Abstract: Under the background of the shortage of workers and the increasing of workers costs， it was very important to complete the manufacturing tasks with a reasonable allocation scheme of the number of workers.  Previous studies of flexible job-shop scheduling considering worker constraints assumed that the number of workers was given.  In order to optimize the number allocation of workers with different technical levels and flexible job-shop scheduling in an integrated way， considering the penalty cost， worker base cost and performance cost， a mixed integer programming model was established to minimize the total cost， and an improved TLBO algorithm was proposed to solve the problems.  In the algorithm， an activity scheduling decoding method was designed based on the three-layer coding of worker number allocation， operation sequencing and machine selection.  A hybrid heuristic initialization method was used for initialization. An effective neighborhood structure was designed for the problem features.  The tests of several groups of examples were verified that the proposed algorithm may determine the actual number of workers with different technical levels and obtain the excellent scheduling scheme， and is superior to the comparison algorithms in performance. 

Key words:  , dual resource constrained flexible job-shop, number of worker, cost, shop scheduling, teaching-learning-based optimization（TLBO） algorithm

摘要： 在工人资源紧缺且工人成本增加的背景下，以合理的工人数量配置方案完成制造任务变得至关重要。以往考虑工人约束的柔性作业车间调度研究假设工人的数量是给定的。为实现不同技术水平工人的数量配置及柔性作业车间调度集成优化，考虑工件拖期惩罚成本、工人基础及绩效成本，建立了最小化总成本的混合整数规划模型，并提出了一种改进教学优化算法进行求解。在算法中，采用基于工人数量配置、工序排序、机器选择的三层编码并设计了活动调度解码方法，采用混合启发式初始化方法进行初始化，针对问题特征设计了有效的邻域结构。通过多组算例测试验证了所提算法能确定不同技术水平工人的实际数量并获得优异的调度方案，且在性能上优于对比算法。

关键词: 双资源柔性作业车间, 工人数量, 成本, 车间调度, 教学优化算法