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Unformatted text preview: What is Stochastic Programming Why use Stochastic Programming Stochastic LP IE426: Optimization Models and Applications: Lecture 20 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University November 16, 2006 Jeff Linderoth IE426:Lecture 20 What is Stochastic Programming Why use Stochastic Programming Stochastic LP Definition of Stochastic Programming Related Decision Making Technologies The Newsvendor Problem The Newsvendor c = . 50 , q = . 70 , r = . 05 Demand: Normally distributed. μ = 100 , σ = 50 Mean Value Solution Buy 100. (Duh!) Expect to profit: 2000 TRUE long run profit ≈ 650 Stochastic Solution Buy 75. Expect to profit: 1500 TRUE long run profit ≈ 880 The difference between the two solutions (880 650) is called the value of the stochastic solution . Jeff Linderoth IE426:Lecture 20 What is Stochastic Programming Why use Stochastic Programming Stochastic LP Definition of Stochastic Programming Related Decision Making Technologies The Newsvendor Problem Spreadsheet and Two Statistics Value of Stochastic Solution How much more money does the newsvendor make in the long run if we uses the optimal stochastic solution instead of the mean value solution Expected Value of Perfect Information How much more money would the newsvendor make in the long run if he could forecast demand perfectly every day? Jeff Linderoth IE426:Lecture 20 What is Stochastic Programming Why use Stochastic Programming Stochastic LP Pontificating The Newsvendor Today’s Main Goal: Making a SuperModel Quick review of Farmer Ted Making the SuperModel The Value of the Stochastic Solution The Expected Value of Perfect Information Jeff Linderoth IE426:Lecture 20 What is Stochastic Programming Why use Stochastic Programming Stochastic LP Pontificating The Newsvendor The Scenario Approach – Review Consider a planning problem with two periods. The following sequence of events occurs. 1 We make a decision now ( firstperiod decision ) 2 Nature makes a random decision ( “stuff” happens ) 3 We make a second period decision that attempts to repair the havoc wrought by nature in (2). ( recourse ) The scenario approach assumes that there are a finite number of decisions that nature can make. Each of these possible decisions is called a scenario . Jeff Linderoth IE426:Lecture 20 What is Stochastic Programming Why use Stochastic Programming Stochastic LP Pontificating The Newsvendor Farmer Ted – Review Farmer Ted can grow Wheat, Corn, or Beans on his 500 acres. Farmer Ted requires 200 tons of wheat and 240 tons of corn to feed his cattle These can be grown on his land or bought from a wholesaler. Any production in excess of these amounts can be sold for $170/ton (wheat) and $150/ton (corn) Any shortfall must be bought from the wholesaler at a cost of $238/ton (wheat) and $210/ton (corn)....
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 Spring '08
 Linderoth
 Operations Research, Optimization, Mathematical optimization, stochastic programming, Farmer Ted

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