Double Treatment in Product Mixture Problem Data Hyperparametric Function and SuperHyperparametric Function

The fundamental focus of operations research is the existence of a problem requiring decision-making. The need for operations research methods increases as the complexity of the problem increases. One important method in operations research is linear programming, which relies on translating the actual situation under study into a linear mathematical model consisting of an objective function and constraints. This method uses data collected from the situation by experts. As we know, this data is suitable for operating conditions similar to those in which it was collected. In other words, this data is subject to change depending on the surrounding conditions. In light of this uncertainty, it was necessary to devise scientific methods suitable for all circumstances. In classical studies, researchers in the field of operations research introduced sensitivity analysis and parametric programming. This method is an expansion of sensitivity analysis because parametric programming studies the effect of simultaneous changes in the data when the coefficients change as a function of a single parameter. It also examines the effect of continuous changes in the coefficients of the objective function and the right-hand side of the constraints on the optimal solution. It provides us with a set of optimal acceptable solutions to the problem under study. In this research, we present a new approach to the product mix problem that aims to reformulate the mathematical model of this problem using the parametric programming method, which is an extension of sensitivity analysis, where the effect of simultaneous changes in the data is studied when the coefficients change as a function of a single parameter, Double treatment in product mixture problem data hyperparametric function and superhyperparametric function and the concept of a Hyperfunction, which associates each of the acceptable values provided by the model study using parametric programming to a subset of outputs. This generalizes classical parametric programming to represent multi-valued results. We will also reformulate it using parametric programming and SuperHyperFunction, through which sets (or groups of sets) are associated with values of higher-order power sets, which enables us to capture complex hierarchical or layered uncertainties. This enables us to obtain solutions that fit all the conditions that the operating environment of the system under study may experience.