On the Problem of Maximizing the Probability of Successful Passing of a Time-Limited Test

Abstract

The problem of finding the optimal sequence of performing a set of tasks in a time-limited test is considered. That is, a task group is allocated for mandatory initial execution in the test, the remaining tasks are performed during the remaining time until the end of the test. For each correctly completed task of the test, the subject is awarded a certain number of points. The proposed criterion is the probability that the total number of points scored for the test exceeds a certain level, which is a fixed parameter, while simultaneously fulfilling the time limit of the test. Random parameters are the user’s response time to each test task. The correctness of the user’s answer to the task is modeled by a random variable with a Bernoulli distribution. The resulting stochastic bilinear programming problem boils down to a deterministic integer problem of mathematical programming.