a mathematical programming model for single round-robin tournament problem: a case study of volleyball nations league

In this study, a mathematical programming model is developed for a single round-robin tournament problem to provide a schedule for the preliminary round of the volleyball nations league. in this setting, the aim is to assign the teams to the pools at each week as well as to specify the host teams of the pools. this schedule is obtained by minimizing the sum of the differences between the total distance traveled by every team and the average of the total distances traveled by all teams. then, to evaluate the performance of the developed model, it is applied to obtain the optimal schedule for the preliminary round of the volleyball men’s nations league in year 2018. the results indicate that the sum of the travel distance deviations from the average of the total travel distances of all teams obtained from the schedule provided by the mathematical model is significantly lower than that calculated from the schedule presented by the international volleyball federation. moreover, the schedule presented by the international volleyball federation leads to a percentage gap of 449.92% in comparison with the optimal schedule provided by the developed model.