Exact solution to a parametric linear programming problem (Q1656667)

The objective of the present paper is to exploit a new type of \(p\)-solution (\(x(p)=Lp+a\)) to address the following parametric linear programming (PLP) problem \(l(x, p)=c^T(p) x\), with \(c_i(p)\) nonlinear functions of \(p\). The PLP problem is a parametric generalization of the interval linear programming (ILP) problem, and more complex since \(x\) is an implicit function of \(p\). In this respect, the authors propose an iterative method for solving a system of linear interval parametric (LIP) equation, its computational scheme of the method and four versions of a simple polynomial complexity iterative method for determining the interval hull solution of the PLP problem. The results obtained for a numerical example show that this version of the method is efficient.