Analytical Hierarchy Process or the AHP method is one of the most famous and, in recent years, one of the most used methods for multiple criteria decision making. Its popularity is based primarily on the fact that it is very close to the way a individual intuitively solves complex problems by dismantling them into easier ones and the availability of software-based solutions such as Super Decisions. This paper examines the historical overview and mathematical background of the AHP method, analyzes its good and bad sides, considers the use of the AHP method in practice in the case of location selection for a nautical tourism harbor and demonstrates the Super Decisions software based on AHP method. The paper also summarizes other methods of multi-criteria decision-making, ELECTRE, TOPSIS and PROMETHEE. The most important conclusion from the study of literature, as well as the analysis of case studies is that the AHP method is a useful management tool in making decisions that require multiple criteria decision making.