Doubling down on its commitment to using off-site construction methods to create faster and less-expensive housing for the formerly homeless, city officials are kicking off a search for a San Francisco site to build a modular factory.

On Tuesday, acting Mayor London Breed, in collaboration with building trades groups, is expected to announce the first steps in establishing a modular factory within city limits, which many housing advocates believe is a vital step in efforts to speed up production of affordable-housing units.

While the process will take a while — the first phase will include hiring a consultant and creating a business plan — the announcement is important because it includes the involvement of the city’s powerful building trades unions, some of which have opposed modular construction because it can lead to less work for its members.

Modular construction, a method in which building components are built somewhere else and then trucked to a construction site for assembly, has been proved in many cases to cut costs by 20 percent and speed up production by between 20 and 40 percent.

“The housing shortages and homelessness issues facing our city are the challenges of our time, and we need to deliver creative solutions,” Breed said. “It is clear that we need more housing, and we need it now.”

The move comes as the city is selecting a developer to use modular construction methods to build supportive housing for formerly homeless people on a parking lot behind the federal courthouse at Mission and Seventh streets.

That request for proposal, issued in October, was not received well by some factions within the building trades and prompted Building Trades Council President Larry Mazzola to write a letter warning the city not to hire Factory OS on Mare Island in Vallejo, the modular manufacturing facility closest to San Francisco.

In particular, Mazzola objected to the Vallejo factory’s “wall-to-wall” labor agreement with the carpenters union, which allows those workers to do everything from painting to plumbing to carpet laying, jobs usually performed by other trades.

Mazzola said that using Factory OS would show “a blatant disregard” for the other craft unions.

But with its endorsement of the idea of establishing a San Francisco factory, Mazzola and the other building trades have agreed to allow the Seventh and Mission project to go forward as planned, according to Kate Hartley, director of the Mayor’s Office of Housing and Community Development. In a statement, Mazzola thanked Breed and the late Mayor Ed Lee for “recognizing building trades workers and the importance of keeping these jobs in San Francisco.”

“Fixing the homeless problem, along with the housing shortage in San Francisco, are two major issues that San Francisco faces, and we are proud to partner with the city to help develop a facility that addresses these issues while keeping jobs in our local economy,” he said.

The city will be looking for a consultant “with substantial experience in the design, construction and operation of modular housing production facilities that can both develop a business plan and facilitate the stakeholder process,” according to a press release from Breed. Funding for the consultant will come from the Mayor’s Office of Housing and Community Development and Office of Economic and Workforce Development.

“We have made growing and retaining good manufacturing jobs a priority in San Francisco,” said Office of Economic and Workforce Development Director Todd Rufo. “This funding is an important first step in developing a facility in partnership with labor that creates good jobs and accelerates affordable housing.”

The selected consultant will start by convening a series of meetings with city staff and labor regarding the construction and long-term operation of a modular housing production facility, including capital investment requirements, construction specifications, site logistics, and transportation requirements for raw materials and finished components. The second phase will consist of a business plan, with recommendations due by the end of the year.

Hartley said modular construction to house the formerly homeless has been a documented success in other markets. She cited Vancouver, British Columbia, where a 48-unit modular development proved so successful the city ordered an additional 600 units.

“Because our homeless crisis is so severe, we have been looking for ways to get more affordable units online faster,” Hartley said. “Studying effective modular facilities around the world, as well as the new facility in Vallejo, city housing leaders came to the conclusion that San Francisco needs its own manufacturing plant.”

J.K. Dineen is a San Francisco Chronicle staff writer. Email: jdineen@sfchronicle.com Twitter: @SFjkdineen