A mathematician from Bell Laboratories has devised a radical new method of programming computers to solve some of the most difficult management problems faced in industry and other large organizations.

But, although early word of the development has stimulated optimistic press accounts, several computer scientists cautioned that no tests had been made with realistic problems.

"If it lives up to its promise, it's quite extraordinary, the kind of advance that transcends the field," said Daniel J. Kleitman, an applied mathematician at the Massachusetts Institute of Technology. "Ideas like this come along maybe every 20 or 30 years. That's if it works."

The method is an algorithm, a kind of strategy to use in writing a computer program to solve a problem. In this case, the problems are so complex that they may take even the biggest mainframe computers several days to solve. According to early estimates, the new method could cut this time to 1 or 2 percent as long. "What this would mean is that you could do problems that you wouldn't have had time to do before," Kleitman said. "You could solve the same problem in less time, or you could solve bigger problems in the same amount of time."

The kinds of problems at issue are those common to many large industries seeking some optimal way to manage complex, interdependent operations. For example, a company might want to plan operations so as to minimize the costs of a large network of manufacturing plants, each drawing on various suppliers of raw materials whose prices fluctuate according to several other factors and in which all the plants need to coordinate production with sales rates that vary seasonally.

The new method was developed by Narendra Karmarkar, 28, an Indian-born mathematician recently hired by Bell Labs, AT&T's research center in Murray Hill, N.J. His method, which has not been named, is seen as an alternative to the so-called simplex method developed more than 30 years ago by George B. Dantzig.

The differences between the methods involve forms of mathematics unfamiliar even to many computer experts. Mathematicians, however, regard Karmarkar's method as unusually clever.

"It's very interesting work," said Michael Overton, a professor of computer science at New York University's Courant Institute of Mathematical Sciences. "But it is only hearsay that it's 50 or 100 times faster than the simplex method. A lot of people are experimenting with this now, and I would expect that in about six months we'll know whether it's really very useful."

Although a story on his method appeared in The New York Times yesterday, Karmarkar himself was unavailable to reporters. A spokesman for Bell Labs said he was spending the day trying to pass the written exam for a New Jersey driver's license.