QUESTIONS
Be certain to state all assumptions, and be sure to show all of your analyses.
1. Use the monthly sales data over the past 4 years on outdoor swimming pools given below
DATA:
|
99
|
00
|
01
|
02
|
|
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
|
12
8
24
90
74
46
24
14
8
6
6
16
|
8
12
2
120
110
66
28
16
26
14
14
12
|
6
12
44
78
84
62
48
48
24
20
12
18
|
14
20
18
72
78
76
40
14
50
20
16
8
|
a. What are the seasonal indices for each month?
b. What's the "best" forecasting method on the deseasonalized data? Provide a summary table of the different forecast methods you looked at (try at least 3 methods, in addition to any naïve ones you may include), along with whatever error measure you calculated for the methods (e.g., MAD, MAPE, or MSE
c. What's your forecast for January 2003?
2. Joseph must order each year's calendar in August for delivery and eventual sale by December 31st. In previous years, standard Business Calendar sales have ranged from a low of 2000 to a high of 2300, so assume that demand is uniformly distributed between 2000 and 2300. Each calendar costs $17.90 and sells for $25.96, and unsold calendars usually sell out at a 1/2 price sale in January. Assume Joseph can only order in quantities of 50.
a. Write out the algebraic formula for profit as a function of both order quantity (Q) and demand (D).
b. What probability distribution will you use to model the random demand?
c. What is the optimal number to order to maximize Joseph's expected profit? What is the expected profit? Prepare a summary table of your Crystal Ball results (i.e., # ordered with its expected [or average] profit for all the order quantities you try).