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Discrete Optimization with Interval Data - Minmax Regret and Fuzzy Approach (Paperback, Softcover reprint of hardcover 1st ed. 2008)
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Discrete Optimization with Interval Data - Minmax Regret and Fuzzy Approach (Paperback, Softcover reprint of hardcover 1st ed. 2008)
Series: Studies in Fuzziness and Soft Computing, 228
Expected to ship within 10 - 15 working days
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Operations research often solves deterministic optimization
problems based on elegantand conciserepresentationswhereall
parametersarepreciselyknown. In the face of uncertainty,
probability theory is the traditional tool to be appealed for, and
stochastic optimization is actually a signi?cant sub-area in
operations research. However, the systematic use of prescribed
probability distributions so as to cope with imperfect data is
partially unsatisfactory. First, going from a deterministic to a
stochastic formulation, a problem may becomeintractable.
Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling
problems like PERT. From the inception of the PERT method in the
1950's, it was acknowledged that data concerning activity duration
times is generally not perfectly known and the study of stochastic
PERT was launched quite early. Even if the power of today's
computers enables the stochastic PERT to be addressed to a large
extent, still its solutions often require simplifying assumptions
of some kind. Another di?culty is that stochastic optimization
problems produce solutions in the average. For instance, the
criterion to be maximized is more often than not expected utility.
This is not always a meaningful strategy. In the case when the
underlying process is not repeated a lot of times, let alone being
one-shot, it is not clear if this criterion is realistic, in
particular if probability distributions are subjective. Expected
utility was proposed as a rational criterion from ?rst principles
by Savage. In his view, the subjective probability distribution was
- sically an artefact useful to implement a certain ordering of
solutions.
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