Explicitly identify the optimal decision policy

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Reference no: EM133430088

Case Study: We have a machine that can be broken or functional. If the machine is functional at the beginning of a week and remains so for the whole week, it brings in an income of $100. On the other hand, if the machine breaks during the week, it does not bring any income for that week. Even if the machine is functional at the beginning of a week, it is possible to carry out preventive maintenance at a cost of $20. It is assumed that this maintenance is carried out instantaneously. If maintenance is done, the machine has a probability of 0.4 to break during the week, while this probability increases to 0.7 if no maintenance is done. If the machine is broken at the beginning of a week, it must be repaired at a cost of $40 or replaced at a cost of $90. Repair and replacement are assumed to be instantaneous. In the case of a repair, the machine has a probability of 0.4 to break during the week. In the case of a replacement, it is guaranteed that the machine will be functional for the whole week. We want to use dynamic programming in order to maximize the expected profit over a period of 4 weeks, assuming that the machine is functional at the beginning of the first week.

Questions:

(a) Define the steps, the states at each step, the possible decisions at each step and the recurrence formula.

(b) Solve the problem defined in (a) using dynamic programming. Explicitly identify the optimal decision policy.

Reference no: EM133430088

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