Scheduling is significant in improving the production efficiency and reducing delivery delays for manufacturing enterprises. Unlike the flexible job-shop scheduling problem, two special constraints are encountered in real-world power supply manufacturing systems: 1) periodic maintenance and 2) mandatory outsourcing. As the characteristics of these constraints are not considered in existing scheduling algorithms, schedules generated by most existing approaches are not optimal or even conflict with these constraints. In this article, a self-organizing neural scheduler (SoNS) is proposed to overcome this limitation. A long short-term memory encoder is developed to transform the variable-length structural information into fixed-length feature vectors. Moreover, the reinforcement learning model is proposed to automatically select policies for improving candidate schedules. To validate the effectiveness of the proposed algorithm, extensive experiments are conducted on over 300 problem instances. The nonparametric Kruskal-Wallis tests confirm that the proposed algorithm outperforms several state-of-the-art methods in terms of effectiveness and robustness within a limited computational budget. It demonstrates that the proposed SoNS can solve scheduling problems with the periodic maintenance and mandatory outsourcing constraints effectively.