Lecture 18 - Forecasting (Continued). The contents of this chapter include all of the following: Compute three measures of forecast accuracy, develop seasonal indexes, conduct a regression and correlation analysis, use a tracking signal.
Lecture 18 Forecasting (Continued) Books • Introduction to Materials Management, Sixth Edition, J. R. Tony Arnold, P.E., CFPIM, CIRM, Fleming College, Emeritus, Stephen N. Chapman, Ph.D., CFPIM, North Carolina State University, Lloyd M. Clive, P.E., CFPIM, Fleming College • Operations Management for Competitive Advantage, 11th Edition, by Chase, Jacobs, and Aquilano, 2005, N.Y.: McGrawHill/Irwin • Operations Management, 11/E, Jay Heizer, Texas Lutheran University, Barry Render, Graduate School of Business, Rollins College, Prentice Hall Objectives When you complete this chapter you should be able to : Compute three measures of forecast accuracy ỵ Develop seasonal indexes ỵ Conduct a regression and correlation analysis ỵ Use a tracking signal ỵ CommonMeasuresofError Mean Absolute Deviation (MAD) ∑ |Actual - Forecast| MAD = n Mean Squared Error (MSE) ∑ (Forecast Errors)2 MSE = n Common Measures of Error Mean Absolute Percent Error (MAPE) n MAPE = ∑100|Actuali - Forecasti|/Actuali i=1 n Comparison of Forecast Error Quarter Actual Tonnage Unloaded Rounded Forecast with α = 10 180 168 159 175 190 205 180 182 175 175.5 174.75 173.18 173.36 175.02 178.02 178.22 Absolute Deviation for α = 10 5.00 7.50 15.75 1.82 16.64 29.98 1.98 3.78 82.45 Rounded Forecast with α = 50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for α = 50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62 Comparison of Forecast Error ∑ |deviations| Rounded Absolute MADActual = Forecast Deviation n Tonnage with for Quarter Unloaded α = 10 α = 10 For α = 10 180 175 5.00 168 = 82.45/8 175.5 = 10.31 7.50 4For α 159 175 = 190 205 180 182 174.75 50 173.18 173.36 = 98.62/8 175.02 178.02 178.22 = 15.75 1.82 16.64 12.33 29.98 1.98 3.78 82.45 Rounded Forecast with α = 50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for α = 50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62 Comparison of Forecast Error ∑ (forecast errors)2 Rounded Absolute MSE = Actual Forecast Deviation n Tonnage with for Quarter Unloaded α = 10 α = 10 For α = 10 180 175 5.00 168 175.5 = 190.82 7.50 = 1,526.54/8 4For α 159 174.75 175 = 50 173.18 190 173.36 = 1,561.91/8 205 175.02 180 178.02 182 178.22 MAD = 15.75 1.82 16.64 195.24 29.98 1.98 3.78 82.45 10.31 Rounded Forecast with α = 50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for α = 50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62 12.33 Comparison of Forecast Error n ∑100|deviationi|/actuali Rounded Absolute Rounded MAPE =Actual i=1 Quarter Tonnage Unloaded Forecast with α = 10 n Deviation for α = 10 For α180= 10 175 5.00 168 175.5 = 44.75/8 = 7.50 5.59% For 159 α175= 190 205 180 182 174.75 15.75 1.82 50 173.18 173.36 16.64 = 54.05/8 =29.98 6.76% 175.02 178.02 1.98 178.22 3.78 82.45 MAD 10.31 MSE 190.82 Forecast with α = 50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for α = 50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62 12.33 195.24 Comparison of Forecast Error Quarter Actual Tonnage Unloaded Rounded Forecast with α = 10 180 168 159 175 190 205 180 182 175 175.5 174.75 173.18 173.36 175.02 178.02 178.22 MAD MSE MAPE Absolute Deviation for α = 10 5.00 7.50 15.75 1.82 16.64 29.98 1.98 3.78 82.45 10.31 190.82 5.59% Rounded Forecast with α = 50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for α = 50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62 12.33 195.24 6.76% Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified Forecast including (FITt) = trend Exponentially smoothed (Ft) + forecast Exponentially (Tt) smoothed trend ... Step 2: Trend for Month 2 T2 = β(F2 - F1) + (1 - β)T1 T2 = (.4)(12.8 - 11) + (1 - 4)(2) = 72 + 1.2 = 1.92 units Exponential Smoothing with Trend Adjustment Example Month(t) 10 Actual Demand (At) 12 17 20 19... Common Measures? ?of? ?Error Mean Absolute Percent Error (MAPE) n MAPE = ∑100|Actuali - Forecasti|/Actuali i=1 n Comparison? ?of? ?Forecast Error Quarter Actual Tonnage Unloaded Rounded Forecast with α = 10 180 ... with for Quarter Unloaded α = 10 α = 10 For α = 10 180 175 5.00 168 = 82.45/8 175.5 = 10.31 7.50 4For α 159 175 = 190 205 180 182 174.75 50 173 .18 173.36 = 98.62/8 175.02 178.02 178.22 = 15.75