Research on bi-objective charge batch planning optimisation method based on improved ε-constraint framework

Charge batch planning (CHBP) is the basis of steelmaking-continuous casting section batch planning (SCCSBP). With the rapid development of the market-oriented demand of steel enterprises in the direction of multi-species, small batch, and just-in-time delivery, the integrated production process of SCCSBP dramatically increases the functional requirements of flexibility, material yield, and time-dynamic balancing of the CHBP. Therefore, the preparation of a high-quality CHBP is of great significance to improve the efficiency of steelmaking production and reduce material and energy consumption. A bi-objective mathematical model is established, and a cooperative optimisation framework combining an improved ε-constraint method (IECM) with branch-and-cut (B&C) is developed. Employing a bisection method-based heuristic, can rapidly detect the valid number of sub-problems, thus avoiding the computational burden of redundant sub-problems in traditional ε-constraint method (ECM). Meanwhile, this method can obtain multiple Pareto non-dominated solutions, providing more schemes for synergistic optimisation at each stage. The B&C can acquire high-quality solutions for sub-problems. Finally, simulation experiments with actual production data validate that the proposed method reduces the objective function values by 7.19%, 7.22% and 0.16% compared to the linear weighting method, traditional ECM and multi-objective optimisation method, respectively; and reduces the CPU time by 46%, 80.7% and 73.64%, respectively.