As people flooded into shelters in recent years, the city did not increase the shelter system’s physical capacity, relying instead on renting hotel rooms and so-called cluster apartments as a short-term solution. That might have seemed cheaper than building and maintaining new shelters, but it now appears shortsighted. The city also did not adequately modernize the way it contracted for shelters.

Steven Banks, the city’s city commissioner of social services, said he and his staff had already identified many of the problems cited in the audit, and that even as auditors began evaluating the shelter system, changes were underway.

In July, two months after eight auditors finished their fieldwork, the city Department of Homeless Services implemented a new model budget that will use a set of templates weighing factors, such as the type of shelter and maintenance, as it negotiates contracts for dozens of new shelters to open by 2021.

Thomas P. DiNapoli, the state comptroller, said in a statement that the city should be commended for its efforts to address shelter rates. “More can be done to negotiate with providers and to pay consistent rates that are within guidelines,” Mr. DiNapoli said in a statement. “We hope this audit assists the city with its ongoing work.”

Mr. Banks said that since the city’s homeless services and welfare agencies were consolidated last year under the new Department of Social Services, homeless services has had more contracting support, which has helped control costs.