Inverse linear programming with interval coefficients

The paper deals with the inverse linear programming problem over intervals. More precisely, given interval domains for the objective function coefficients and constraint coefficients of a linear program, we ask for which scenario a prescribed optimal value is attained. Using continuity of the optima...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 292; pp. 591 - 608
Main Authors: Mostafaee, Amin, Hladík, Milan, Černý, Michal
Format: Journal Article
Language:English
Published: Elsevier B.V 15.01.2016
Subjects:
Casinos
Games
Interval analysis
Interval linear programming
Intervals
Inverse
Inverse linear programming
Linear programming
Mathematical analysis
Mathematical models
Matrix game
Optimization
Parametric analysis
Interval analysis
Parametric analysis
65G40
90C05
Interval linear programming
Matrix game
Inverse linear programming
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The paper deals with the inverse linear programming problem over intervals. More precisely, given interval domains for the objective function coefficients and constraint coefficients of a linear program, we ask for which scenario a prescribed optimal value is attained. Using continuity of the optimal value function (under some assumptions), we propose a method based on parametric linear programming techniques. We study special cases when the interval coefficients are situated in the objective function and/or on the right-hand sides of the constraints as well as the generic case when possibly all coefficients are intervals. We also compare our method with the straightforward binary search technique. Finally, we illustrate the theory by an accompanying numerical study, called “Matrix Casino”, showing some approaches to designing a matrix game with a prescribed game value.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.07.034