1
Introduction
and Ex~mples
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This chapter presents stochastic
progt8.InrQing examples from a
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of
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areas with wideapplicationin stochastic progrsunmi"g.TheseexamPk!S~.~
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intended to help the reader build intuition on how to model ~;;
They a1soreflectcWferentstructural aspects of the problems.In ~~lil~~.
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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.
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In the firstsection,we'corlsiaera farmerwhomust decideon the
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of various crops to plant. The yields'of the crops vary 8CCOrdiu&,~ifi;'
weather. From this example,we illustrate the basic foundation of
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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
trDostagestochastic linear prognrinsviith
,
recourse.
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The
second
section
contains
an example
in plRnning
finances
fur'a'~d'8
edUcation.This example fits the situation in many discrete time control
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problems. Decisionsoccur'at different points in time so that the prob~
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canbeviewedasbavingmultiplestagesofobservationsand actions.
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