P times the amount from the previous period PLUS (1-P) times the prediction for the previous period.
Begin a exponential smoothing problem by assuming that the prediction for the first week is equal to the actual outcome for the first week.
For example, look at the data in Demo Problem again.
| Week | Inventory | Week | Inventory | Week | Inventory |
| 1 | 1,210 | 6 | 1,219 | 11 | 1,226 |
| 2 | 1,181 | 7 | 1,205 | 12 | 1,217 |
| 3 | 1,194 | 8 | 1,199 | 13 | 1,214 |
| 4 | 1,207 | 9 | 1,208 | 14 | 1,221 |
| 5 | 1,225 | 10 | 1,215 | 15 | 1,209 |
Assume P = .4 (40%).
EXPONENTIAL SMOOTHING PREDICTION FORMULAS
.4 times previous actual plus (1-.4) times previous prediction
Week 1 prediction: (first prediction assumes actual) = 1210
Week 2 prediction: (.4 * 1210) plus [(1-.4) * 1210] = 1210
Week 3 prediction: (.4 * 1181) plus (.6 * 1210) = 1198.4
Week 4 prediction: (.4 * 1194) plus (.6 * 1198.4) = 1196.64
Week 5 prediction: (.4 * 1207) plus (.6 * 1196.64) = 1200.784
Week 6 prediction: (.4 * 1225) plus (.6 * 1200.784) = 1210.47
etc.
(When you do a problem by hand, round to three decimal places)