Question

Check my work Problem 3-34 points A manager uses a trend equation plus quarterly relatives to predict demand. Quarter relatives are SR = 0.9, SR2 = 0.95, SR3 = 1.05, and SR4 = 1.1. The trend equation is: Ft= 10 + 3t. Over the past nine quarters, demand has been as follows: eBook Print Period, t: Demand: 1 2 3 4 5 6 7 8 9 15 17 19 23 25 27 32 36 41 References Compute the MAD and tracking signal for each period. (Negative values should be indicated by a minus sign. Round your intermediate calculations and final answers to 3 decimal places.) Period, t Demand MAD Tracking signal 19

Answer 1

The first step is to find the trend adjusted forecast using the trend equation F_t = 10 + 3t .

The trend adjusted forecast is then multiplied with the corresponding quarter relatives to obtain the seasonalized trend adjusted forecast.

Period, t	Demand	Trend adjusted forecast	Seasonalized adjusted forecast
1	15	10 + 3 x 1 = 13	13 x 0.9 = 11.7
2	17	10 + 3 x 2 = 16	16 x 0.95 = 15.2
3	19	10 + 3 x 3 = 19	19 x 1.05 = 19.95
4	23	10 + 3 x 4 = 22	22 x 1.1 = 24.2
5	25	10 + 3 x 5 = 25	25 x 0.9 = 22.5
6	27	10 + 3 x 6 = 28	28 x 0.95 = 26.6
7	32	10 + 3 x 7 = 31	31 x 1.05 = 32.55
8	36	10 + 3 x 8 = 34	34 x 1.1 = 37.4
9	41	10 + 3 x 9 = 37	37 x 0.9 = 33.3

Period, t	Demand	Seasonalized adjusted forecast	Error = Actual demand - forecast demand	Cumulative error	Absolute forecast error	Cumulative absolute forecast error	MAD = Cumulative absolute forecast error $\div$ period	Tracking signal = Cumulative error $\div$ MAD
1	15	11.7	3.3	3.3	3.3	3.3	3.3	1
2	17	15.2	1.8	5.1	1.8	5.1	2.55	2
3	19	19.95	-0.95	4.15	0.95	6.05	2.017	2.058
4	23	24.2	-1.2	2.95	1.2	7.25	1.813	1.627
5	25	22.5	2.5	5.45	2.5	9.75	1.95	2.795
6	27	26.6	0.4	5.85	0.4	10.15	1.692	3.457
7	32	32.55	-0.55	5.3	0.55	10.7	1.529	3.466
8	36	37.4	-1.4	3.9	1.4	12.1	1.513	2.578
9	41	33.3	7.7	11.6	7.7	19.8	2.2	5.273