Robustness and duality in linear programming

• Published in: The Journal of the Operational Research Society Vol. 61; no. 8; pp. 1288 - 1296
• Main Authors: Gabrel, V, Murat, C
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.08.2010; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Subjects: Applied sciences; Approximation; Business and Management; Coefficients; decision analysis; Decision theory. Utility theory; Exact sciences and technology; Expected values; Linear programming; Management; Mathematical duality; Mathematical intervals; Mathematical programming; Mathematical robustness; Mathematical vectors; Objective functions; Operational research and scientific management; Operational research. Management science; Operations research; Operations Research/Decision Theory; Optimal solutions; Optimization; robustness; Studies; Theoretical Paper; Theoretical Papers; Uncertainty; robustness; linear programming; decision analysis; Uncertain system; Worst case method; Linear programming; Duality; Robustness; Objective function; Decision analysis; Modeling; Mass spectrometry; Interval arithmetic

In this paper, we consider a linear program in which the right hand sides of the constraints are uncertain and inaccurate. This uncertainty is represented by intervals, that is to say that each right hand side can take any value in its interval regardless of other constraints. The problem is then to...