A comprehensive examination of the process of developing specialized safety-oriented software is conducted. The incongruity of the presently known development methodologies with the circumstances in which innovative safety-oriented software systems are created is unveiled. For this reason, the purpose of this article is to investigate the existing methods and formulate novel approaches to managing the life cycle of specialized software (safety-oriented services), which are relevant to the specific requirements of the State Emergency Service of Ukraine and align with the principles of a flexible software life cycle management methodology. A thorough exploration is conducted on the current agile methods and approaches employed in the development of critical services, specifically in sectors such as military, railway, aerospace, medical, and other domains of operation. The aim is to establish the merits of flexibility in fostering innovation within specialized safety-oriented software. The fundamental concepts of agile methods for software system life cycle management are synergistically integrated, taking into consideration the unique requirements of rescue service development. Furthermore, the existing empirical data on the feasibility and advantages of implementing agile methods in the security industry are expanded upon. Especially, the agile Scrum method is enhanced through the proposal of employing the mathematical framework of graph theory (network planning method) to automate the planning stage and identify critical functions, including the critical path, the early execution time of events, the late execution times of events, and reserved time for tasks. This method aids in developing a minimum viable product for a safety-oriented system. A conceptual model of the life cycle management process for safety-oriented services has been meticulously developed. This model is predicated on a flexible approach to software development, which aims to automate the tasks performed by project teams and enhance the overall efficacy of specialized software development. On its basis, it is proposed to develop a decision support system for managing the life cycle of safety-oriented software systems development, which is relevant for the State Emergency Service of Ukraine.
