Mixed-integer programming models for mid-term production planning in integrated steel production

This work addresses a tactical planning problem at a German steel manufacturer within a hierarchical production planning system. Operations managers must align booked orders with limited capacities of multiple production facilities over a mid-term planning horizon. For each order, a single process plan and start period must be selected, adhering to time-dependent capacities and no-wait constraints. The goal is to meet associated due windows (e.g. for intermediate milestones and final delivery) as closely as possible, aligning with just-in-time scheduling problems. We propose two mixed-integer programming models: a job shop-based model and a more compact knapsack-type model. We prove that the problem is strongly NP-hard. Experimental results using benchmark instances derived from the literature and a standard solver demonstrate that the knapsack-type formulation consistently outperforms the job shop-based one in terms of optimal solutions and average optimality gap. Additionally, structural experiments offer practical insights into how resource profile choices impact workload distribution across resources and time.