Discrete particle swarm optimisation combined with no-wait algorithm in stages for scheduling mill roller annealing process

In this paper, a mill roll annealing operation scheduling problem is investigated against the background of a cast steel plant of Machinery Mill Roll Co., Ltd in mainland China. During the annealing processes, a roller needs to be processed in multistage process with different types of furnaces and there is no waiting between the stages. Based on the analysis of the feature of the mill roll annealing process, this problem can be formulated as a no-wait hybrid flow shop scheduling problem, of which the 'job' is a batch of rough roll, and the 'machine' is a heating furnace. As each batch will be of different sizes, the jobs will have different sizes and processing times. According to the no-wait characteristic between two sequential operations of a job, the no-wait algorithm in stages is designed to obtain the initial solution. Combined with the no-wait algorithm in stages, a discrete particle swarm optimisation algorithm has been developed to solve the integer programming model. In the simulation experiment with real data, the applicability and the effectiveness of algorithms are demonstrated by the comparisons and the analysis of the experiment results, and the equipment reformation strategies of the actual reference value are given as well which is beneficial for the policy-maker to arrange production reasonably. Furthermore, some large-scale instances about the no-wait hybrid flow shop scheduling problem are studied effectively.