Question

Unconstraining Using Double Exp Smth (Holt's Model) Cumulative Per iod Sales Level Trend Forecast -0.3 8,000+0.7 (20000) 0.216400-0)+0.8 20000 8,000 0 20,000 20,000 2 1,000 | 16,400 | 19,280 | 35,680 K 44,000 78,000 88,000 106,000 29,000 167,000 179,000 92,000 92,000 92,000 = I 6400 + I 9280 4 6 7

What is the forecasted cumulative sales over all 12 Periods?

Answer 1

		Level	trend	forecast
1	8000	0	20000	20000
2	21000	0.3*8000+0.7*20000          =16400	0.2*(16400-0)+0.8*20000                   =19280	(16400+19280) =35680
3	44000	0.3*21000+0.7*19280        =19796	0.2*(19796-16400)+0.8*19280            =16103.2	(19796+16103.2)      =35899.20
4	78000	0.3*44000+0.7*16103.2     =24472.24	0.2*(24472.24-19796)+0.8*16103.2     =13817.81	(24472.24+13817.81)=38290.05
5	88000	0.3*78000+0.7*13817.81   =33072.47	0.2*(33072.47-24472.24)+0.8*13817.81=12774.29	(33072.47+12774.29)=45846.76
6	106000	0.3*88000+0.7*12774.29   =35342	0.2*(35342-33072.47)+0.8*12774.29   =10673.34	(35342+10673.34)    =46015.24
7	129000	0.3*106000+0.7*10673.34 =39271.34	0.2*(39271.34-35342)+0.8*10673.34   =9324.54	(39271.34+9324.54) =48595.88
8	167000	0.3*129000+0.7*9324.54 =45227.18	0.2*(45227.18-39271.34)+0.8*9324.54 =8650.80	(45227.18+8650.80) =53877.98
9	179000	0.3*167000+0.7*8650.80 =56155.56	0.2*(56155.56-45227.18)+0.8*8650.80 =9106.32	(56155.56+9106.32) =65261.88
10	192000	0.3*179000+0.7*9106.32 =60074.42	0.2*(60074.42-56155.56)+0.8*9106.32 =8068.83	(60074.42+8068.83) =68143.25
11	192000	0.3*192000+0.7*8068.83 =63248.18	0.2*(63248.18-60074.42)+0.8*8068.83 =7089.81	(63248.18+7089.81) =70337.99
12	192000	0.3*192000+0.7*7089.81 =62562.87	0.2*(62562.87-63248.18)+0.8*7089.81 =5534.79	(62562.87+5534.79) =68097.66