Economics at your fingertips  

Interval linear programming under transformations: optimal solutions and optimal value range

Elif Garajová (), Milan Hladík () and Miroslav Rada ()
Additional contact information
Elif Garajová: Charles University
Milan Hladík: Charles University
Miroslav Rada: University of Economics, Prague

Central European Journal of Operations Research, 2019, vol. 27, issue 3, 601-614

Abstract: Abstract Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb independently within the given lower and upper bounds. However, contrarily to classical linear programming, an interval program cannot always be converted into a desired form without affecting its properties, due to the so-called dependency problem. In this paper, we discuss the common transformations used in linear programming, such as imposing non-negativity on free variables or splitting equations into inequalities, and their effects on interval programs. Specifically, we examine changes in the set of all optimal solutions, optimal values and the optimal value range. Since some of the considered properties do not holds in the general case, we also study a special class of interval programs, in which uncertainty only affects the objective function and the right-hand-side vector. For this class, we obtain stronger results.

Keywords: Interval linear programming; Optimal set; Optimal value range; Transformations (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed

Downloads: (external link) Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10100

DOI: 10.1007/s10100-018-0580-5

Access Statistics for this article

Central European Journal of Operations Research is currently edited by Ulrike Leopold-Wildburger

More articles in Central European Journal of Operations Research from Springer, Slovak Society for Operations Research, Hungarian Operational Research Society, Czech Society for Operations Research, Österr. Gesellschaft für Operations Research (ÖGOR), Slovenian Society Informatika - Section for Operational Research, Croatian Operational Research Society
Bibliographic data for series maintained by Sonal Shukla ().

Page updated 2020-03-07
Handle: RePEc:spr:cejnor:v:27:y:2019:i:3:d:10.1007_s10100-018-0580-5