Dual Processing of Product Mix Problem Data Using Hyperfunctions and Superhyperfunctions Dual Processing of Product Mix Problem Data

Using Hyperfunctions and Superhyperfunctions is the title of a scientific study conducted at the International University for Science and Technology and published in the Journal of King Saud University – Science, a journal indexed in the D1 category with an Impact Factor of 3.7 and a CiteScore of 7.2. This study belongs to the field of Operations Research, which focuses on analyzing problems that require decision-making in complex and dynamic operational environments.

Linear programming is one of the most important tools in this field, as it relies on representing real-world problems through linear mathematical models consisting of an objective function and a set of constraints in order to determine the optimal solution. However, the data used in traditional models are often associated with specific operating conditions, making them susceptible to change as the surrounding environment evolves. Consequently, there is a growing need to develop approaches capable of handling uncertainty and simultaneous changes in model parameters.

The study adopted the concept of parametric programming as an extension of sensitivity analysis.

This approach examines the impact of continuous and simultaneous variations in the coefficients of both the objective function and the constraints when these coefficients are expressed as functions of a single parameter. Such an approach enables the generation of a set of acceptable optimal solutions that can accommodate different operating conditions.

The study aims to reformulate the product mix problem using parametric programming, thereby constructing a more flexible model capable of representing changing operational realities. In addition, the concept of a hyperfunction was employed, whereby each admissible value of the parameters is associated with a subset of possible solutions or outcomes. This significantly enhances the model’s ability to represent multi-valued results.

To further improve the accuracy of the mathematical representation, the study also explored the concept of a superhyperfunction, which maps sets of inputs to higher-order power sets.

This framework enables the representation of hierarchical and layered uncertainty within complex operational environments.

The results demonstrated that reformulating the product mix model using parametric programming, combined with the application of hyperfunctions and superhyperfunctions, provides highly accurate optimal solutions that can adapt to a wide range of potential operating conditions. Moreover, this approach accommodates complex data variations in a more comprehensive manner than traditional models, thereby enhancing decision-making efficiency in production and operational systems.