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 product lines. Here is demand over the past 12 quarters:

   

TWO YEARS AGO	UNITS	LAST YEAR	UNITS	THIS YEAR	UNITS
I	4,793	I	3,493	I	3,196
II	3,493	II	2,693	II	2,097
III	4,293	III	3,493	III	2,693
IV	2,993	IV	2,393	IV	1,693

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

For decomposition analysis, Demand D_t is the function of (trend, seasonality and irregular component).

Trend is average of demand from Jan to Current month demand;

Seasonality is calculated as Demand for current month / average of trend for entire year; and then take the average of entire seasonality factor S_t, which will be used for Irregular component.

Irregular component is seasonality component of current month divided by seasonality component for entire year S_t.

Thus,calculating the same we have -

Year	Quarter	Current Month Demand	Trend	Seasonality	Irregular component
1	1	4793.00	4793.00	1.00	1.24
1	2	3493.00	4143.00	0.84	1.05
1	3	4293.00	4193.00	1.02	1.27
1	4	2993.00	3893.00	0.77	0.96
2	1	3196.00	3753.60	0.85	1.06
2	2	2097.00	3477.50	0.60	0.75
2	3	2693.00	3365.43	0.80	1.00
2	4	1693.00	3156.38	0.54	0.67

hus we have trend, seasonality and irregular component .

Using the seasonality and irregular component same for the next year and updating trend;

Forecasted demand D_t? = Trend*Seasonality component 1 year back*Irregular component 1 year back, we have -

Year	Quarter	Current Month Demand	Trend	Seasonality	irregular component	Forecast for next period
1	1	4793.00	4793.00	1.00	1.24
1	2	3493.00	4143.00	0.84	1.05
1	3	4293.00	4193.00	1.02	1.27
1	4	2993.00	3893.00	0.77	0.96
2	1	3196.00	3753.60	0.85	1.06
2	2	2097.00	3477.50	0.60	0.75
2	3	2693.00	3365.43	0.80	1.00
2	4	1693.00	3156.38	0.54	0.67	2848.40
3	1	2848.40	3122.16			1413.23
3	2	1413.23	2951.26			2352.31
3	3	2352.31	2896.81			1037.41
3	4	1037.41	2741.86

Thus forecast is -

Period	Forecast (units)
I	2848.40
II	1413.23
III	2352.31
IV	1037.41