Integrated optimization of batch splitting and scheduling for parallel production lines

A kind of problem of simultaneously optimizing batch splitting and scheduling for parallel production lines was discussed. Firstly, a formula was derived to determine completion time of a batch, which was produced continuously on production line. Then a lower bound was given to the starting time of a batch considering production time of which overlapped that of the immediately previous batch. And a sufficient condition to secure an available buffer during a continuous batch delivery was proved. Based on it, an algorithm was proposed to obtain the batch starting time. Complexity of algorithm was not related to the batch size. Finally, with the batch delivery model and proposed batch splitting heuristic algorithm, a genetic evolution based heuristic method was constructed to solve the problem. Numerical experiments show that this method can effectively balance loads of the production lines with a batch splitting.