Ogunmodede Medical Company stocks medical devices for hospitals in the state of Colorado. The average rate of demand for the prostheses is 100 per month and appears to be described quite well by a Normal distribution with standard deviation of 10. The procurement lead-time τ = 6 months. Each medical device costs $2,000. The cost of placing an order with the manufacturer, incoming inspection, etc. is estimated to be $100.00. The annual inventory carrying cost rate is 0.20. All stock outs are backordered. It is difficult to estimate the cost of being out of stock. Instead, it is required that the probability of being out of stock not be greater than 0.0005.

(a) If the facility is to operate as a [Q, r] system, determine Q∗ and r ∗ .

(b) What is the imputed cost of a backorder π?

(c) What is the cost of uncertainty?