Robust optimal solutions in interval linear programming with forall-exists quantifiers

First step immersion in interval linear programming with linear dependencies

‎We consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals‎. ‎Contrary to classical models‎, ‎where parameters can attain any value from the interval domains independently‎, ‎we study problems with linear dependencies between the parameters‎. ‎We present a class of problems that are easily solved by reduction to the classi...

Optimal value range in interval linear programming

first step immersion in interval linear programming with linear dependencies

‎we consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals‎. ‎contrary to classical models‎, ‎where parameters can attain any value from the interval domains independently‎, ‎we study problems with linear dependencies between the parameters‎. ‎we present a class of problems that are easily solved by reduction to the classi...

Interval Linear Programming with generalized interval arithmetic

Generally, vagueness is modelled by a fuzzy approach and randomness by a stochastic approach. But in some cases, a decision maker may prefer using interval numbers as coefficients of an inexact relationship. In this paper, we define a linear programming problem involving interval numbers as an extension of the classical linear programming problem to an inexact environment. By using a new simple...

Robust solutions of Linear Programming problems contaminated with uncertain data

Optimal solutions of Linear Programming problems may become severely infeasible if the nominal data is slightly perturbed. We demonstrate this phenomenon by studying 90 LPs from the well-known NETLIB collection. We then apply the Robust Optimization methodology (Ben-Tal and Nemirovski [1-3]; El Ghaoui et al. [5,6]) to produce “robust” solutions of the above LPs which are in a sense immuned agai...