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Quiz_3 - (b The expected inventory cost per month as a...

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02 April 2009 IE 304 OPERATIONS RESEARCH III: STOCHASTIC MODELS QUIZ # 3 Duration: 40 mins Question 1) An appliance store can place orders for refrigerators at the beginning of each month for immediate delivery. A fixed cost of $100 is incurred every time an order is placed. The storage cost per refrigerator per month is $5. The penalty for running out of stock is estimated as $150 per refrigerator per month. The monthly demand is given by the following probability density function: Demand, x 0 1 2 p(x) 0,2 0,5 0,3 The store s policy is that the maximum stock level should not exceed two refrigerators in any single month. Determine the followings: (a) The transition probabilities for different decision alternatives of the problem.
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Unformatted text preview: (b) The expected inventory cost per month as a function of the state of the system and the decision alternative. (c) The optimal ordering policy over the next 3 months. Question 2) When I borrow a book from the BU library, I usually try to return it after one week. Depending on the length of the book and my free time, there is a 30% chance that I may keep it for another week. If I have had the book for two weeks, there is a 10% chance that I ’ ll keep it for an additional week. Under no condition do I keep it for more than three weeks. (a) Express the situation as a Markov chain. (b) Determine the average number of weeks I keep the book before returning it to the library....
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