Simultaneous batch splitting and scheduling on identical parallel production lines

This paper explores the simultaneous batch splitting and scheduling problem for identical parallel production lines, which is different from the parallel machine scheduling in that the processing time of a batch on parallel production lines is not fully proportional to that of a product. To solve the problem, a formula is derived to determine the processing time of a batch on a production line which is not taken as a single machine for each item in the batch. A lower bound is provided for the starting time of a batch production, which overlaps the previous one. A sufficient condition for guaranteeing the constant availability of the end buffer is given and proven mathematically with respect to a continuously delivered batch. Based on the above, an algorithm whose complexity is unrelated to the batch size is proposed to obtain the starting time of a batch production. Finally, a heuristic method based on genetic algorithm is constructed to solve the splitting and scheduling problems simultaneously. Numerical experiments show that this method functions well to balance the loads of the production lines. In fact, the proposed approach is significantly more effective than the existing methods for production planning and scheduling on production lines (each of which is considered as a single machine for both batch and item).