The copy center at the college of business at State University has become an increasingly contentious item among the college administrators. The department heads have complained to the associate dean about the long lines and waiting times for their secretaries at the copy center. They claim that it is a waste of scarce resources for the secretaries to stand in line talking when they could be doing more productive work in the office. Alternatively, Handford Burris, the associate dean, says the limited operating budget will not allow the college to purchase a new copier, or several copiers, to relieve the problem. This standoff has been going on for several years.
To make her case for improved copying facilities, Lauren Moore, the department head for management science, assigned students a class project to gather some information about the copy center. The students were to record the arrivals at the center and the length of time it took to do a copy job once the secretary actually reached a copy machine. In addition, the students were to describe how the copy center system worked.
When the students completed the project, they turned in a report to Professor Moore. The report described the copy center as containing two machines. When secretaries arrived for a copy job, they joined a queue, which looked more like milling around to the students. But they acknowledged that the secretaries knew when it was their turn, and, in effect, they formed a single queue for the first available copy machine. Also, because copy jobs are assigned tasks, secretaries always stayed to do the job, no matter how long the line was or how long they had to wait. They never left the queue.
From the data the students gathered, Professor Moore is able to determine that secretaries arrive every 8 minutes for a copy job and that the arrival rate is Poisson distributed. Furthermore, she was able to determine that the average time it takes to complete a job is 12 minutes and that this is exponentially distributed.
Using her own personnel records and some data from the university's personnel office, Dr. Moore determines that a secretary's average salary is $8.50 per hour. From her academic calendar she adds up the actual days in the year when the college and departmental offices are open and finds there are 247. However, as she adds up working days, it occurs to her that during the summer months, the workload is much lighter, and the copy center also probably gets less traffic. The summer includes about 70 days, during which she expects the copy center traffic to be about half of what it is during the normal year, but she speculates that the average time of a copying job remains about the same.
Professor Moore next calls a local office supply firm to check the prices on copiers. A new copier of the type in the copy center now would cost $36,000. It would also require $8,000 per year for maintenance and would have a normal useful life of 6 years.
Do you think Dr. Moore will be able to convince the associate dean that a new copier machine will be cost-effective?