Forecasting Chapter 15 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15-1 Chapter Topics ■Forecasting Components ■Time Series Methods ■Forecast Accuracy ■Time Series Forecasting Using Excel ■Time Series Forecasting Using QM for Windows ■Regression Methods Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15-2 Forecasting Components ■ A variety of forecasting methods are available for use depending on the time frame of the forecast and the existence of patterns ■ Time Frames: Short-range (one to two months) Medium-range (two months to one or two years) Long-range (more than one or two years) ■ Patterns: Trend Random variations Cycles Seasonal pattern Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15-3 Forecasting Components Patterns (1 of 2) Trend - A long-term movement of the item being forecast Random variations - movements that are not predictable and follow no pattern Cycle - A movement, up or down, that repeats itself over a lengthy time span Seasonal pattern - Oscillating movement in demand that occurs periodically in the short run and is repetitive Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15-4 Forecasting Components Patterns (2 of 2) Figure 15.1 (a) Trend; (b) Cycle; (c) Seasonal; (d) Trend w/Season Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15-5 Forecasting Components Forecasting Methods Times Series - Statistical techniques that use historical data to predict future behavior Regression Methods - Regression (or causal ) methods that attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does Qualitative Methods - Methods using Copyright © 2010 Pearson Education, Inc Publishing as expertise and opinion to make Prenticejudgment, Hall 15-6 Forecasting Components Qualitative Methods “Jury of executive opinion,” a qualitative technique, is the most common type of forecast for long-term strategic planning Performed by individuals or groups within an organization, sometimes assisted by consultants and other experts, whose judgments and opinions are considered valid for the forecasting issue Usually includes specialty functions such as marketing, engineering, purchasing, etc in which individuals have experience and knowledge of the forecasted item Supporting techniques include the Delphi Method, 15-7 market research, surveys, etc Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Time Series Methods Overview Statistical techniques that make use of historical data collected over a long period of time Methods assume that what has occurred in the past will continue to occur in the future Forecasts based on only one factor - time Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15-8 Time Series Methods Moving Average (1 of 5) Moving average uses values from the recent past to develop forecasts This dampens or smoothes random increases and decreases Useful for forecasting relatively stable items that not display any trend or seasonal pattern Formula for: n ∑ Di MA = i=1 n n where : n = number of periods in the moving average D = data in period i i Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15-9 Time Series Methods Moving Average (2 of 5) Example: Instant Paper Clip Supply Company forecast of orders for the month of November Three-month moving average: ∑ Di MA = i=1 = 90 +110 +130 =110 orders 3 Five-month moving average: ∑ Di MA = i=1 = 90 +110 +130 + 75 + 50 = 91 orders 5 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Regression Analysis with Excel (6 of 6) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 15.13 15- Multiple Regression with Excel (1 of 4) Multiple regression relates demand to two or more independent variables General form: y = β0 + β 1x1 + β 2x2 + + β kxk where β β = the intercept β k = parameters representing contributions of the independent variables x1 xk = independent variables Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Multiple Regression with Excel (2 of 4) State University example: Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Multiple Regression with Excel (3 of 4) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 15.14 15- Multiple Regression with Excel (4 of 4) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall Exhibit 15.15 15- Example Problem Solution Computer Software Firm (1 of 4) Problem Statement: For data below, develop an exponential smoothing forecast using α = 40, and an adjusted exponential smoothing forecast using α = 40 and β = 20 Compare the accuracy of the forecasts using MAD and cumulative error Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Example Problem Solution Computer Software Firm (2 of 4) Step 1: Compute the Exponential Smoothing Forecast Ft+1 = α Dt + (1 - α)Ft Step 2: Compute the Adjusted Exponential Smoothing Forecast AFt+1 = Ft +1 + Tt+1 Tt+1 = β(Ft +1 - Ft) + (1 - β)Tt Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Example Problem Solution Computer Software Firm (3 of 4) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Example Problem Solution Computer Software Firm (4 of 4) Step 3: Compute the MAD Values Dt − Ft 41.97 ∑ MAD(Ft ) = = = 5.99 n ∑ Dt − AFt 37.39 MAD( AFt ) = = = 5.34 n Step 4: Compute the Cumulative Error E(Ft) = 35.97 E(AFt) = 30.60 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Example Problem Solution Building Products Store (1 of 5) For the following data: Develop a linear regression model Determine the strength of the linear relationship using correlation Determine a forecast for lumber given 10 building permits in the next quarter Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Example Problem Solution Building Products Store (2 of 5) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Example Problem Solution Building Products Store (3 of 5) Step 1: Compute the Components of the Linear Regression Equation x = 92 = 92 10 y = 128.6 =12.86 10 b = ∑ xy − n x y = (1,290.3) − (10)(9.2)(12.86) =1.25 2 ( 932 ) − ( 10 )( ) x − n x ∑ a = y − b x =12.86 − (1.25)(9.2) =1.36 Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Example Problem Solution Building Products Store (4 of 5) Step 2: Develop the Linear regression equation y = a + bx, y = 1.36 + 1.25x Step 3: Compute the Correlation Coefficient r= n∑ xy − ∑ x∑ y 2 n x − ∑ x n∑ y − (∑ y ) ∑ r= (10)(1,170.3) − (92)(128.6) (10)(932) − (92)(92) (10)(1,810.48) − (128.6) Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall = 925 15- Example Problem Solution Building Products Store (5 of 5) Step 4: Calculate the forecast for x = 10 permits Y = a + bx = 1.36 + 1.25(10) = 13.86 or 1,386 board ft Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- Copyright © 2010 Pearson Education, Inc Publishing as Prentice Hall 15- ... forecast can be developed by multiplying the normal forecast by a seasonal factor ■ A seasonal factor can be determined by dividing the actual demand for each seasonal period by total annual demand:... historical data to predict future behavior Regression Methods - Regression (or causal ) methods that attempt to develop a mathematical relationship between the item being forecast and factors... slowly to changes in demand than shorterperiod moving averages The appropriate number of periods to use often requires trial-and-error experimentation Moving average does not react well to changes