An Efficient Augmented Lagrange Multiplier Method for Steelmaking and Continuous Casting Production Scheduling

Abstract

The steelmaking and continuous casting (SCC) process is one of the vital processes in iron and steel plants since it determines chemical compositions of slabs and is often a bottleneck for iron and steel manufacturing. In this paper, we first develop a discrete-time mixed-integer linear programming (MILP) formulation for a new SCC scheduling problem where different processing routes are used to produce diversified and personalized slab products. To solve the proposed MILP formulation efficiently, we then propose a novel efficient solution algorithm using Augmented Lagrange multiplier method (e-ALM) through relaxation of the coupling constraints and incorporation of penalty components. A heuristic-based list scheduling approach as well as adjacent pairwise swap operations is used to construct a high-quality feasible schedule. A fine-adjusting strategy based on the subgradient direction is proposed to update Lagrangian multipliers dynamically to speed up the convergence. It is shown that the proposed e-ALM is able to generate optimal or near-optimal solutions with 5% optimality for 150 industrial-scale instances and outperform the commercial solver GAMS/CPLEX and the existing Lagrangian relaxation algorithms with better feasible solutions and smaller duality gap within the specified computational time.