An improved Lagrangean relaxation algorithm for the dynamic batching decision problem

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan, sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 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. 1. Introduction Batch annealing is the last processing in steel cold rolling plants. The process improves mechanical properties of the steel coils by a series of heating and cooling operations in annealing furnaces. A huge amount of energy is consumed during the process. Managers are most concerned about how to maximise the throughput, minimise the energy consumption of the batch annealing process and improve the quality of products, since these are closely linked to the profit of the company. In this article, we investigate a dynamic batching decision problem …