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Sem 5 Prep
← OperationsMoving averages and smoothing

Formulas for this chapter

Simple moving average

MA = SUM(Di) / n

A stable series with no trend or seasonality. Larger n means more smoothing and less responsiveness.

n
Number of periods in the moving average
Di
Actual demand in period i, the n most recent periods

Weighted moving average

WMA = SUM(Wi x Di), with SUM(Wi) = 1.00

When recent periods deserve more weight than older ones. Check the weights sum to 1.00 and that the largest is on the most recent period.

Wi
Weight for period i, between 0 and 1
Di
Demand in period i

Exponential smoothing

F(t) = F(t-1) + alpha ( D(t-1) - F(t-1) ) = alpha x D(t-1) + (1 - alpha) x F(t-1)

When only the last forecast and last actual are available, and the level moves but does not trend. State the starting forecast you assume.

alpha
Smoothing constant between 0 and 1; the fraction of the last error fed back
F(t-1)
Previous period's forecast
D(t-1)
Previous period's actual demand

Alpha and moving-average length

alpha = 2 / (n + 1)

To justify a chosen alpha, or to convert a familiar moving-average length into a smoothing constant.

n
Equivalent number of periods in a moving average
alpha
Smoothing constant with roughly the same behaviour
Step 1 of 21
The ideaTheory

Averaging out the noise

A shop's daily sales bounce around: 40, 55, 38, 61, 44. Tomorrow's number is not going to be any of those exactly.

Take the average of the last few days and the bouncing calms down. That average is the forecast.

The only real decision is how many days to average. A few days follows every wobble; many days ignores real change. Everything in this chapter is that one trade-off, dressed three different ways.

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