Question: A dentist is buying sterilized cotton wool in boxes. Her annual consumption of cotton wool is normally distributed with a mean value of 3200 and a standard deviation of 150. For each order the supplier charges a fixed cost of $120 and a unit purchasing cost of $0.5. Shipment time whenever an order is made is exactly 22 days. Inventory holding cost is $3 per year per box. In case of any stock-out there is a backordering cost of $9 per box. (Assume that 1 year equals 365 days.)

a) Is demand during lead time a normally distributed random variable? If yes, what are the parameters of the distribution of lead-time-demand?

b) What will be the expected annual cost if Q=800 and R=200 boxes? What will be a and b (service level policy 1 and policy 2 values) with this choice of decision variables?

c) What should be the reorder level if the dentist is willing to fix the probability of not having any backorders in any order cycle as 0.75? What will be the expected annual cost? (Choose EOQ value for the order quantity using average annual demand.)

d) What should be the reorder level if the dentist fixes the fill rate (annual percentage fulfilled from the stocks) to 98%? What will be the expected annual cost? (Choose EOQ value for the order quantity using average annual demand.)

e) (What will be the optimal order lot-size and reorder level for cotton wool boxes. What will be the optimal expected annual cost?

f) If you use the optimal (Q,R) pair found in part-a, what will be the: (i) average inventory level during any cycle, and (ii) expected number of shortages in one year.