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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 3 of 21
Worked examplePractical

Worked example: three months against five months

The class's orders series. Jan 120, Feb 90, Mar 100, Apr 75, May 110, Jun 50, Jul 75, Aug 130, Sep 110, Oct 90.

Forecast November with a three-month and with a five-month moving average, and say what the difference tells you.

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