Lecture Introduction to Management Science with Spreadsheets: Chapter 2 - Stevenson, Ozgur

Chapter 2 Forecasting, after completing this chapter, you should be able to: Explain the importance of forecasting in organizations, describe the three major approaches to forecasting, use a variety of techniques to make forecasts, measure the accuracy of a forecast over time using various methods,...

Stevenson and Ozgur

First Edition

Introduction to Management Science

2 Describe the three major approaches to forecasting.

3 Use a variety of techniques to make forecasts

4 Measure the accuracy of a forecast over time using

various methods

5 Determine when a forecast can be improved

6 Discuss the main considerations in selecting a

forecasting technique

7 Utilize Excel to solve various forecasting problems

After completing this chapter, you should be able to:

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The Importance of Forecasting

The Importance of Forecasting

• Forecasting

–is important because it helps reduce uncertainty

–provides decision makers with an improved picture of probable future events and, thereby, enable decision makers to plan accordingly

–is used for planning the system itself

–is used for planning the use of the system

–as a process has an inherent tendency for inaccuracy

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The Importance of Forecasting

The Importance of Forecasting

• The Forecasting Process

1 Determine the purpose of the forecast

2 Determine the time horizon

3 Select an appropriate technique

4 Identify the necessary data, and gather it if

necessary

5 Make the forecast

6 Monitor forecast errors in order to determine if the

forecast is performing adequately If it is not, take appropriate corrective action

• Forecasts That Use Time Series Data

–involve the assumption that past experience reflects probable future experience (i.e., the past movements

or patterns in the data will persist into the future)

• Explanatory Models

– incorporate one or more variables that are related to the variable of interest and, therefore, they can be used to predict future values of that variable

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Selecting the Forecasting Technique

Selecting the Forecasting Technique

• Factors affecting the choice of the forecasting technique to be used:

–the importance (purpose) of the forecast

–the desired accuracy of the forecast

–the cost of developing the forecast

–resources available to support and conduct the

forecasting process

–the planning horizon (long- or short-term)

–the sophistication of the users of the forecast

–A good rule is to choose the simplest technique that

gives acceptable results.

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Table 2–7 Forecasting Approaches

Table 2–7 Forecasting Approaches

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Table 2–7 Forecasting Approaches (cont’d)

Table 2–7 Forecasting Approaches (cont’d)

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Figure 2–1 Examples of Simple Patterns Sometimes Found in Time

Series Data Figure 2–1 Examples of Simple Patterns Sometimes Found in Time

Series Data

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Figure 2–2 Data with Trend and Seasonal Variations

Figure 2–2 Data with Trend and Seasonal Variations

Source: E Turban, Jay Aronson, and Ting-Peng Liang, Decision Support Systems and Intelligence Systems, 7th ed (Upper Saddle River, NJ: Prentice Hall, 2005), p 109.

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Figure 2–3 Averaging Applied to Three Possible Patterns

Figure 2–3 Averaging Applied to Three Possible Patterns

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Example 2-1

Example 2-1

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Figure 2–4 A Moving Average Forecast Tends to Smooth and Lag

Changes in the Data Figure 2–4 A Moving Average Forecast Tends to Smooth and Lag

Changes in the Data

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Figure 2–5 The More Periods in a Moving Average, the Greater the

Forecast Will Lag Changes in the Data Figure 2–5 The More Periods in a Moving Average, the Greater the

Forecast Will Lag Changes in the Data

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Example 2-2

Example 2-2

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Exhibit 2-1 Moving Average Input and Output

Exhibit 2-1 Moving Average Input and Output

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Exhibit 2-2 Moving Average Preparation Screen

Exhibit 2-2 Moving Average Preparation Screen

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Figure 2–6 Relative Weights in Exponential Smoothing

Figure 2–6 Relative Weights in Exponential Smoothing

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Figure 2–7 A Small Value of α Will Smooth More Than a Larger Value Figure 2–7 A Small Value of α Will Smooth More Than a Larger Value

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Exhibit 2-3 Exponential Smoothing Input, Output, and Chart

Exhibit 2-3 Exponential Smoothing Input, Output, and Chart

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Exhibit 2-4 Exponential Smoothing Preparation Wizard

Exhibit 2-4 Exponential Smoothing Preparation Wizard

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Table 2–1 Values of Σt, t2, and Σt2

Table 2–1 Values of Σt, t2, and Σt2

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Example 2-3

Example 2-3

Monthly demand for Dan’s Doughnuts

over the past nine months for trays (six

dozen per tray) of sugar doughnuts was

1 Plot the data to determine if a linear

trend equation is appropriate.

2 Obtain a trend equation.

3 Forecast demand for the next two

months.

