A scheduling framework based on Petri net modeling and sequential Lagrangian relaxation approach

Job shop scheduling problems with weighted quadratic tardiness costs are formulated as a class of transition firing problems of timed Petri nets, and a sequential Lagrangian relaxation approach is proposed to solve the scheduling problems. It is shown that the approach can not only avoid the solution oscillation in the Lagrangian relaxation approach proposed by Hoitomt and Luh, but also generate good near-optimal schedules.<
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