sp - 1 Introduction and Ex~mples .,. fJ ." , ':;1 -...

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1 Introduction and Ex~mples .,. < ' !. This chapter presents stochastic progt8.InrQing examples from a ~~ of .~, areas with wideapplicationin stochastic progrsunmi"g.TheseexamPk!S~.~ ..' intended to help the reader build intuition on how to model ~;; They a1soreflectcWferentstructural aspects of the problems.In ~~lil~~. .\~~ij we show the variety of stochastic progrRmmi~gmodels in termsfOf;'~;,'2f' objectivesof the'd~on"process, the fx>nstta.intson those decisiODS,~d their relationships to the random dements.,' In each example,weinvestigatethe wJue of the stochastic p~ model over a similar.determinjstic,problem. We show that eveJl'SiiJ;kple models can lead to sigIWicantsavings. These results provide the. DlOtm;. tion'to lead us into the fullOWing chapters on stochastic programs, ~~ properties, and.tedmiqttes. ,: . .,' In the firstsection,we'corlsiaera farmerwhomust decideon the ~~~. of various crops to plant. The yields'of the crops vary 8CCOrdiu&,~ifi;' weather. From this example,we illustrate the basic foundation of ~~ tic 'programmiDgand the' advantage of the Stochasticp~~1u- tion over deterministic appioaches. We a.1So introduce the classical"bevis vendor (or newsboy)problem and giVethefunilRmenta1properties.of~ problems' generaI class, called trDo-stagestochastic linear prognrinsviith ,- recourse. ' The second section contains an example in plRnning finances fur'a'~d'8 edUcation.This example fits the situation in many discrete time control _. problems. Decisionsoccur'at different points in time so that the prob~ ' -, canbeviewedasbavingmultiplestagesofobservationsand actions. ., , I' ." fJ , ':;;1 1 - "q ; 'i . "I ..1 J )1 >Ii nil , l' .' . ;; :H i':! ,'il .'ft i ,-I j j ' I ' , , , . I i tl HI ~
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; I II I. i: I, Ii, i!' If. . I"~ 4 1. Introduction and Examples The third section considers power system capacity expansion. Here, de- cisions are taken dynamically about additional capacity and about the decision stages and a valuable property known as block separable f'eCOurse that allows efficient solution. The problem also provides a natural example of constraints on reliability within the area called probabilistic or Chance- constrained programming. The fourth example concerns the design of a simple axle. It includes market reaction to the design and performance characteristics of products made by a manufacturing system with variable performance. The essen- tial characteristics of the maximum performance of the product illustrate a problem with fundamental nonlinearities incorporated directly into the stochastic program. The final section of this chapter briefly describes several other ~jor application areas of stochastic programs. The exercises at the end of the chapter develop modeling techniques. This chapter illustrates some of the range of stochastic programming applications but is not meant to be ex- haustive. Applications in routing and location, for example, are discussed
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This note was uploaded on 08/06/2008 for the course IE 426 taught by Professor Linderoth during the Fall '08 term at Lehigh University .

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sp - 1 Introduction and Ex~mples .,. fJ .&quot; , ':;1 -...

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