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This study investigates a challenging problem of rescheduling a hybrid flow shop in the steelmaking-continuous casting (SCC) process, which is a major bottleneck in the production of iron and steel. In consideration of uncertain disturbance during SCC process, we develop a time-indexed formulation to model the SCC rescheduling problem. The performances of the rescheduling problem consider not only the efficiency measure, which includes the total weighted completion time and the total waiting time, but also the stability measure, which refers to the difference in the number of operations processed on different machines for the different stage in the original schedule and revised schedule. With these objectives, this study develops a Lagrangian heuristic algorithm to solve the SCC rescheduling problem. The algorithm could provide a realizable termination criterion without having information about the problem, such as the distance between the initial iterative point and the optimal point. This study relaxes machine capacity constraints to decompose the relaxed problem into charge-level subproblems that can be solved using a polynomial dynamic programming algorithm. A heuristic based on the solution of the relaxed problem is presented for obtaining a feasible reschedule. An improved efficient subgradient algorithm is introduced for solving Lagrangian dual problems. Numerical results for different events and problem scales show that the proposed approach can generate high-quality reschedules within acceptable computational times.

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