Linear programming with interval right hand sides

Linear programming with interval right hand sides In this paper, we study general linear programs in which right hand sides are interval numbers. This model is relevant when uncertain and inaccurate factors make difficult the assignment of a single value to each right hand side. When objective function coefficients are interval numbers in a linear program, classical criteria coming from decision theory (like the worst case criterion) are usually applied to determine robust solutions. When the set of feasible solutions is uncertain, we identify a class of linear programs for which these classical approaches are no longer relevant. However, it is possible to compute the worst optimum solution. We study the complexity of this optimization problem when each right hand side is an interval number. Then, we exhibit some duality relationships between the worst optimum solution problem and the best optimum solution to the dual problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Transactions in Operational Research Wiley

Linear programming with interval right hand sides

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Publisher
Wiley
Copyright
© 2010 The Authors. Journal compilation © 2010 International Federation of Operational Research Societies
ISSN
0969-6016
eISSN
1475-3995
D.O.I.
10.1111/j.1475-3995.2009.00737.x
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study general linear programs in which right hand sides are interval numbers. This model is relevant when uncertain and inaccurate factors make difficult the assignment of a single value to each right hand side. When objective function coefficients are interval numbers in a linear program, classical criteria coming from decision theory (like the worst case criterion) are usually applied to determine robust solutions. When the set of feasible solutions is uncertain, we identify a class of linear programs for which these classical approaches are no longer relevant. However, it is possible to compute the worst optimum solution. We study the complexity of this optimization problem when each right hand side is an interval number. Then, we exhibit some duality relationships between the worst optimum solution problem and the best optimum solution to the dual problem.

Journal

International Transactions in Operational ResearchWiley

Published: May 1, 2010

References

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