1. (6 points) Daily demand for the ice creams at I-Scream parlor is normally distributed with a mean of 160 quarts and a standard deviation of 100 quarts. The owner has the ice cream supplied by a wholesaler who charges $2.20 per quart. The ice cream sells for $4 per quart. The wholesaler charges a $400 delivery charge independent of order size. It takes 4 days for an order to be supplied. The opportunity cost of capital to I-Scream is estimated to be 25% per year. Assume 360 days in the year.

(a) The optimal order size of each order is (in quarts):

D = 160 x 360 quarts per year, S = $400, h = 0.25 $ per year, C = $2.20, H = hC = 0.25 x 2.20 = $0.55 per quart per year

EOQ = sqrt ( ( 2 D S)/H) = sqrt ( (2 x 160 x 360 x 400)/0.55) = 9153

(b) The owner would like to ensure no stock-outs in 95% of the cycles (i.e., the service level is 95%). The safety stock the store should have is (in quarts):

SS = z σ sqrt(L) = 1.645 x 100 x sqrt(4) = 329

(c) Currently the owner orders 4000 quarts of ice cream when they have 1680 quarts on hand. Compute the total annual inventory cost including the cost of holding the safety stock.

Ordering cost = D/Q S = (160 x 360)/4000 x 400 = $5,760/year

Cycle inventory = Q/2 = 4000/2 = 2000; safety stock = ROP – mean leadtime demand = 1680 – 160 x 4 = 1040 Total inventory = 2000 + 1040 = 3040 (i.e., cycle inventory + safety stock) Annual inventory holding cost = 3040 x 0.55 = $1672/year

Total annual inventory cost = 5,760 + 1672 = $7,432 per year

2. [6 points] A small cafeteria serves four customers per hour. There is one server who takes twelve minutes to serve a customer. State what type of queueing system this is and compute the average number of customers in queue. If the cost of waiting to be served is $15 per hour to a customer compute the expected cost of customers waiting in line. What is the 99%