For fed-up San Franciscans wondering just what City Hall is doing about the frustrating problem of homelessness, Jeff Kositsky’s office whiteboard provides some heartening answers.

On Monday, Kositsky officially becomes the director of the city’s first Department of Homelessness and Supportive Housing. He’s been on the job since June 1, but because of a quirk in the city’s byzantine budgeting system he has technically been deputy director of the Human Services Agency.

Kositsky and his team are squeezed into a small, temporary office on Van Ness Avenue where a whiteboard is filled with 28 immediate priorities and 23 longer-term goals. The latter column is called the “parking lot,” but — considering Kositsky’s obvious determination — the ideas probably won’t be parked there for long.

He’s already making headway on many of the department’s goals, which align closely with the four solutions offered by The Chronicle’s S.F. Homeless Project series in June. As part of a first-of-its-kind Bay Area media project — in which more than 80 organizations participated — The Chronicle outlined ways to create supportive housing, add Navigation Centers and improve traditional shelters, bolster mental health care and provide stronger law enforcement.

Some concrete improvements in those areas are taking shape. A third Navigation Center — a shelter with intensive case management that allows entire homeless camps to move in with partners, pets and belongings — will open in a few months at the eastern end of 25th Street in Dogpatch.

The first such center in the Mission is scheduled to close next summer because the site will be developed. A second at the Civic Center Hotel opened earlier this summer. A fourth is in the works — we hear the Salvation Army will operate it, though Kositsky wouldn’t confirm that.

The city this year also will pay for additional staffing so that one traditional shelter, yet to be selected, can offer 24-hour access. Currently, traditional shelters close during the day, forcing homeless people onto the streets, where they lack places to rest, shower and use the bathroom. The city also will pay to send extra staff, including nurses and social workers, to shelters on a roving basis to try to make them more like the helpful and welcoming Navigation Centers.

And there’s plenty more built into the budget:

•Three hundred new units of supportive housing.

• Additional subsidies for families and seniors who lose their housing.

• Rehabbing a permanent space for the new homeless department at 440 Turk St. in the Tenderloin, the former site of the San Francisco Housing Authority’s headquarters. The idea is to locate the city officials within the community they serve.

• An expanded Homeless Outreach Team, some of whose members will join workers in other departments, including the Police Department, Fire Department and the Department of Public Works, to tackle the burgeoning tent encampment problem.

Lt. Michael Nevin, who heads the police homeless unit, said officers continue to “see an upward trend” in calls for service related to homeless complaints. In June alone, there were 4,971 such calls, 634 more than in June of last year.

Kositsky said the new encampment team will aim to distinguish between campers who are desperately poor and need services and those using camps to run bicycle chop shops, prostitution rings and shooting galleries — people, he said, with whom law enforcement needs to intervene.

Supervisor Mark Farrell, who has made homelessness his signature issue, said he’s excited by the intense focus on the problem that was long ignored by City Hall.

“It was extremely frustrating my first few years at City Hall, when no one else was talking about the issue despite the fact it was a huge concern for residents of our city,” said Farrell, who first took office in 2011.

Mayor Ed Lee didn’t talk about homelessness much in his first term, but began to focus on it during his re-election campaign last fall. Since then, Lee has created the new homeless department, slowly expanded the Navigation Center program and pledged to get 8,000 people off the streets.

Last year, the city spent an eye-popping $241 million on homeless services and supportive housing. This year, that dollar figure will grow even bigger. In his budget book for 2016-17, Lee said he has devoted an additional $25 million in general fund money for homelessness to make it “rare, brief and one-time through the provision of coordinated, compassionate and high-quality services.”

The extra funding will go to Kositsky’s new department, which has a budget of $220 million this fiscal year. The remaining money for homelessness goes mostly to the Department of Public Health.

One sticking point is that about $12 million of the new homeless spending this fiscal year comes from a sales tax hike that won’t go to voters until November and wouldn’t go into effect until April 1 if it passes.

Supervisor Aaron Peskin was the only supervisor who voted against passing this year’s budget because, he said, it’s “fiscally irresponsible to vote on a budget that’s predicated on a sales tax that voters haven’t even voted on yet.”

He also has an issue with the way it was placed on the ballot. Any tax hike in California that is intended to pay for a specific purpose requires two-thirds voter support. The three-quarter-cent sales tax increase is expected to raise $150 million in its first full year: $100 million for transit projects and $50 million for homeless services.

But despite the specific purpose intended by the mayor and supervisors, the sales tax measure doesn’t spell out how it would be spent and requires only a simple majority of votes. A separate measure would set aside $100 million a year for transit and $50 million a year for homeless services. If the sales tax fails and the set-aside measure passes, the latter is written in such a way that Lee can void the voters’ intent and not set aside the money.

“I feel this scheme is leaving us vulnerable to a legal challenge. It’s not consistent with what the voters of the state of California mandated,” Peskin said, referring to the 1996 ballot measure that set the two-thirds requirement.

The mayor’s office said the strategy is nothing new and has been affirmed as perfectly legal by the city attorney’s office.

Another aspect of the homeless department’s budget that is cause for concern is that the vast majority of it — $155 million — continues to fund 400 contracts with 76 private organizations, most of them nonprofits, that deal with homeless issues.

Sure enough, “nonprofit contracting” is in Kositsky’s “parking lot” column on the whiteboard — that means building a clearer picture of how those contracts help the homeless people they’re supposed to be designed to serve. He praised nonprofits for doing “God’s work,” but said there is some duplication of services and a culture of expecting a city contract to last forever once it’s obtained.

He has tentatively selected a vendor for a new database tracking system that will allow everybody who works in the homeless arena to track an individual’s progress as they receive services.

He pointed to a woman in Union Square who recently has been throwing bottles at cars and appears to have a major mental health problem. It is believed she lives in city-funded supportive housing, but officials don’t know where so they can’t determine which nonprofit operates her housing to discuss the issue with staffers there. A database would easily answer that question.

The system should also help streamline the nonprofit contracting system to eliminate duplication, Kositsky said. He said he wants to use some of the potential savings to give raises to no nprofit workers.

As he continues to make his way through his whiteboard list, Kositsky has the mayor, the supervisors, irritated residents and more than 80 media outlets — including this one — watching. So, you know, no pressure. And he knows it.

“All I can ask for now is continued pressure by the public and by the media to focus on commonsense, compassionate solutions — to not let the department be buffeted by the political winds,” he said.

Heather Knight is a San Francisco Chronicle staff writer who covers City Hall politics. Email: hknight@sfchronicle.com Twitter: @hknightsf