Solution

1 The data seem to show an upward, roughly linear trend:

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Example 2-3 (cont’d)

Example 2-3 (cont’d)

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Exhibit 2–5 Data for Linear Trend/Regression Analysis

Exhibit 2–5 Data for Linear Trend/Regression Analysis

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Exhibit 2–6 Scatter Plot Development

Exhibit 2–6 Scatter Plot Development

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Exhibit 2–7 Scatter Plot

Exhibit 2–7 Scatter Plot

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Exhibit 2–8 Scatter Plot Titles, Axes, and Labels

Exhibit 2–8 Scatter Plot Titles, Axes, and Labels

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Exhibit 2–9 Scatter Diagram

Exhibit 2–9 Scatter Diagram

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Exhibit 2–10 Scatter Diagram

Exhibit 2–10 Scatter Diagram

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Exhibit 2–11 Regression Output

Exhibit 2–11 Regression Output

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Example 2-4

Example 2-4

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Exhibit 2–12 Trend-Adjusted Exponential Smoothing

Exhibit 2–12 Trend-Adjusted Exponential Smoothing

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Figure 2–8 Naive Approaches with Seasonality

Figure 2–8 Naive Approaches with Seasonality

A seven-period centered moving average is used because there are seven days (seasons) per week.

The estimated Friday relative is 136 + 140 +

133 + 3 + 136 Relative for other days can be computed in a similar manner For example, the estimated Monday relative is 0.77 + 0.72 + 0.69/3 = 0.73

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Figure 2–9 A Centered Moving Average Closely Tracks the Data

Figure 2–9 A Centered Moving Average Closely Tracks the Data

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Example 2-6

Example 2-6

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Exhibit 2–13 Seasonal Relative Computations

Exhibit 2–13 Seasonal Relative Computations

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Explanatory Models

Explanatory Models

• Simple Linear Regression

–A model of two variables thought to be related

• Dependent variable: the variable to be forecasted.

• Independent variable is used to “explain” or predict the value 

of the dependent variable.

• Using the regression approach

–Identify an independent variable or variables

–Obtain a sample of at least 10 observations

–Develop an equation

–Identify any restrictions on predictions

–Measure accuracy in a given forecast

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Table 2–2 Data for Regression Problem

Table 2–2 Data for Regression Problem

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Figure 2–10 A Linear Relationship Appears to Exist

Figure 2–10 A Linear Relationship Appears to Exist

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Table 2–2 Calculations for Regression Coefficients

Table 2–2 Calculations for Regression Coefficients

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Figure 2–11 Graph of Regression Line

Figure 2–11 Graph of Regression Line

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Table 2–4 Selected Values of t.025 for n-2 Degrees of Freedom (df)

Table 2–4 Selected Values of t.025 for n-2 Degrees of Freedom (df)

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Figure 2–12 The Conditional Distributions of y’s Are Assumed to be

Normal Figure 2–12 The Conditional Distributions of y’s Are Assumed to be

Normal

– For any given value of x, there is a distribution of possible y

values that has a mean equal to the expected value (i.e., y = a + bx) and the distribution is normal.

– Values of y should not be correlated over time If they are, it may

be more appropriate to use a time series model.

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Figure 2–13 The Scatter around the Line Is Not Uniform

Figure 2–13 The Scatter around the Line Is Not Uniform

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Figure 2–14 There Should Not Be Any Patterns around the Line

Figure 2–14 There Should Not Be Any Patterns around the Line

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Exhibit 2–14 Linear Regression-Explanatory Model Output

Exhibit 2–14 Linear Regression-Explanatory Model Output

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Table 2–5 Expansion of Data Used in Simple Regression Section

Table 2–5 Expansion of Data Used in Simple Regression Section

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Exhibit 2–15 Input Box for Multiple Regression

Exhibit 2–15 Input Box for Multiple Regression

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Exhibit 2–16 Multiple Regression Output with Excel

Exhibit 2–16 Multiple Regression Output with Excel

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Summarizing Forecast Accuracy Summarizing Forecast Accuracy

• The mean absolute

deviation (MAD)

– measures the average

forecast error over a number

of periods, without regard to

the sign of the error:

• The mean squared error

(MSE)

– is the average squared error

experienced over a number

of periods

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Example 2-7

Example 2-7

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Figure 2–15 Monitoring Forecast Errors

Figure 2–15 Monitoring Forecast Errors

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Relative Measures of Forecast Accuracy

Relative Measures of Forecast Accuracy

• Percentage error (PE)

– for a given time series data

measures the percentage

point deviation of the

forecasted value from the

actual value.

• Mean percentage error

(MPE)

– measures the forecast bias

• Mean absolute percentage

error (MAPE)

– measures overall forecast

accuracy.

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Example 2-8

Example 2-8

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Example 2-8 cont’d

Example 2-8 cont’d

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Example 2-8 cont’d

Example 2-8 cont’d

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Tracking Signal

Tracking Signal

• The tracking signal

–Is the ratio of cumulative forecast error at any point in time to the corresponding MAD at that point in time.–A value of a tracking signal that is beyond the action limits suggests the need for corrective action

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Example 2-9

Example 2-9

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Exhibit 2–17 Measuring Forecast Accuracy Using MAD, MSE, MPE, and

MAPE Exhibit 2–17 Measuring Forecast Accuracy Using MAD, MSE, MPE, and

MAPE

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Table 2–6 Comparison of Types of Forecasts

Table 2–6 Comparison of Types of Forecasts