Planning the duration of works in order to optimize the implementation time is an important component of an efficient company’s project management. The optimization economic-mathematical model for determining the duration of implementation of project stages was created in the research. The objective function is the maximization of the probability of successful project implementation and generation of new organizational knowledge at each stage. The model assumes that the sum of the duration of project stages should not exceed the specified project duration. The model assumes that the following stage can begin after the previous one at the probability of task implementation and generation of new knowledge of the previous one at the level that is not below the established one. The model takes into account that the combination with the minimal total project duration and with minimal costs for realization are chosen from the possible combinations of the durations of project stages. The model involves the use of combinatorics elements to determine the possible combinations of the duration of stages. In addition, the experts’ knowledge and the direct estimation method were used to determine the weight factors of the project stages. The total probability of successful project implementation was determined as the sum of probabilities of successful realization of tasks and generation of new knowledge at each project stage, taking into consideration the corresponding weight factors. Practical implementation of the model was carried out for the project of development, content creation, and implementation of the information system and the database for the management of activity of the regional center of physical education of school youth lasting 10 months. The project consists of three stages: designing, development and testing, and implementation. It was established that the following duration of the project stages will be optimal: stage 1 – 4 months, stage 2 – 5 months, stage 3 – 1 month. At this distribution of time, the probability of successful project implementation is 0.81, costs are USD 5,440. The created model can be used for any enterprise with the purpose of planning the duration of the project works and its successful implementation within the set period