Question

A company forecasts the weekly demand of oxygen cylinders using exponential smoothing with smoothing constant $\alpha = 0.2$. The actual demands in Week 1 to Week 4 were 375, 412, 592 and 439 units. The forecast for Week 3 was 500 units. The forecast (in unit) for Week 5 is \(\underline{\hspace{1cm}}\). [in integer]

Hint:

In exponential smoothing, each new forecast moves partway toward the last actual demand based on the smoothing constant $\alpha$.

Answer 1

Correct Answer: 500 - 505

Exponential smoothing formula: \[ F_{t+1} = \alpha D_t + (1-\alpha)F_t \] Given: \[ \alpha = 0.2 \] \[ D_3 = 592, D_4 = 439 \] \[ F_3 = 500 \] Compute forecast for Week 4: \[ F_4 = 0.2(592) + 0.8(500) \] \[ F_4 = 118.4 + 400 = 518.4 \] Now compute forecast for Week 5: \[ F_5 = 0.2(439) + 0.8(518.4) \] \[ F_5 = 87.8 + 414.72 = 502.52 \] Rounded to nearest integer: \[ \boxed{500\text{ to }505} \]