Consider the following continuous-time machine operation and repair problem. A machine can be in…

Consider the following continuous-time machine operation and repair problem. A machine can be in one of two states; 0 denotes it is working, 1 that it is broken down. Two operating rates for the machine can be selected, either fast or slow. When the machine operates at the fast rate it yields greater revenue, but breaks down more frequently&#39;than when it operates at the slow rate. Two repair rates are available when the machine is broken down; one slow but cheap, and another fast but expensive.

Assume that failure time and repair time distributions are exponential and independent with failure rates and repair rates as follows.

a. Formulate this as a semi-Markov decision process.

b. Using the approach of Sec. 11.3, find a policy that maximizes the cxpected infinite-horizon discounted reward when the continuous-time discount rate is LY = 0.1.

c. Using the approach of Sec. 11.4, find a policy that maximizes the long-run expected average reward.

d. Give a uniformization of the model and solve it using the approach of Secs. 11.5.2 and 11.5.3.

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