A Distributionally Robust Scheduling Approach for Uncertain Steelmaking and Continuous Casting Processes

This article presents a new model to handle the cast break problem caused by small daily disruptions in the processing time of the steelmaking and continuous casting (SCC) production process. In this model, the exact distribution of the uncertain parameters is unknown, and support set, mean, and covariance information is used to describe the uncertain processing time. The problem aims to determine the assignments, sequences, and time points of the charges to be processed on corresponding machines. The main goal is to minimize the expected value of the production objective while reducing the number of cast break occurrences. The problem is solved in two steps. First, a subproblem is developed by fixing the sequences and the assignments of the charges. This subproblem is formulated as a distributionally robust chance-constrained (DRCC) model, in which the constraints are established with certain probabilities even when the uncertain processing times are in their worst cases. A dual approximation method is proposed to convert the model into a semidefinite programming problem so that it can be solved by standard solvers. Additionally, a linear programming approximation method is used to accelerate the solving procedure. A Tabu search algorithm incorporated with a speed-up strategy is also designed to determine the assignments and sequences of the charges. Both simulated data generated from different distributions and actual production data are used to test the efficacy of our model. Results of the numerical experiments show that the schedule obtained from the DRCC model is more robust, i.e., it causes fewer cast breaks than the nominal schedule obtained from a deterministic model.