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With fewer available seats in good public schools than families who want them, many cities face a vexing challenge: How do you decide which children go where?

Enter Neil Dorosin.

鈥淵ou have to allocate public school seats fairly, transparently, and efficiently, but it turns out that鈥檚 not so easy to do,鈥� said Mr. Dorosin, the executive director of the Institute for Innovation in Public School Choice, based in New York City. 鈥淲e help cities solve that problem.鈥�

Over the past decade, Mr. Dorosin and the nonprofit IIPSC have used a combination of economic theory and custom software to help overhaul the school choice and student-assignment systems in New York, Boston, Denver, and New Orleans. That work has converted a tangled web of school applications, deadlines, and admissions preferences into algorithms that generate one best school offer for every student.

鈥淭here is a science to giving parents what they want in greater numbers,鈥� Mr. Dorosin explained.

For the time being, at least, IIPSC has almost totally cornered the market on providing that service, and the group is now poised to expand. In March, the Michael & Susan Dell Foundation awarded the institute $1.2 million that will be used to do work in Philadelphia, Washington, and a third city, likely Detroit. A fourth city could soon follow.

鈥淪chool choice exists in most cities. It can either be organized and facilitated, or it can be the Wild West,鈥� said Joe Siedlecki, the program and policy officer for the foundation鈥檚 U.S. education team.

While IIPSC鈥檚 initial efforts included only district-managed schools, the group鈥檚 focus now is on creating 鈥渦niversal enrollment鈥� programs that bring district and charter schools together in one centralized school assignment system. Proponents say that rationalizing the mechanisms that govern messy school choice marketplaces can help fix a host of problems, including opaque rules that unfairly benefit middle-class families, sometimes-sneaky admissions practices at charter schools, and long student waiting lists that hinder both families鈥� and schools鈥� ability to plan.

Because the assignment systems generate reams of data on parental demand for different schools and programs, they are also seen as a pillar of the 鈥減ortfolio鈥� approach to district management, in which families are offered an array of education options that may be expanded or closed based on performance and other factors.

But there is some evidence that algorithm-based school assignment doesn鈥檛 help more disadvantaged children actually gain access to better schools, and some observers worry that such systems force parents to make choices without adequate information.

In some cities, universal enrollment has also sparked opposition from advocates for regular public schools.

鈥淲e鈥檝e become obsessed with moving children around rather than investing in schools to improve them,鈥� said activist Helen Gym, a founder of the group Parents United for Public Education, based in Philadelphia. 鈥淚 think that鈥檚 a bad approach.鈥�

Allocating Scarce Resources

Mr. Dorosin of IIPSC described the field of 鈥渕arket design鈥� that underlies the institute鈥檚 work in lay terms: Some scarce goods, like expensive women鈥檚 shoes, can be distributed by selling them to the highest bidder, he said. But others鈥攈uman organs, for instance鈥攃annot.

The latter is not an abstract example. IIPSC鈥檚 board chairman, Alvin E. Roth, a professor at Stanford University who won a Nobel Prize in economics in 2012, designed an overhaul of the nation鈥檚 system for matching the limited number of kidneys donated each year to the much longer list of those who need a transplant.

To match students with seats in public schools, IIPSC creates algorithms that draw from three sets of data: The schools鈥� families actually want their children to attend, listed in order of preference; the number of available seats in each grade at every school in the system; and the set of rules that governs admission to each school.

Selective magnet schools might screen for test scores, for example, while charters may give preference to low-income families or to the children of their board members. Most systems prioritize giving siblings the opportunity to attend the same school, and different schools offer dozens of other types of preferences. Fitting all the pieces together makes for an extremely complicated logic problem.

IIPSC software doesn鈥檛 guarantee that every family or school will get exactly what it desires, said board member Atila Abdulkadiroglu, an economics professor at Duke University. But the algorithm-building process 鈥渉elps us to identify the trade-offs, determine what is achievable, and come up with the optimal compromise.鈥�

The benefits are evident in the 1.1 million-student New York City school system, where in 2004, Mr. Dorosin, then the district鈥檚 director of high-school-admissions operations, helped lead the nation鈥檚 first adoption of an algorithm-based school assignment program. The focus was on district-run high schools.

Entering the 2013-14 school year, three-quarters of the city鈥檚 75,000-plus rising 9th graders now receive one of their top three high school choices. Only about 1,000 students have to be manually placed outside of the algorithm-matching process, via administrative assignments. That鈥檚 way down from 30,000 annually before the switch, when a murky 鈥済ray market鈥� of high school choice flourished.

In addition, student waitlists have been eliminated, meaning that schools can begin allocating their budgets, hiring staff members, and planning programs鈥攁nd that all families know where they stand鈥攎uch earlier in the selection process.

鈥淧reviously, those who knew how to work the system were able to get a number of options, and others were left behind,鈥� said Robert Sanft, the CEO of the New York district鈥檚 office of student enrollment.

Denver Reaps Benefits

Since the Denver school system paid IIPSC $350,000 in 2011 to help design its new student assignment system, formally known as the SchoolChoice program, the 88,000-student district has reaped similar rewards, said Shannon Fitzgerald, Denver鈥檚 director of choice and enrollment services.

