Key Equations

(5-1)

MAD = \frac{\sum | Forecast error |}{n}

$MAD = \frac{\sum | Forecast error |}{n}$

A measure of overall forecast error called mean absolute deviation.

(5-2)

MSE = \frac{\sum {(Error)}^{2}}{n}

$MSE = \frac{\sum {(Error)}^{2}}{n}$

A measure of forecast accuracy called mean squared error.

(5-3)

MAPE = \frac{\sum | \frac{Error}{Actual} |}{n} 100 %

$MAPE = \frac{\sum | \frac{Error}{Actual} |}{n} 100 %$

A measure of forecast accuracy called mean absolute percent error.

(5-4)

\begin{array}{l} Moving \\ average = \frac{Sum of demands in previous n periods}{n} \\ forecast \end{array}

$\begin{array}{l} Moving \\ average = \frac{Sum of demands in previous n periods}{n} \\ forecast \end{array}$

An equation for computing a moving average forecast.

(5-5)

F_{t + 1} = \frac{Y_{t} + Y_{t - 1} + \dots + Y_{t - n + 1}}{n}

$F_{t + 1} = \frac{Y_{t} + Y_{t - 1} + \dots + Y_{t - n + 1}}{n}$

A mathematical expression for a moving average forecast.

(5-6)

F_{t + 1} = \frac{\sum (Weight in period i) (Actual value in period i)}{\sum (Weights)}

$F_{t + 1} = \frac{\sum (Weight in period i) (Actual value in period i)}{\sum (Weights)}$

An equation for computing a weighted moving average forecast.

(5-7)

F_{t + 1} = \frac{w_{1} Y_{t} + w_{2} Y_{t - 1} + \dots + w_{n} Y_{t - n + 1}}{w_{1} + w_{2} + \dots + w_{n}}

$F_{t + 1} = \frac{w_{1} Y_{t} + w_{2} Y_{t - 1} + \dots + w_{n} Y_{t - n + 1}}{w_{1} + w_{2} + \dots + w_{n}}$

A mathematical expression for a weighted moving average forecast.

(5-8) New forecast $=$ $=$ Last period’s forecast $+ α$ $+ α$ (Last period’s actual demand $-$ $-$ Last period’s forecast)

An equation for computing an exponential smoothing forecast.

(5-9)

F_{t + 1} = F_{t} + α (Y_{t} - F_{t})

$F_{t + 1} = F_{t} + α (Y_{t} - F_{t})$

Equation 5-8 rewritten mathematically.

(5-10)

F_{t + 1} = F I T_{t} + α (Y_{t} - F I T_{t})

$F_{t + 1} = F I T_{t} + α (Y_{t} - F I T_{t})$

Equation to update the smoothed forecast $(F_{t + 1})$ $(F_{t + 1})$ used in the trend-adjusted exponential smoothing model.

(5-11)

T_{t + 1} = T_{t} + β (F_{t + 1} - F I T_{t})

$T_{t + 1} = T_{t} + β (F_{t + 1} - F I T_{t})$

Equation to update the smoothed trend value $(T_{t + 1})$ $(T_{t + 1})$ used in the trend-adjusted exponential smoothing model.

(5-12)

F I T_{t + 1} = F_{t + 1} + T_{t + 1}

$F I T_{t + 1} = F_{t + 1} + T_{t + 1}$

Equation to develop forecast including trend (FIT) in the trend-adjusted exponential smoothing model.

(5-13)

\begin{array}{l} Tracking signal & = & \frac{RSFE}{MAD} \\ = & \frac{\sum (Forecast error)}{MAD} \end{array}

$\begin{array}{l} Tracking signal & = & \frac{RSFE}{MAD} \\ = & \frac{\sum (Forecast error)}{MAD} \end{array}$

An equation for monitoring forecasts with a tracking signal.

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Table of Contents for Key Equations