Hierarchical Decomposition based Optimization Method for Production and Inventory Planning in Steel Galvanizing Operations

Galvanizing operations in steel manufacturing face significant challenges in balancing setup and inventory costs while maintaining customer satisfaction. Frequent zinc bath changes not only cause production downtime but also disrupt process continuity due to repeated thermal rebalancing. In addition, destination-specific storage locations impose release capacity limits that restrict dispatch quantities in each period, thereby tightly coupling production planning, inventory allocation, and order fulfillment decisions across multiple periods. The intricate interactions among setup continuity, time-window constraints, and storage-release limitations create a structurally interdependent planning environment, rendering fragmented decision-making ineffective. These structural complexities underscore the necessity of integrated and intelligent planning methodologies within modern smart manufacturing systems. To address these challenges, this study proposes an intelligent planning framework grounded in mathematical modeling and optimization algorithm. A mixed-integer programming (MIP) model is developed to comprehensively capture setup carryover, order-specific time windows, multi-period capacity constraints, and storage-release restrictions, while explicitly representing the trade-offs among setup switching, inventory holding, and unmet-demand penalties. To overcome the computational difficulty of directly solving large-scale MIP instances, a hierarchical decomposition-based matheuristic is introduced. The method exploits the underlying problem structure by performing family-level aggregation for dimensionality reduction, coordinating inter-period carryover decisions within a hierarchical optimization stage, and restoring feasibility through order-level re-optimization. This abstraction–refinement mechanism significantly reduces computational complexity while preserving global coordination. Computational experiments based on real industrial data demonstrate that the proposed approach consistently achieves higher solution quality and shorter solution time compared with both baselines and planning practices, confirming its effectiveness as a practical decision-support tool for intelligent production planning in continuous galvanizing line operations.