An Effective Subgradient Method for Scheduling a Steelmaking-Continuous Casting Process - Kun Mao; Quan-Ke Pan; Tianyou Chai; Luh, Peter B. (IEEE transactions on automation science and engineering, 2015)
The steelmaking-continuous-casting (SCC) process, which includes steelmaking, refining and continuous casting, is one of the major bottlenecks of iron and steel production. Efficient and effective scheduling of this process is essential to improve the productivity and reduce the production costs of the entire production system. We present a time-index formulation for this scheduling problem and a Lagrangian relaxation (LR) approach based on the relaxation of the machine capacity constraints. The relaxed problem is solved using an efficient polynomial dynamic programming algorithm. The corresponding Lagrangian dual (LD) problem is solved using a deflected conditional subgradient level method. Unlike the conventional subgradient algorithms for the LD problem, our method guarantees convergence using the Brannlund's level control strategy to replace the strict convergence condition that the optimum of the dual problem is known a priori. Furthermore, our method enhances the efficiency by introducing a deflected conditional subgradient to weaken the zigzagging phenomena that slows the convergence of conventional subgradient algorithms. The computational results demonstrate that the approaches can quickly obtain high-quality solutions and are notably promising for the SCC scheduling. Note to Practitioners-Efficient and effective SCC schedule is vital for the manufacturing system of iron and steel production. Unfortunately, the scheduling is extremely difficult because of its combinatorial nature and practical complex constraints such as job grouping constraints, precedence constraints, different transport time, and setup times. To obtain high-quality solutions within an acceptable computational time, we can use a problem-oriented approach, which can be the LR. However, there are two deficiencies in this approach: its empirical termination criteria, such as maximal iteration number or running time, which make it difficult to find a golden rule for various problems, and the inefficiency, which is caused by the so-called zigzagging phenomena. To overcome these deficiencies, this paper develops an effective subgradient method for SCC scheduling based on the machine capacity relaxation. This method gives an objective termination criterion based on the convergence condition of the method, and improves the efficiency based on a new search direction or a new subgradient. Then, the work shows how this method can be applied to solve an SCC scheduling problem. The computational results confirm their effectiveness and efficiency. The approaches can also be applied to other similar production scheduling problems.