The top law enforcement officers of almost all of the nation's largest cities arrived at Harvard over the weekend to participate in on intensive, three-week management institute at the Business School.

The first of its kind in the country, the Institute is financed under the Law Enforcement Assistance Act of 1965. The police chiefs will be exposed to the traditional Business School case-approach to management problems.

"Chiefs of police are administering very large organizations--for example, the budget of the New York Department is more than $300 million--and yet, many chiefs have not had opportunities for management training," Patrick V. Murphy, assistant director of the office of law enforcement and an ex-chief himself said in an interview.

Under the Business School's approach, the police chiefs will examine actual case studies. Thomas J. O. Raymond, the program's Faculty director, said yesterday that most of the cases are from industry, but that "we hope there is some transferability to police problems."

The Institute will also bring in a large number of outside speakers who will talk on a variety--of non-management problems. Attorney General Nicholas Katsenbach and a number of Harvard Faculty members will be included in this group; the topics they discuss will range from race relations to the impact of recent Supreme Court decisions on police practices.

According to Murphy, recent studies of police departments all over the country have pinpointed a number of serious problems. He cited these common difficulties:

* poor organizational structure

* poor personnel and budgeting practices

* low level of discipline

* inadequate training

* severe recruitment problems

* poor public and community relations programs

Murphy said the value of the institute lies in the long period of time the chiefs would have to discuss their mutual problems, and the availability of Business School professors to add another viewpoint. For example, he said that may chiefs have strong but conflicting feelings on the distribution of police officers: some value the foot patrolman, while others rely on squad cars.

Both sides can gain a great deal from looking at it through the eyes of a professor who view it on a cost-analysis, cost-efficiency basis," he said.

Almost all the large police forces in the country are represented. The 50 largest cities were invited and 40 of these accepted, although a few, such as the commissioners in New York and Chicago, could not attend themselves. In both cases, they dispatched top-level assistants to the institute. The three-week period will be, Murphy said, the longest period of time that so many chiefs have been together. There is an annual meeting of the International Association of Police Chiefs, but this lasts only four or five days.

Murphy constantly emphasized what he termed "the changing role of police" in dealing with problems of race and poverty. One part of the program will deal specifically with the "social and legal environment" in which police departments operate. This section will draw on outside speakers.

"Getting away from your own environment and getting together with other chiefs should be extremely valuable," Murphy said.

To finance the program, the Office of Law Enforcement Assistance made a $64,000 grant to the Academy of Police Science in New York City. The Academy then contracted with individual members of the Harvard Faculty; thus, the program is technically not being run by the University, although virtually all the staff are members of the Faculty