On the problem of probabilistic optimization of time-limited testing

For the distance learning systems, consideration was given to generation of individual tasks with limited performance time, and an algorithm was suggested to solve it. Such problem comes to that of integer stochastic programming with probabilistic constraints. Considered were the distributions of the random student's time of response to the task such as the Van der Linden lognormal model and the discrete model based on empirical data. It was assumed that task complexities are estimated either by an expert or by using corresponding algorithms. For the case of continuous distribution, an algorithm was proposed based on the branch-and-bound principle. Results of the numerical experiments were presented.