The analytic hierarchy process (AHP) is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. The method was developed by Thomas L. Saaty in the 1970s and has been extensively studied and refined since then. It has particular application in group decision making and is used around the world in a wide variety of decision situation. Rather than prescribing a "correct" decision, the AHP helps decision makers choose one that best suits their goal and their understanding of the problem. The technique provides a comprehensive and rational framework for structuring a decision problem, for representing and quantifying its elements, for relating those elements to overall goals, and for evaluating alternative solutions. Decision making is the choice of one alternative, from two or more, to which the course of the activity is directed and the problem is solved. The decision-making process is a rational attempt by the manager to achieve the goals of the organizational unit. The decision-making process can be thought of as a "brain and nervous system" of an enterprise. Decisions are made when a person wants things to be different in the future. Given each specific situation, making the right decisions is probably one of the most difficult challenges for managers. Managers in day-to-day work deliver programmed and unprogrammed decisions that solve simple or complex problems. Simple decisions have an impact on the short-term performance of the enterprise, and complex decisions have an impact on the long-term future and success of the enterprise. Users of the AHP first decompose their decision problem into a hierarchy of more easily comprehended sub-problems, each of which can be analyzed independently. Once the hierarchy is built, the decision makers systematically evaluate its various elements by comparing them to each other two at a time, with respect to their impact on an element above them in the hierarchy. The AHP converts these evaluations to numerical values that can be processed and compared over the entire range of the problem. In this article, it is explained the application of the AHP method in order to evaluate and promote employees in the enterprise "X" with several criteria. The obtained results enable the manager to evaluate the employees in an objective way and make an objective decision for their promotion. Its application for selecting the best among employees, in their assessment and promotion, allows managers to use a specific and mathematical tool to support the decision. This tool not only supports and qualifies decisions, it also allows managers to justify their choice, as well as to simulate possible results.