The board and the director shall make a study of all matters touching the administration and enforcement of this part and the rules and regulations adopted thereunder. To this end, the board or the director may visit all offices and places of employment to ascertain information and to advise with the heads of the various departments concerning their method of handling matters affecting the service; and to ascertain if this part and the adopted rules and regulations are fully complied with. The board or director, in the course of such inquiries, shall have the power to administer oaths, subpoena, and require the attendance of witnesses and the production of records, books, papers, and documents pertaining to the subject matter under investigation. The board, or the director, shall have the authority to inquire into the number of employees in any office or department and, after notice and an opportunity to be heard by the appointing authority and the employees affected, the board may determine there is an excessive number of employees in such office or department, in proportion to the amount of work required, and in that event, it shall issue an order in writing to the appointing authority to eliminate the number of employees found to be excessive, in the manner prescribed by this part or the rules and regulations, and such order shall be forthwith complied with by the appointing authority. The board and the director shall also study the organization of the system, procedure of administration, and other matters which affect the successful operation of the system and make such lawful changes as may increase efficiency or economy.