An improved Lagrangean relaxation algorithm for the dynamic batching decision problem

In this article, a dynamic batching decision problem arising in the batch annealing plant of an iron and steel complex is investigated. For each planning horizon, the problem is to decide which steel coils should be selected to form batches, each for an annealing furnace, to be annealed. The objective is to maximise the utilisation of furnaces, minimise the waiting time of steel coils and minimise the mismatching of coils in each batch. We formulate the problem in one planning horizon as a 0–1 integer programming model. Lagrangean relaxation algorithm is adopted to solve it. An improved Lagrangean relaxation algorithm which incorporates the variable splitting method is proposed to obtain better solutions. Different from the common variable splitting, both the variables and the constraints are replicated in this article. Computational experiments are carried out to test the performance of the algorithms both on a set of standalone one-horizon problem instances and in a rolling horizon frame. The problem parameters are set based on the real data collected from a batch annealing plant in China. The results show that the improved Lagrangean relaxation algorithm outperforms the classical one and can obtain near optimal solutions in a reasonable time.