Milan Hladík's Publications:

Sensitivity analysis of linear programming in the presence of correlation among right-hand side parameters or objective function coefficients

Amir Shahin, Payam Hanafizadeh, and Milan Hladík. Sensitivity analysis of linear programming in the presence of correlation among right-hand side parameters or objective function coefficients. Cent. Eur. J. Oper. Res., 24(3):563–593, 2016.

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Abstract

In the literature, sensitivity analysis of linear programming (LP) has been widely studied. However, only some very simple and special cases were considered when right-hand side (RHS) parameters or objective function coefficients (OFC) correlate to each other. In the presence of correlation when one parameter changes, other parameters vary, too. Here principal component analysis is used to convert the correlation of the LP homogenous parameters into functional relations. Then, using the derivatives of the functional relations, it is possible to perform classical sensitivity analysis for the LP with correlation among RHS parameters or OFC. The validity of the devised method is corroborated by open literature examples having correlation among homogenous parameters.

BibTeX

@article{ShaHan2016a,
 author = "Shahin, Amir and Hanafizadeh, Payam and Hlad\'{\i}k, Milan",
 title = "Sensitivity analysis of linear programming in the presence of correlation among right-hand side parameters or objective function coefficients", 
 journal = "Cent. Eur. J. Oper. Res.",
 fjournal = "Central European Journal of Operations Research",
 volume = "24",
 number = "3",
 pages = "563-593",
 year = "2016",
 doi = "10.1007/s10100-014-0353-8",
 issn = "1613-9178",
 bib2html_dl_html = "http://dx.doi.org/10.1007/s10100-014-0353-8",
 bib2html_dl_pdf = "https://rdcu.be/7t1X",
 abstract = "In the literature, sensitivity analysis of linear programming (LP) has been widely studied. However, only some very simple and special cases were considered when right-hand side (RHS) parameters or objective function coefficients (OFC) correlate to each other. In the presence of correlation when one parameter changes, other parameters vary, too. Here principal component analysis is used to convert the correlation of the LP homogenous parameters into functional relations. Then, using the derivatives of the functional relations, it is possible to perform classical sensitivity analysis for the LP with correlation among RHS parameters or OFC. The validity of the devised method is corroborated by open literature examples having correlation among homogenous parameters.",
 keywords = "Correlated parameters; Linear programming; Perturbation analysis; Principal component analysis; Sensitivity analysis",
}

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