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

  • Elif Garajová
  • Milan Hladík
  • Miroslav Rada
Original Paper

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 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
  2. 2.Department of Financial Accounting and AuditingUniversity of Economics, PraguePragueCzech Republic

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