Expected Shortfall for the Makespan in Activity Networks With Fuzzy Durations

This article deals with the evaluation of the expected shortfall or the conditional value-at-risk for the makespan in scheduling problems represented as temporal activity networks where we assume that only a type-1 fuzzy representation for the activity-integer-valued durations is known to the scheduler. More precisely, we address the evaluation of the expected shortfall associated to a feasible schedule, and we extend the approach recently proposed for the case of interval-valued durations. We develop and analyze a suitable computational method to obtain the fuzzy evaluation of the expected shortfall of the makespan of a given schedule. The proposed method enables to use the expected shortfall as quality criterion for wide classes of scheduling approaches considering risk aversion in different practical contexts when only a fuzzy representation of activity durations is known.