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Mad Exponential Smoothing

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Mad Exponential Smoothing


1. **State the problem:** We are given actual demand and forecast values for 10 weeks using exponential smoothing with $\alpha=0.60$ and initial forecast 21.0. 2. **Recall the formula for MAD (Mean Absolute Deviation):** $$\text{MAD} = \frac{1}{n} \sum_{t=1}^n |\text{Demand}_t - \text{Forecast}_t|$$ where $n=10$ weeks. 3. **Calculate absolute errors for each week:** - Week 1: $|21 - 21.0| = 0.0$ - Week 2: $|21 - 21.0| = 0.0$ - Week 3: $|27 - 21.0| = 6.0$ - Week 4: $|38 - 24.6| = 13.4$ - Week 5: $|25 - 32.64| = 7.64$ - Week 6: $|28 - 28.06| = 0.06$ - Week 7: $|36 - 28.02| = 7.98$ - Week 8: $|20 - 32.81| = 12.81$ - Week 9: $|25 - 25.12| = 0.12$ - Week 10: $|28 - 25.05| = 2.95$ 4. **Sum the absolute errors:** $$0 + 0 + 6 + 13.4 + 7.64 + 0.06 + 7.98 + 12.81 + 0.12 + 2.95 = 50.96$$ 5. **Calculate MAD:** $$\text{MAD} = \frac{50.96}{10} = 5.10$$ **Final answer:** The MAD for the exponential smoothing forecast is **5.10** (rounded to two decimal places).