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Unformatted text preview: SinglePeriod Stochastic Decision Models The News Vender Problem Other Oneperiod Models Reference Single Period Stochastic Inventory Model: News Vendor Problem Siqian Shen 1 1 Dept. of Industrial and Systems Engineering University of Florida Fall 2009 1 / 24 SinglePeriod Stochastic Decision Models The News Vender Problem Other Oneperiod Models Reference Outline 1 SinglePeriod Stochastic Decision Models 2 The News Vender Problem 3 Other Oneperiod Models 4 Reference 2 / 24 SinglePeriod Stochastic Decision Models The News Vender Problem Other Oneperiod Models Reference Stochastic Demands and Evaluation Methods Recall that we assumed the demand is a known constant in our deterministic EOQ model. However, this assumption is usually unrealistic. Demand usually behaves randomly following a specific distribution in real life. Assume that demand D is an integervalued discrete random variable with probability P ( D = d ) = p ( d ) . For instance, P ( D = 40 ) = p ( 40 ) = . 5 and P ( D = 60 ) = p ( 60 ) = . 5 means there is a “5050" chance that the next day’s demand will be 40 or 60. 3 / 24 SinglePeriod Stochastic Decision Models The News Vender Problem Other Oneperiod Models Reference Stochastic Demands and Evaluation Methods We evaluate our decision of order size q by using the expected value E ( q ) = X d p ( d ) TC ( q , d ) TC ( q , d ) is the total annual cost given order size q and demand realization d (for the stochastic case, we have a pool of values that might become a realization with corresponding probability of p ( d ) ). We also assume that our decision q only made once under this assumption (i.e., singleperiod decision models). 4 / 24 SinglePeriod Stochastic Decision Models The News Vender Problem Other Oneperiod Models Reference Marginal Analysis Given a demand distribution, how to find the q that minimize E ( q ) ? Definition and Illustration of convex functions : In plain words, convex function is something that if you try to connect any two points on the function by using a line segment, the function itself will be always beneath the line. 5 / 24 SinglePeriod Stochastic Decision Models The News Vender Problem Other Oneperiod Models Reference Marginal Analysis Given a demand distribution, how to find the q that minimize E ( q ) ? Definition and Illustration of convex functions : In plain words, convex function is something that if you try to connect any two points on the function by using a line segment, the function itself will be always beneath the line. 6 / 24 SinglePeriod Stochastic Decision Models The News Vender Problem Other Oneperiod Models Reference Marginal Analysis Interpreted by our problem, the total cost will decrease as we increase the order size q , and then start increase beyond a “point of no return"....
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This note was uploaded on 03/01/2010 for the course FFDFD dssss taught by Professor Aabb during the Spring '10 term at Abraham Baldwin Agricultural College.
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