The union that represents professional firefighters in Fairfax County declared last week that its members are "totally fed up" with the management of the county fire department and that "drastic changes are needed."

The Fairfax County Professional Fire Fighters asked that a management study of the department be undertaken and claimed that such a study will uncover "gross inefficient operations."

The union, which in March claimed the county had a critical manpower shortage, said in a press conference last week that the Fairfax fire department has alienated firefighters by not listening to their grievances and by allowing supervisors to run roughshod over firefighters' rights.

County Fire Chief George H. Alexander said he knew of no reason why the firefighters should be upset with the management and supervision of the fire department. "The supervisory personnel in the department come from the ranks of the firefighters. I don't understand their complaint," Alexander said.

The county Board of Supervisors has appointed a subcommittee, made up of three supervisors, to look into the need for a management study. That subcommittee has not yet met, according to one member, Supervisor Warren I. Cikins (D-Mt. Vernon).

Glenn Benerick, a spokesman for the firefighters, said the union feels that a management study of the department; which has 686 paid firefighters, "very well could prove we need a new (fire chief)."

Benerick said, however, that disaffection within the department has not affected its ability to fight fires. He said the union has not considered a strike to publicize its grievances. "I wouldn't even want to think of a strike. It is too dangerous," Benerick said.

In the press conference, one county firefighter, James H. Harrison, who was fired from the department early last week, claimed that he is losing his job because he pursued a union grievance for a black fireman.

Harrison, 41, a 9-year veteran with the department, said he is appealing his dismissal to the county Civil Service Commission.

Alexander refused to comment on Harrison's firing, except to say that Harrison is not being fired for his work as a union grievance representative.

In a letter of dismissal, Alexander said that Harrison committed acts that "have undermined, and indeed appear designed to undermine, the necessary command structure of an effective and reliable" fire department.

Harrison is accused, among other acts, of "posting a cartoon portraying the station commander in an uncomplimentary and derogatory manner." Harrison, who admitted to posting cartoons, brought some of his cartoons to the press conference.

One cartoon, which was clipped from The Washington Post and is called "Crock," depicts a bearded leader who proudly announces that he scored 34 on his I.Q. test. Harrison had renamed the "Crock" cartoon "Fire Services."

County Executive Leonard Whorton said last week that Harrison's appeal will be dealt with in accordance with established civil service procedure. Whorton said also that he is "at a loss to understand" the bitter complaints by the union of mismanagement in the fire department. He said he has heard "no unusual number of complaints" from firefighters.