Exact Lexicographic Scheduling and Approximate Rescheduling
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In industrial scheduling, an initial planning phase may solve the nominal problem and a subsequent recovery phase may intervene to repair inefficiencies and infeasibilities, e.g. due to machine failures and job processing time variations. This work investigates the minimum makespan scheduling problem with job and machine perturbations and shows that the recovery problem is strongly NP-hard, at least as hard as solving the problem with full input knowledge. We explore recovery strategies with respect to the (i) planning decisions and (ii) permitted deviations from the original schedule. The resulting performance guarantees are parameterized by the degree of uncertainty. The analysis derives from the optimal substructure imposed by lexicographic optimality, so lexicographic optimization enables more efficient reoptimization. We revisit state-of-the-art exact lexicographic optimization methods and propose a novel lexicographic optimization approach based on branch-and-bound. Numerical analysis using standard commercial solvers substantiates the method.
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