1. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast 1180175 2168 3159 4175 5190 6205 7180 8182 9?

2. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using  =0.10 1180175 2168176= 175.00+0.10(180-175) 3159175 =175.50+0.10(168-175.50) 4175173 =174.75+0.10(159-174.75) 5190173 =173.18+0.10(175-173.18) 6205175 =173.36+0.10(190-173.36) 7180178 =175.02+0.10(205-175.02) 8182178 =178.02+0.10(180-178.02) 9? 179= 178.22+0.10(182-178.22)

3. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using  =0.50 1180175 2168178 =175.00+0.50(180-175) 3159173 =177.50+0.50(168-177.50) 4175166 =172.75+0.50(159-172.75) 5190170 =165.88+0.50(175-165.88) 6205180 =170.44+0.50(190-170.44) 7180193 =180.22+0.50(205-180.22) 8182186 =192.61+0.50(180-192.61) 9? 184 =186.30+0.50(182-186.30)

4. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example To evaluate the accuracy of each smoothing constant, we can compute the absolute deviations and MADs.

5. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Selecting a Smoothing Constant

6. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Port of Baltimore Exponential Smoothing Example Based on this analysis, a smoothing constant of  =0.10 is preferred to  =0.50 because its MAD is smaller.

7. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Trend Projections A trend line is simply a linear regression equation in which the independent variable (X) is the time period. The form is a = - b

8. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company Let us consider the case of Midwestern Manufacturing Company. That firm's demand for electrical generators over the period 1996- 2002 is shown in the table below: YearSales 199674 199779 199880 199990 2000105 2001142 2002122

9. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company A trend line to predict demand (Y) based on the period can be developed using a regression model. We let 1996 be time period 1 (X = 1) then 1997 is time period 2 (X = 2), and so forth. YearTimeSales 1996174 1997279 1998380 1999490 20005105 20016142 20027122

10. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company Time period Generator demand XY 1 741 2 794158 3 809240 4 9016360 5 10525525 6 14236852 712249854

11. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna Example/ Midwestern Manufacturing Company a = 98.86- 10.54(4)=56.7 Hence, the least squares trend equation is Y= 56.70 + 10.54 X. To project demand in 2003, we first denote the year 2003 in our new coding system as X = 8 (sales in 2003) = 56.7 + 10.54 (8) = 141 generators (sales in 2004) = 56.7 + 10.54 (9) = 152 generators