A certain large shop doing light fabrication work uses a single central storage facility (dispatch station) for material in process storage. The typical procedure is that each employee personally delivers his finished work (by hand, tote box, or hand cart) and receives new work and materials at the facility. Although this procedure worked well in earlier years when the shop was smaller, it appears that it may now be advisable to divide the shop into two semi-independent parts, with a separate storage facility for each one. You have been assigned the job of comparing the use of two facilities and of one facility from a cost standpoint.
The factory has the shape of a rectangle 150 by 100 yards. Thus, by letting 1 yard be the unit of distance, the (x, y) coordinates of the corners are (0, 0), (150, 0), (150, 100), and (0, 100). With this coordinate system, the existing facility is located at (50, 50), and the location available for the second facility is (100, 50).
Each facility would be operated by a single clerk. The time required by a clerk to service a caller has an exponential distribution, with a mean of 2 minutes. Employees arrive at the present facility according to a Poisson input process at a mean rate of 24 per hour. The employees are rather uniformly distributed throughout the shop, and if the second facility were installed, each employee would normally use the nearer of the two facilities. Employees walk at an average speed of about 5,000 yards per hour. All aisles are parallel to the outer walls of the shop. The net cost of providing each facility is estimated to be about $20 per hour, plus $15 per hour for the clerk. The estimated total cost of an employee being idled by traveling or waiting at the facility is $25 per hour.
Given the preceding cost factors, which alternative minimizes the expected total cost?