Evaluation of VaR and CVaR for the makespan in interval valued blocking job shops

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

“…These cases can be considered as scheduling problems with incomplete or imperfect information [15,16,27,39,70,71], assuming that the realized duration of an activity is only known when the execution of the activity is completed, and the uncertainty on these parameters implies that the objective value is also uncertain. These quantilebased risk assessment issues can arise in different real contexts including project management [49], industrial scheduling [51] and transportation [50] requiring fast and accurate computation methods. On the basis of the availability of these methods, different application schemes can be considered enabling further studies and researches, the main being:…”

“…Although the seminal approach proposed in [49] offers good results, applications (e.g., see [21,50,51]) may require better performance on both computation time and solution quality, especially in real-time applications. Therefore, in this paper we improve the counting based approach introduced in [49] for the makespan of a IIN, and extend it by proposing and testing a set of new algorithms to compute both q α (C max ) and Q α (C max ).…”