production and inventory system

industrial engineering

operation management

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The ratio that determines the optimal order quantity in the newsvendor modelis given by: F(Q) = cu where F(Q) is the value of the cumulative demand distribution at Q.c, is the underage cost and c, is the overage cost. For any probability density function f (x), the cumulative distribution F(x) is given by F(x) = f(x) dx. If the demand for a single period is uniformly distributed between 10 and 20 items, that is: 20 sx s 30 f(x) otherwise) 1. Find the cumulative distribution F(x) of this uniform distribution. 2. Use part 1 to find the probability that the demand is less than or equal to 26, i.e. p(x S 26). 3. If the underage cost is $10 and the overage cost is $15, what is the optimal order quantity? 4. Sketch the pdf and cdf of the given uniform distribution and show the best order quantity