In an exponentially weighted moving average, what will the forecast demand for April be if the smoothing constant is 0.8?

In an exponentially weighted moving average (EWMA), the forecast for the next period is calculated using the equation:

[ F_t = \alpha D_{t-1} + (1 - \alpha) F_{t-1} ]

where:

• ( F_t ) is the forecast for the current period,

• ( D_{t-1} ) is the actual demand from the previous period,

• ( F_{t-1} ) is the forecast for the previous period,

• ( \alpha ) is the smoothing constant.

In this scenario, with a smoothing constant of 0.8, the formula emphasizes recent data much more than older data, allowing the forecast to respond quickly to changes in demand.

Assuming the actual demand for March is known (let's say it was 1200 units), and if the forecast for March (from February) was 1000 units, the calculation for April would proceed as follows:

1. Using the known values:

• ( \alpha = 0.8 )

• ( D_{March} = 1200 )

• ( F_{March} = 1000 )

2. Plugging into the formula:

\