A robust optimization approach for steeling-continuous casting charge batch planning with uncertain slab weight

The volatility of slab weight in steelmaking-continuous casting (SCC) production, attributed to factors such as flexible order demand, is addressed in this paper. A robust optimization mathematical model for charge batch planning (CBP) with uncertain slab weight is established, and a collaborative optimization method using the surrogate Lagrangian relaxation (SLR) framework and improved objective feasibility pump (IOFP) is developed to solve the problem. In the SLR method, new step-size updating conditions are developed, eliminating the need for pre-estimating the optimal dual value. Additionally, only a subset of subproblems that satisfy the optimality conditions of the surrogate needs to be solved to overcome the low optimization efficiency resulting from oscillations in the feasible domain during internal searches in traditional Lagrangian relaxation (LR) methods. The IOFP method is employed to match the structure of the subproblem model of 0-1 mixed integer programming (MIP). During the search for integer solutions, a weighted objective function is added to the auxiliary model to improve the quality of solutions. Furthermore, it combines a variable neighborhood branching method to prevent the algorithm from entering into cycles. Finally, the effectiveness of the proposed model and the performance of the algorithm are validated through simulation experiments.