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

The paper deals with the job shop scheduling problem with complex blocking constraints (BJSS) under uncertainties. It proposes a method for the evaluation of the risk that the makespan of a deterministic feasible schedule assumes worse extreme values, considering uncertain activity durations represented by intervals. An interval-valued network approach is proposed to model the feasible solutions characterized by uncertain values for jobs' releases, processing and setup times. The study assumes the Value-at-Risk (VaR) and the Conditional Value-at-Risk (CVaR) as risk measures for the makespan of the feasible solutions, and addresses both modeling and computational issues. They include the implementation and test of a network-based model used with an innovative algorithm for the first time applied to complex BJSS problems to provide an accurate, rapid and viable computation of both risk indices. The impact of different sources of uncertainty (including setups, releases and processing times) on the overall performance of the proposed approach are analyzed. The results of a wide experimental campaign show that the method, for both the computational time and the quality of the evaluations, has broad applicability. It can support the decision-makers for a wide range of practical scheduling cases taking into account their risk sensibility.