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Flexible solutions to linear programs under uncertainty: Inequality constraints
Author(s) -
Friedman Y.,
Reklaitis G. V.
Publication year - 1975
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690210109
Subject(s) - linear programming , mathematical optimization , column (typography) , linear fractional programming , mathematics , matrix (chemical analysis) , inequality , plane (geometry) , linear inequality , cutting plane method , algorithm , computer science , integer programming , geometry , mathematical analysis , materials science , connection (principal bundle) , composite material
In most industrial applications the linear model used for optimization by linear programming involves significant uncertainties and inaccuracies in the model parameters. This paper presents a framework which allows uncertainties in the matrix elements of the linear program to be taken into account without requiring detailed knowledge of the statistical characterstics of these uncertainties. Three cases for the inequality constrained problem are considered: independent variations in the array elements, column dependent variations, and row dependent variations. In each case the problem can still be solved as a linear program. In the first two cases, the problem size is doubled, while for the row dependent case a finitely terminating cutting plane algorithm is constructed.