Question

16) Sales of tablet computers at Ted​ Glickman's electronics store in​ Washington, D.C., over the past 10 weeks are shown in the table​below:

                                                                                                                     

Week	1	2	3	4	5	6	7	8	9	10
Demand	20	21	27	38	26	29	37	24	25	29

​a) The forecast for weeks 2 through 10 using exponential smoothing with alphaα ​= 0.55 and a week 1 initial forecast of 20.0 are ​(round your responses to two decimal​ places):

Week	1	2	3	4	5	6	7	8	9	10
Demand	20	21	27	38	26	29	37	24	25	29
Forecast	20.0	....	....	....	....	....	....	....	....	....

- THIS QUESTION HAS EXTRA STEPS SO PLEASE BE PREPARED TO ANSWER THE OTHER PARTS AS WELL....

Answer 1

(a) Here for weeks 2 through 10 usng exponential smoothing with alpha = α = 0.55

initital forecast = 20.0

here if F_t+1 is the forecast of (t+1) week, F_t is the forecst of t week and y_t is the actual forecast for t^th week.

F_t+1 = α y_t + (1 - α) F_t

so here

F₂ = 0.55 * 20 + 0.45 * 20 = 20

F₃ = 0.55 * 21 + 0.45 * 20 = 20.55

F₄ = 0.55 * 27 + 0.45 * 20.55 = 24.0975

F₅ = 0.55 * 38 + 0.45 * 24.0975 = 31.744

F₆ = 0.55 * 26 + 0.45 * 31.744 = 28.585

F₇ = 0.55 * 37 + 0.45 * 28.585 = 28.813

F₈ = 0.55 * 37 + 0.45 * 28.813 = 33.316

F₉ = 0.55 * 24 + 0.45 * 33.316= 28.192

F₁₀ = 0.55 * 25 + 0.45 * 28.192 = 26.436

F₁₁ = 0.55 * 29 + 0.45 * 26.436 = 27.846

Week	Demand	Forecast
1	20	20
2	21	20
3	27	20.55
4	38	24.0975
5	26	31.74388
6	29	28.58474
7	37	28.81313
8	24	33.31591
9	25	28.19216
10	29	26.43647