Supply chain management interested in the selection of suppliers against multiple criteria rather than the single criterion as a cost only. These criteria may be quantitative, qualitative or both. To choose the best supplier, the criteria are being measured or weighted for ranking. The supplier selection problem is considered as a multi-decision problem and it can be solved by the Analytical Hierarchical Process. It allows the decision maker to structure such complex problems in the form of a hierarchy, or a set of integrated levels. In this paper, a mathematical model is combined with an analytical hierarchical process in two phases, the first phase starts by the weighted mathematical model from an exciting example, and the second phase makes the check and refines the result from the first phase by checking the consistency. And finally, a new ranking of the suppliers are obtained.