Logistics Management LSM 730 Lecture 23 Dr. Khurrum S. Mughal.

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Logistics Management LSM 730 Lecture 23 Dr. Khurrum S. Mughal

Moving Average Naive forecast Simple moving average demand in current period is used as next period’s forecast Simple moving average uses average demand for a fixed sequence of periods stable demand with no pronounced behavioral patterns Weighted moving average weights are assigned to most recent data

Exponential Smoothing Ft +1 = Dt + (1 - )Ft where: Ft +1 = forecast for next period Dt = actual demand for present period Ft = previously determined forecast for present period = weighting factor, smoothing constant

Effect of Smoothing Constant 0.0  1.0 If = 0.20, then Ft +1 = 0.20Dt + 0.80 Ft If = 0, then Ft +1 = 0Dt + 1 Ft = Ft Forecast does not reflect recent data If = 1, then Ft +1 = 1Dt + 0 Ft =Dt Forecast based only on most recent data

Classic Time Series Decomposition Model Basic formulation F = T  S  C  R where F = forecast T = trend S = seasonal index C = cyclical index (usually 1) R = residual index (usually 1) CR (2004) Prentice Hall, Inc.

Regression Forecasting Using Bobbie Brooks Sales Data (1) (2) (3) (4) (5) (6)= (2)/(5) Sales period Time Sales (Dt ) Trend value Seasonal Forecast period, t ($000s) Dt  t t2 (Tt ) index ($000s) Summer 1 $9,458 9,458 1 $12,053 0.78 Trans-season 2 11,542 23,084 4 12,539 0.92 Fall 3 14,489 43,467 9 13,025 1.11 Holiday 4 15,754 63,016 16 13,512 1.17 Spring 5 17,269 86,345 25 13,998 1.23 Summer 6 11,514 69,084 36 14,484 0.79 Trans-season 7 12,623 88,361 49 14,970 0.84 Fall 8 16,086 128,688 64 15,456 1.04 Holiday 9 18,098 162,882 81 15,942 1.14 Spring 10 21,030 210,300 100 16,428 1.28 Summer 11 12,788 140,668 121 16,915 0.76 Trans-season 12 16,072 192,864 144 17,401 0.92 Fall 13 ? 17,887 * $18,602 Holiday 14 ? 18,373 * 20,945 Totals 78 176,723 1,218,217 650 N = 12 å Dt å ´ t = 1,218,217 t2 = 650 = ( 176 , 723 / 12 ) = 14 , 726 . 92 = 78 / 12 = 6 . 5 Regression equation is: Tt = 11,567.08 + 486.13t *Forecasted values CR (2004) Prentice Hall, Inc. 8-35

Regression Analysis Basic formulation F = o  1X1  2X2  …  nXn Example Bobbie Brooks, a manufacturer of teenage women’s clothes, was able to forecast seasonal sales from the following relationship F = constant  1(Time)  2(consumer debt ratio) + 3(no. nonvendor accounts) CR (2004) Prentice Hall, Inc.

Combined Model Forecasting Combines the results of several models to improve overall accuracy. Consider the seasonal forecasting problem of Bobbie Brooks. Four models were used. Three of them were two forms of exponential smoothing and a regression model. The fourth was managerial judgement used by a vice president of marketing using experience. Each forecast is then weighted according to its respective error as shown below. Calculation of forecast weights Model type (1) Forecast error (2) Percent of total (3)= 1.0/(2) Inverse of proportion (4)= (3)/48.09 weights MJ 9.0 0.466 2.15 0.04 R 0.7 0.036 27.77 0.58 ES 1 1.2 0.063 15.87 0.33 2 8.4 0.435 2.30 0.05 Total 19.3 1.000 48.09 1.00 CR (2004) Prentice Hall, Inc.

Combined Model Forecasting (Cont’d) type (1) Model forecast (2) Weighting factor (3)= ´ Weighted proportion Regression model (R) $20,367,000 0.58 $11,813,000 Exponential Smoothing ES 1 20,400,000 0.33 6,732,000 Combined exponential smoothing-- regression model (ES 2 ) 17,660,000 0.05 883,000 Managerial judgment (MJ) 19,500,000 0.04 780,000 Weighted average forecast $20,208,000 Weighted Average Fall Season Forecast Using Multiple Forecasting Techniques CR (2004) Prentice Hall, Inc.

Multiple Model Errors CR (2004) Prentice Hall, Inc. 8-38