance was because of a cross-state rivalry that was a one-time event, then it should not be included in the model.

59. Exhibit 11.31
Data for Solved Problem #3

60. Exhibit 11.32
Example Call Volume Data by Day for BankUSA (see the file BankUSA Forecasting Case Data.xls on the Student CD-ROM)

61. Exhibit 11.33
Help Desk Inquiry Volumes by Hour of Day (B)