Reference no: EM132848119

The following problem: During any hour, and potential reaches a certain service facility with probability 1/3. And it is found that there are two people in the facility (including the one being serviced), the potential customer leaves the facility immediately and never comes back. However, if there are less than 2, go in and become a real customer. The installation manager has two service configurations available. At the beginning of each hour you must make the decision of which of the two to use or decide whether to turn off the equipment. The "slow" configuration is used at a cost of $ 7 and there are customers present during the period, and will continue with probability 4/7. If you use the "fast" configuration at a cost of $ 12 and there are customers present during that hour, you will be served with probability 6/7. When the equipment is shut down, it is considered a cost of $ 9 because when it is started again there is a very high peak in power consumption. The probability that more than one customer will arrive or more than one will be served during an hour is zero. When the customer leaves the facility they are charged $ 45 for the service.

a) Raise the Markov chain associated with the system and the basic elements of the general model of Markovian decision processes

b) How many possible valid policies are there?

c) What is the ideal method to obtain the optimal policy and why?

d) Carry out two iterations using the discounted cost criterion with an interest rate of 0.3% per period