Expected Shortfall for the Makespan in Activity Networks with Fuzzy Durations

The paper 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.