Integrating Order Splitting and Acceptance with Batch Delivery in Parallel Machine Scheduling

Multiple production lines can work together to efficiently manufacture certain products. Thus, when capacity is insufficient, it is necessary to decide whether to develop new production lines to ensure the timely completion of all orders. For example, running a new production line for a small number of orders is not cost-effective. Therefore, decision-making involves choosing between paying tardiness costs for a few orders, abandoning some orders, or developing new production lines to maximize efficiency. Additionally, the timely transportation of completed orders is crucial and depends on vehicle usage efficiency. From a transportation perspective, fully loading vehicles is the most efficient, but this may impact the timeliness of orders, leading to potential tardiness costs. By comprehensively considering these aspects, a multi-machine production model is constructed that incorporates transportation batch sequences and uses heuristic algorithms to solve the problem. Finally, designed case examples validate the effectiveness of the model and algorithm.