Operations Management: Processes and Supply Chains, 12th Edition

Key Equations

Forecast Error

1. 1. Forecast error measures:

   $$\begin{array}{ccc}{E}_t& =& D_t-F_t\\ \text{CFE}& =& \Sigma E_t\\ \overline{E}& =& \frac{\text{CFE}}{n}\\ \text{MSE}& =& \frac{\Sigma E_t^2}{n}\end{array}$$

   $$\begin{array}{ccc}\sigma & =& \sqrt{\frac{\Sigma {(E_t-\overline{E})}^2}{n-1}}\\ \text{MAD}& =& \frac{\Sigma \left|E_t\right|}{n}\\ \text{MAPE}& =& \frac{(\Sigma |E_t|/D_t)(100\%)}{n}\end{array}$$

Causal Methods: Linear Regression

1. 2. Linear regression:

   $$Y=a+bX$$

Time-Series Methods

1. 3. Naïve forecasting:

   $$\text{Forecast}=D_t$$

2. 4. Simple moving average:

   $$F_{t+1}=\frac{D_t+D_{t-1}+D_{t-2}+\cdot \cdot \cdot +D_{t-n+1}}{n}$$

3. 5. Weighted moving average:

   $$F_{t+1}={\text{Weight}}_1\left(D_t\right)+{\text{Weight}}_2\left(D_{t-1}\right)+{\text{Weight}}_3\left(D_{t-2}\right)+\mathrm{.\; .\; .}+{\text{Weight}}_n\left(D_{t-n+1}\right)$$

4. 6. Exponential smoothing:

   $$F_{t+1}=\alpha D_{}$$