Question

Zeus Computer Chips, Inc., used to have major contracts to produce the Centrino-type chips. The market has been declining during the past three years because of the dual-core chips, which it cannot produce, so Zeus has the unpleasant task of forecasting next year. The task is unpleasant because the firm has not been able to find replacement chips for its production lines. Here is demand over the past 12 quarters: TWO YEARS AGO UNITS LAST YEAR UNITS THIS YEAR UNITS I 4,785 I 3,495 I 3,210 II 3,475 II 2,696 II 2,078 III 4,195 III 3,475 III 2,705 IV 2,995 IV 2,375 IV 1,695 Use the decomposition technique to forecast demand for the next four quarters. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Period Forecast (Units) I II III IV

Answer 1

Decomposition -the process of isolating linear trend and seasonal factors to develop an accurate forecast

Step 1

First find whether there is a trend by creating a line chart out of data.

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In this data there is an obvious downward trend

Also notice a peak in 1 and 3 rd quarters (seasonality)

Step 2

When there is a trend, we use Centered moving average method to calculate seasonal index (When there is no trend we use a simple method)

• First we find CMA for each quarter and corresponding seasonal ratio
• Find CMA of a quarter- we have to use data of four quarters, with average centered around that quarter.

So we have to take 1.5 quarters before and 1.5 quarters after the required quarter to calculate CMA (so that we get four quarters of an year) E.g.

CMA of quarter 3= ( (0.5)*4785+3475+4195+2995+ (0.5)*3495 )/ 4

Seasonal ratio= Actual demand/CMA

Seasonal index of a quarter = average of seasonal ratios of the corresponding quarter

Step 3

De-seasonalize data by divining the demand by corresponding seasonal index. This shows the demand for the quarter, without seasonal effect

Step 4

Find a trend line using this de-seasonalized data

step 5

• Unadjusted forecast is made using trend line equation
• then it is multiplied by seasonal index to find the forecast adjusted for seasonality