Linear programming with linear restricted parameters

The parameters of linear programming models are often not (in a deterministic or stochastic sense) fixed, nor totally freely selectable. Classic linear optimization as an example proceeds on the assumption that prices for different products to be produced are predetermined by the market and on this basis defines quantities for productions that maximize the profit. Only in perfect and polypolistic structured markets, prices are fixed by supply and demand. In parametric linear programming models this assumption is modified in a way that the parameters of the model (e.g. the prices) depend on an additional parameter t ∈ IR. Stochastic linear programming replaces determined parameters by stochastic ones. None of the upper models offer the possibility to select parameters out of a constrained area (e.g. prices are constrained by costs and also by the prices of the competition) to maximize the objective function. Hence the following optimization problem with the objective function g(x,p) = p^Tx → max and the restrictions Axx ≤ bx1 x ∈ IR0+ⁿ, Ax ∈ IR^m,n, bx ∈ IR^m, App ≤ bp, p ∈ IR0+ⁿ, Ap ∈ IR^m,n, bp ∈ IR^m will be regarded. Two procedures, based on the Simplex-Algorithm, will be presented as the solution.