We introduce methods for dealing with linear programming (LP) problems
with uncertain data, using the notion of weighted analytic centers.
Our methods are based on high interaction with the decision maker (DM) and try to
find solutions which satisfy most of his/her important criteria/goals.
Starting with the drawbacks of different methods for dealing with
uncertainty in LP, we explain how our methods improve most of them. We prove
that, besides many practical advantages, our approach is theoretically
as strong as robust optimization. Interactive cutting-plane algorithms are
developed for concave and quasi-concave utility functions. We present some
probabilistic bounds for feasibility and evaluate our approach by means
of computational experiments.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/7178 |
| Date | January 2012 |
| Creators | Karimi, Mehdi |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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