Parameterization of all the Coefficients of a Linear Programming Problem [antikvár]

Introduction Linear programming models can very seldom be regarded as consisting of only one set of numerical coefficients. Their solution is usually only the first step of a later analysis, when the question has to be answered: how does the solution depend on the changes of the coefficients of the model. If we are interested only in small changes, sensitivity analysis may serve this purpose, but often the problem is that some or all of the coefficients are varying as functions of one or more parameters, that is they are parameterized, and the investigations have to be extended beyond the existing basis. The simpler case of parametric linear programming is parameterizing only the coefficients of the objective function or/and the capacity vector and keeping the coefficient-matrix constant. This question has an extensive literature; a comprehensive treatment of the linear case and a list of references is found in Dinkelbach's book Gál and Nedoma [8:, as well as Sokolova c23d were also dealing with the multiparametric case. Orchard-Hays clS] describes an algorithm for the simultaneous parameterization of the objective function and the right-hand side, which he calls the "rim" of the problem /see also Gál ill j. A general treatment of the problem of parametric programming with fixed constraint matrix is found in Weinert's paper C25].