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The supply of a certain good is inspected periodically. If an order is placed of size x>0 (integer), the ordering costs are 8+2.x. The delivery time is zero. The demand is stochastic en equals 1 or 2 with probability ½ . Demand in subsequent periods are independent. The size of an order must be such that (a) demand in a period is always satisfied, and (b) the stock at the end of a period never exceeds 2. The holding costs in a period are 2 per unit remaining at the end of a period. Target is to minimize the expected discounted costs over infinite horizon, use discount factor 0.8.
(a) Give the optimality equations for the Markov decision problem.
(b) Give an LP-model that allows you to determine the optimal policy.
(c) Carry out two iterations of the value iteration algorithm
(d) Choose an odering policy, and investigate using the policy iteration algorithm whether or not this policy is optimal. "
These models are used when one must decide the optimal time to replace equipment for one reason or the other for instance, in the case of equipment whose efficiency dete
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A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
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a paper mill prodecs two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper in
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A paper mill products two grade of paper viz., X & Y. Because of raw material restriction, it cannot produce more than 400 tons of grade X paper & 300 tons of grade Y paper in a we
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