With the consultants who engineered Mayor Bloomberg’s latest overhaul of the public schools reaching the end of their $15.8 million contract, a dispute over how well they performed could soon escalate.

The Department of Education maintains that its contract with Alvarez & Marsal, a Midtown management consulting firm, will pay for itself in hundreds of millions of dollars trimmed. The firm was hired in June 2006 to cut excess bureaucracy from the city school system, such as bus lines the Bloomberg administration said were carrying no students at all.

But estimations of exactly how much the city will save from the Alvarez & Marsal consultants’ time here are being scaled back, raising concerns from city officials, including the comptroller, William Thompson, who is considering an audit of the contract, his spokeswoman, Laura Rivera, said.

Projected savings from the high-profile bus-rerouting project, which left many children stranded in the cold, have been cut in half to $10 million annually from $20 million. Five million dollars was saved in the last fiscal year, Department of Education officials said, explaining that the figure is lower because changes were implemented late in the school year. Estimations of how much the firm will save the city on other projects, such as restructuring school facilities operations, also appear to have dropped, with officials reporting $171 million, down from $200 million in total.

The Alvarez & Marsal contract will expire November 15. Some of its consultants have already ended their work with the city.

Part of the criticism of the contract is that it was awarded without seeking bids from other companies, adding to a number of no-bid contracts the Bloomberg administration has awarded. The city handed out more than $60 million in no-bid contracts between last July and June 30 of this year, 18 of which were valued at more than $1 million, according to figures provided by the office of the public advocate, Betsy Gotbaum.

An education historian, Diane Ravitch, said the Department of Education, which is preparing to release its first ever report cards grading public schools, should also pass out an evaluation of Alvarez & Marsal. “What are the measures of their performance? They can say it’s dollars, but what was the cost of parents and families and kids standing out in the cold last January?” she said.

The city’s contract with Alvarez & Marsal calls for biweekly “contractor’s reports” updating the schools chancellor, Joel Klein, on progress, and for more detailed evaluations every six months. A Department of Education spokesman, David Cantor, praised Alvarez & Marsal for rerouting $171 million annually directly to principals’ budgets.

“They’ve already paid for themselves many times over, and that money is going to keep coming every year,” he said.