Problem: Queuing 

Pharma Dev develops and markets new technological products to be used in health care. The development of a new product operates as follows: when a new technology meets the requisite market potential, a new patent is filed. Patents are granted for a period of 12 years starting from the date of issue. Once the patent is filed, the new technology is developed at one of its three independent development centers, and is then launched to the market. Each product is developed at only one center, and each center can only develop a single patented technology at a time.

On average, Pharma Dev files a new patent every 5 months (with standard deviation of 5 months). The average development process lasts 12 months (with standard deviation of 24 months).

a) What is the utilization of Pharma Dev's development facilities?

b) How long does it take for the average technology from filing a patent to the start of the development process?

c) How many years of patent life remain on average when a product is launched to the market?

d) On average how many patented products are undergoing development or waiting to be developed?

Pharma Dev is considering leasing an additional development center to shorten the time to market of patented products. If this center is used in addition to the three centers, by how will the total time-to-market (waiting time plus development time) of a patented product change?

e) After a product is launched to the market, it generates gross margins of US$40 million per year of patent life. After the patent expires, the product generates no gross margins. By how much would leasing the new facility increase Pharma Dev's average total annual gross margins?