BlueD is an online retailer for high-quality game audio equipment. Recently, customers around the Chicago area have increasing complaints about the delays in receiving the orders of the Snowball USB microphone, a popular item. BlueD collected 40 weeks of past demands and would like improve the stocking policy for the distribution center located at suburb Chicago. The demand data is given in the following table. BlueD believes that the weekly customer demand is stable and is about normally distributed.
The inventory record is reviewed on a weekly basis. A purchasing order is issued every Tuesday and the manufacturer delivers on the Tuesday three weeks later. The purchasing price is $115 with the shipping cost paid by the manufacturer. The online selling price is $199. The average storage cost for each microphone is $1.5. When stockout happens, BlueD provides the each customer a $10 voucher for store credit for every week of delay in fulfilling the customer order. Not all customers end up using the voucher. The past experience suggests that about 72% of the issued vouchers are redeemed. The capital cost for the company is 0.5% per week. Note that the cash for invoice payment is reserved immediately upon placing the order.
Q1 What is the optimal OUT level? (Rounded to whole number)
Q2 Suppose that BlueD decided to maintain a (type I) service level of 75%, what is the corresponding OUT level?
Historical Inventory Data
Week	Demand
1	573
2	548
3	497
4	548
5	381
6	635
7	520
8	449
9	562
10	585
11	448
12	768
13	226
14	607
15	681
16	507
17	385
18	513
19	659
20	244
21	403
22	485
23	500
24	304
25	242
26	538
27	573
28	393
29	563
30	392
31	566
32	701
33	587
34	380
35	528
36	296
37	399
38	531
39	582
40	538