The article deals with the conflict situation that occurred in the recently formed commercial organization, which is engaged in the provision of sports services in the field of rock climbing. It is a modern sports center with a complex hierarchical structure and staff. Since the organization and the team are young, the staff had ideas on how to improve performance and improve efficiency. Some innovations were adopted by almost all employees unanimously, while others were divided into supporters and opponents. One of these controversial innovations was the new track update system, which led to a conflict between employees, some of whom understood the benefits of the new system, but they needed more weighty arguments. To do this, one of the employees proposed to justify the options with the help of mathematical modeling and start with the stage of analysis and formation of a verbal model of the situation. Indicators are identified: object, subject, subjects, their interests, the essence of the problem, which, together with expert assessments obtained during the negotiations, constitute the initial information for the method of analysis of hierarchies (AHP). Solution options have both advantages and disadvantages, therefore, within the AHP, hierarchies of Benefits, Opportunities, Costs and Risks with the same alternatives are built and studied. During the application of the AHP by hierarchy, it was found that the priority of the implementation of the alternative «1. New upgrade system runs» than the version «2. Old system of updating of routes». At the final stage of the settlement process, it was decided to discuss the problem in the light of the new results, and to assess how the solution obtained by mathematical modeling meets the interests of the parties who came to an agreement. The application of this approach requires the participation of a professional conflictologist who has the appropriate tools and negotiation technologies.