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<CENTER>Traditional Optimization Techniques</CENTER>
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<LI>Computer oriented solution<BR>
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<LI>Iterative and sequential<BR>
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<LI>Real variable and calculus based<BR>
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<LI>A huge literature & many success stories<BR>
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<LI>Best known examples:
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<LI>Nobel prize winning <I>Linear Programming</I>
<LI>Guidance and control of <I>Apollo Moon landing</I>
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However, we submit that increasingly modern civilization has created
problems which are not necessarily real variable or calculus/differential
equation based. Mathematical models of systems now involve integer, discrete,
combinatorial, and even symbolic variables. On the hardware front, main frame
sequential computers with limited memory have given way to general purpose
parallel computation with essentially unlimited memory. Object oriented
programming and graphical user interfaces have replaced custom crafted software
with old fashioned printed input/output forms. These changes call for a <b>NEW
PARADIGM IN PROBLEM SOLVING</b>. The purpose of this talk is to advocate such
a paradigm shift not so much as a replacement of but as a worthy complement to
the successful traditional techniques. Let us give some example of such system
problems.<BR>
<p>
One familiar example to consider is the operation of a busy international
airport such as the Chicago
<A HREF="../../../../../../../www.ci.chi.il.us/WorksMart/Aviation/ohare.html">O'Hare</A>.
On the land side, you have buses, taxis, private cars, and trains competing
for access roadways and parking spots; in the terminal, passengers and
luggage compete for ticket counters, security gates, waiting areas, and
luggage handlers; finally on the air side, commercial and private planes need
air space, runways, and gates. The smooth operation and coordination of this
multitude of interlocking tasks (customers) seeking service from limited
resources (servers) under the stochastic environment of weather, equipment
breakdowns, schedule changes, and personnel absenteeism can be a daunting
task.<BR>
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