A hospital orders its blood from a regional blood bank.

Each year, the hospital uses an average of 1040 pints of type O blood. Each order placed with the regional blood bank incurs a cost of $250. The lead time for each order is five days. It costs the hospital $20 to hold one pint of blood in inventory for a year. The stockout cost per pint is estimated to be $50. Annual demand for type O blood is normally distributed with standard deviation 43.26 pints.

a. Determine the optimal order quantity, reorder point, and safety stock level. Assume that 365 days equal one year and that all demand is backlogged.

b. What service level requirement (from model 2) is equivalent to this $50 stockout cost?