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~~..\~~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.
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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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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
&nocation of capacity to meet demand. The resulting problem has multiple
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
in Chapter 2.
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 Fall '08
 Linderoth
 Optimization, WI, Sugar beet, sugar beets

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