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PS12 - 20 May 2009 IE 304 OPERATIONS RESEARCH III...

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20 May 2009 IE 304 OPERATIONS RESEARCH III: STOCHASTIC MODELS PS # 12 Question 1) A bakery at a local grocery store bakes fresh muffins every morning. The daily demand for muffin has an exponential distribution with a mean of 400. Muffin costs 20 cents per unit to make and they are sold for 30 cents each. Unsold muffins are sold to a nearby coffee shop for 14 cents each at the end of the day. (a) What is the optimal number of muffins to bake each morning? (b) What is the value of Type 1 service level (probability of incurring no shortage) corresponding to the optimal quantity found in part (a)? What is the probability of incurring a shortage (stock-out) of muffins on any given day? (c) What is the expected number of shortages of muffins on any given day? (d) Calculate the expected daily profit. (e) Now consider the inventory policy of baking 540 muffins each morning. Which value of the discounted price for 1-day-old muffin makes this inventory policy optimal?

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PS12 - 20 May 2009 IE 304 OPERATIONS RESEARCH III...

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