Evaluation of the quantiles and superquantiles of the makespan in interval valued activity networks

This paper deals with the evaluation of quantile-based risk measures for the makespan in scheduling problems represented as temporal networks with uncertainties on the activity durations. More specifically, for each activity only the interval for its possible duration values is known in advance to both the scheduler and the risk analyst. Given a feasible schedule, we calculate the quantiles and the superquantiles of the makespan which are of interest as risk indicators in various applications.To this aim we propose and test a set of novel algorithms to determine rapid and accurate numerical estimations based on the calculation of theoretically proven lower and upper bounds. An extensive experi-mental campaign computationally shows the validity of the proposed methods, and allows to highlight their performances through the comparison with respect to the state-of-the-art algorithms.