Research into engineering and technology, as in other areas of knowledge, presents common issues when it is required to allocate an insufficient number of resources in the most optimal manner possible; in the case of this research paper this means assigning a greater number of satellites to a lesser number of ground stations, considering the input variables generated by the cost function. The Hungarian optimization algorithm constitutes an initial possible solution that can be applied to various cases. However, its approach and mathematical formulation leads to a non-square matrix of variables; therefore, it requires an adaption of the algorithm called the Adapted Hungarian Algorithm, making use of dummy variables. Thus, the objective of this study is to present an adaptation and formalization of the Hungarian algorithm for the case of non-square matrices, in the framework of the problems in allocating n satellites to m ground stations, with m<n. It is concluded that the formalization of the optimization structure of the Adapted Hungarian Algorithm generates plausible or coherent solutions to a cost function, facilitates its application and implementation to a wide range of situations and it can be executed through easy access software.