A "strong mayor" in the mayor-council system has the authority to manage city departments. A "strong-mayor" is a type of mayor-council. The mayor´s responsibility is to ensure that people do not face any problem. So, he/she has to manage the city departments well. This kind of leader has the authority to manage his or her own departments (regulations made can not contradict the federal government´s regulations).
It is a system operated by the executive/legislative. The council has the power to appoint or deny department heads without popular approval. A chief of staff is appointed to act as a local administrator.