Distributionally robust fixed interval scheduling on parallel identical machines under uncertain finishing times

Abstract We deal with fixed interval scheduling (FIS) problems on parallel identical machines where the job starting times are given but the finishing times are subject to uncertainty. In the operational problem, we construct a schedule with the highest worst-case probability that it remains feasible, whereas in the tactical problem we are looking for the minimum number of machines to process all jobs given a minimum level for the worst-case probability that the schedule is feasible. Our ambiguity set contains joint delay distributions with a given copula dependence, where a proportion of marginal distributions is stressed and the rest are left unchanged. We derive a trackable reformulation and propose an efficient decomposition algorithm for the operational problem. The algorithm for the tactical FIS is based on solving a sequence of the operational problems. The algorithms are compared on simulated FIS instances in the numerical part.

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