Transportation officials with Howard County public schools revealed plans Thursday to maximize school bus efficiency, using a mathematical modeling program developed by University of Maryland students to determine the best bus routes should schools start and dismissal times change in the coming year.

The Baltimore Sun reports,

Last week, the Board of Education motioned to delay any changes to start and dismissal times until at least the 2018-19 school year to give administrators, staff and parents time to prepare for schedule adjustments.

While any potential changes to the start and dismissal times will not be implemented next year, school system director of transportation David Ramsay said transportation is a major factor in the decision-making process. Alternative start and dismissal times could not only increase the number of general and specialized bus fleets needed, but also increase overall costs.

“Transportation has, historically, been the area in which there are cost implications with adjusting bell times,” Ramsay said. “The tools that we had weren’t sufficient to the degree that we were happy with to really analyze this problem.”

Haghani, a Fulton resident, said the tool uses a mathematical optimization model that can minimize or maximize a particular function. In this case, he said, the goal was to minimize the total number of buses as well as the deadhead time, the time when buses are running without any students onboard.

“A solution that is 1 percent worse can lead to three or four more buses,” Haghani said.

Using data provided by the school system, Haghani said students used the bus start and end times, location and order of stops and the deadhead distance in the program.

“The optimization model tries to match up these routes together in a way that as many routes as possible are served by one bus,” he said. “We had a working model in about a month, but when we ran it, it took a long time.”

Five months later, Haghani said, results for each given scenario were available in under a minute.

While Haghani said the model was free-of-charge to the school system, Ramsay added that the school system paid $5,000 toward the QUEST program’s involvement and an additional $24,800 for consultation with Haghani. Other vendor price quotes for developing a model had exceeded $50,000, Ramsay said.

Once the school board makes a decision on school start and dismissal times, Ramsay said they will give Haghani a spreadsheet outlining the proposal to calculate the most efficient bus routes for the county’s elementary, middle and high schools.

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