Luxe is a new optic store located in Florence which has been operating for a couple of years. Luxe is open for six days in a week and assume there are 48 weeks in a year. There are two types of glasses that Luxe sells: regular glasses and sunglasses. The distributors for both glasses are in China. It costs 3000 to place an order for regular glasses and 4000 to place an order for sunglasses. The lead time of the orders is expected to be six weeks. The orders of the regular glasses and sunglasses are independent from each other.

For the sunglasses, Luxe keeps the data of monthly sales. Most of the sunglasses are sold in summer and the sales considerably increase in December and January due to the skiing season. Luxe purchases sunglasses for 60 per unit and sells them for 150 per unit. The holding cost for sunglasses is 6 per unit per month. In Case 1, you forecasted the monthly demand and computed the forecast error term for the normally distributed demand values. The forecasted demand values for the coming year you found using the best forecasting procedure are given in the following table. Based on your results, you assume that the standard deviation of the monthly demand is 9 (constant regardless of the month).

For the sunglasses, compute a safety stock level by targeting a 95% Type 1 service level as if it was a continuous review system. However, since there is more uncertainty in a periodic review system compared to the continuous review counterpart, use the demand distribution over the response time rather than the lead time (the response time is the sum of the lead time and the length of one period). Hence, the 95% Type 1 service level implies that the probability of the response time demand exceeding the reorder level should be 0.05. Thus, you compute the reorder level from the service level definition and deduct the expected response time demand to obtain the safety stock level.

Months Jan Demand 105 Feb 64 March April May June July Aug Sep 65 93 113 122 67 Oct 61 Nov Dec 26 74 76 66