Milan Hladík. Optimal value range in interval linear programming. Fuzzy Optim. Decis. Mak., 8(3):283–294, 2009.
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We deal with the linear programming problem in which input data can vary in some given real compact intervals. The aim is to compute the exact range of the optimal value function. We present a general approach to the situation the feasible set is described by an arbitrary linear interval system. Moreover, certain dependencies between the constraint matrix coefficients can be involved. As long as we are able to characterize the primal and dual solution set (the set of all possible primal and dual feasible solutions, respectively), the bounds of the objective function result from two nonlinear programming problems. We demonstrate our approach on various cases of the interval linear programming problem (with and without dependencies).
@article{Hla2009b,
author = "Milan Hlad\'{\i}k",
title = "Optimal value range in interval linear programming",
journal = "Fuzzy Optim. Decis. Mak.",
fjournal = "Fuzzy Optimization and Decision Making",
volume = "8",
number = "3",
pages = "283-294",
year = "2009",
doi = "10.1007/s10700-009-9060-7",
url = "https://doi.org/10.1007/s10700-009-9060-7",
bib2html_dl_html = "https://link.springer.com/article/10.1007/s10700-009-9060-7",
bib2html_dl_pdf= "https://rdcu.be/cnoTA",
abstract = "We deal with the linear programming problem in which input data can vary in some given real compact intervals. The aim is to compute the exact range of the optimal value function. We present a general approach to the situation the feasible set is described by an arbitrary linear interval system. Moreover, certain dependencies between the constraint matrix coefficients can be involved. As long as we are able to characterize the primal and dual solution set (the set of all possible primal and dual feasible solutions, respectively), the bounds of the objective function result from two nonlinear programming problems. We demonstrate our approach on various cases of the interval linear programming problem (with and without dependencies).",
keywords = "linear interval systems, linear programming, optimal value range, interval matrix, dependence",
}
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