=The plotting machines are highly reliable, with the exception of the four sophisticated ink pens that are built in. The pens constantly clog and jam in a raised or lowered position. When this occurs, the plotter is unusable.

Currently, Brennan Aircraft replaces each pen as it fails. The service manager has, however, proposed replacing all four pens every time one fails.

This should cut down the frequency of plotter failures. At present, it takes one hour to replace one pen.

All four pens could be replaced in two hours. The total cost of a plotter being unusable is $50 per hour.

Each pen costs $8.

If only one pen is replaced each time a clog or jam occurs, the following breakdown data are thought to be valid:

Hours Between Plotter Failures if One Pen is Replaced During a Repair Probability 10 0.05 20 0.15 30 0.15 40 0.20 50 0.20 60 0.15 70 0.10 Based on the service manager’s estimates, if all four pens are replaced each time one pen fails, the probability distribution between failures is as follows:

Hours Between Plotter Failures if all Four Pens are Replaced During a Repair Probability 100 0.15 110 0.25 120 0.35 130 0.20 140 0.00

(a) Simulate Brennan Aircraft’s problem and determine the best policy. Should the firm replace one pen or all four pens on a plotter each time a failure occurs?

(b) Develop a second approach to solving this problem, this time without simulation. Compare the results. How does it affect Brennan’s policy decision using simulation?