چكيده به لاتين
In the current era, identifying and nurturing talents, particularly in the field of sports, has significantly contributed to improving athletic performance and generating financial revenue for clubs through the discovery and development of sports talents. This thesis introduces a bi-objective integer linear programming model for a sports talent identification network, which operates in two phases. In the first phase, potential locations are evaluated using the Data Envelopment Analysis (DEA) method based on factors such as genetic aspects, the number of medals won, and the number of sports clubs available in each province. In the second phase, these evaluations are incorporated into a bi-objective mathematical model aimed at minimizing costs and maximizing efficiency. Due to the shortage of specialists in talent identification centers and the lack of related facilities, the allocation of coaches and equipment is also considered in this model. Naturally, the system forms queues due to the congestion of applicants, and this aspect is addressed in the mathematical model. Additionally, minimum and maximum distances between the nearest centers are taken into account. The proposed mathematical model plans the capacity of talent identification centers to meet the needs of athletes and prevent inefficiencies, directly impacting the quality of training, waiting times, and costs. To model the referral system to the centers and account for inherent uncertainties, probability distribution functions are utilized. Furthermore, since the number of applicants to these centers follows a Poisson distribution, the time between two arrivals adheres to an exponential distribution. To solve this mathematical model, the ε-constraint method is first employed to convert it into a single-objective model. Then, considering the complexity of the model on a large scale, an exact method based on Lagrangian relaxation is proposed. Finally, to demonstrate the practical applicability of this model, a real-world case study from Iran is presented. The results showed that by eliminating inefficient locations, the number of local centers was reduced to 157 and specialized centers to 245, improving the efficiency of the network. Additionally, the proposed model in the Iranian case study successfully reduced costs and increased the productivity of the centers.