Now, there is a single application process for all district and charter schools, compared with 64 separate processes in 2010-11. Just over 88 percent of participating students were assigned to one of their preferred school options for this fall, Ms. Fitzgerald said. And now, she said, the district knows how every child got placed in each seat in the city鈥攁 major problem in years past.

鈥淭here [used to be] a lot of blind spots,鈥� she said. 鈥淔or roughly one-fourth of our kindergarten kids, nobody could really account for how they got into their seats.鈥�

From a technical standpoint, implementing Denver鈥檚 new assignment system was relatively easy, she said. It took a total of four months for IIPSC and district technology staff members to create a custom algorithm and the software to run it. There was a monthlong whirlwind of quality-control tests. The biggest 鈥渉iccups,鈥� Ms. Fitzgerald said, were related to data entry.

The far greater challenge, she said, came on the front end. District leaders went on a summerlong 鈥渞oad show鈥� to sell the plan to worried parents and skeptical charter operators, some of whom were reluctant to cede control of a process so fundamental to their operations.

鈥淚t speaks volumes to the collaborative relationships we have in Denver with our charters that they were all able to put aside their desire to do what鈥檚 best for their school alone and to see how this could benefit the greater community,鈥� Ms. Fitzgerald said.

Now in its third year, Denver鈥檚 SchoolChoice program costs an estimated $575,000 annually to support.

The troubled school choice and assignment system currently in place in Philadelphia seemed like a prime target for a similar overhaul.

In 2012, the 131,000-student Philadelphia district identified 鈥�significant barriers to entry鈥� at dozens of city charter schools, including one that made its application available on only one day each year, requiring families to attend an open house at a suburban country club to obtain a copy.

And in 2010, Research for Action, an independent nonprofit education research organization based in the city, found that blacks, Latinos, males, and special education students fared far worse than other groups at every stage of the city鈥檚 high-school-selection process. All told, the researchers found, just 45 percent of Philadelphia 8th graders who completed a high school application in the fall of 2006 ultimately enrolled in any of the district high schools to which they had applied.

Eager to address those problems, Mayor Michael A. Nutter led a delegation of city education leaders on a visit to Denver in January of 2012. Lori A. Shorr, the mayor鈥檚 chief education officer, said the group got in touch with Mr. Dorosin shortly after its return. Preliminary work began late last year, Ms. Shorr said, and the Michael & Susan Dell Foundation awarded its grant to IIPSC not long after.

The consultants鈥� efforts in the District of Columbia, funded by the same pot of money, have proceeded quickly. Officials there announced last month that all of Washington鈥檚 regular public schools, which serve 45,000 students, and a majority of its charters would move to a unified system to assign students to schools for next fall.

But the work in Philadelphia has run into significant stumbling blocks.

The school district, beset by a financial crisis, has yet to sign on, and leaders of two major charter school coalitions have balked at the plan, according to Mr. Dorosin.

And when activists caught wind that the Philadelphia School Partnership, a nonprofit that has been leading the city鈥檚 push for universal enrollment, sought to include Catholic schools in a new student-assignment system that would be operated by a private entity, a firestorm ensued.

鈥淚t鈥檚 an extreme proposal that goes further than what any other city has done,鈥� said Ms. Gym of Parents United for Public Education.

Skeptical of Algorithms

Despite the problems Research for Action documented in Philadelphia鈥檚 existing system, the group鈥檚 executive director, Kate Shaw, is also cool to the idea of universal enrollment. Adopting such a program would amount to little more than 鈥渁 technical improvement in the process,鈥� she said.

Ms. Shaw pointed to a recent study by researchers at New York University that found the concentration of at-risk students in low-performing New York City schools had not changed appreciably since the adoption of an algorithm-based assignment system. While 8th graders from all backgrounds are now getting matched to their top high school choices more often, it found, the most-disadvantaged students have either remained ineligible for the city鈥檚 top high schools or have chosen not to select those schools, which are often located outside their neighborhoods.

鈥淎 universal enrollment process likely won鈥檛 change the universe for Philadelphia鈥檚 lowest-performing students,鈥� Ms. Shaw concluded.

While acknowledging that universal enrollment is not a 鈥渟ilver bullet,鈥� Mr. Siedlecki of the Michael & Susan Dell Foundation said the data such systems generate can be an invaluable tool in helping school systems 鈥済row their footprint of good schools.鈥�

In New York City, for example, such information has been used to make decisions about which city schools should be replicated or closed鈥攁nd to create new bilingual and other specialty programs in underserved areas of the city where there is evidence of high demand.

鈥淵ou get the information you need to change the dynamic,鈥� Mr. Siedlecki said.

Overall, IIPSC is bullish about the future of its approach: The group recently retained a management consultant to help plot its anticipated growth in the coming years, and Mr. Dorosin said that both districts and his own team are just beginning to tap into the power of the parent-demand data that new universal enrollment systems are generating.

鈥淚t鈥檚 an unprecedented, incredibly large, wonderful opportunity,鈥� he said. 鈥淲e truly believe that we鈥檝e figured out a system for doing this so parents, schools, and the education reform movement all win.鈥