The Hot Strip Mill Scheduling Problem With Uncertainty: Robust Optimization Models and Solution Approaches

In this article, we focus on a biobjective hot strip mill (HSM) scheduling problem arising in the steel industry. Besides the conventional objective regarding penalty costs, we have also considered minimizing the total starting times of rolling operations in order to reduce the energy consumption for slab reheating. The problem is complicated by the inevitable uncertainty in rolling processing times, which means deterministic scheduling models will be ineffective. To obtain robust production schedules with satisfactory performance under all possible conditions, we apply the robust optimization (RO) approach to model and solve the scheduling problem. First, an RO model and an equivalent mixed-integer linear programming model are constructed to describe the HSM scheduling problem with uncertainty. Then, we devise an improved Benders' decomposition algorithm to solve the RO model and obtain exactly optimal solutions. Next, for coping with large-sized instances, a multiobjective particle swarm optimization algorithm with an embedded local search strategy is proposed to handle the biobjective scheduling problem and find the set of Pareto-optimal solutions. Finally, we conduct extensive computational tests to verify the proposed algorithms. Results show that the exact algorithm is effective for relatively small instances and the metaheuristic algorithm can achieve satisfactory solution quality for both small- and large-sized instances of the problem.