Enrollment and School Assignment
The Board of Trustees approved a [Board Policy 5116 ] governing student enrollment and school assignment in October 2011. In adopting this new policy, the Board’s priority was to preserve the community’s commitment to neighborhood schools while providing flexibility for variations in enrollment over time. The policy eliminates school attendance areas, the former geographic boundaries for each of the six elementary schools, and establishes a district-wide attendance area with the goal of assigning students to schools near their homes.
The policy directs the Superintendent to establish an unbiased enrollment process and an objective assignment criteria. All of our enrollment information can be found at the links to the right.
Process for school assignment
Under the new process for school assignment, students will be assigned to elementary schools based on the walking distance from their homes. The assignment criteria will take into account the walking distance from each new incoming student’s home to each of the six elementary schools as well as the limited capacity of each of the schools. Each enrollment period is a self-contained cycle.
The District will use a well-studied algorithm to optimize school assignment by assigning students to the closest schools that have available room.
How does the Algorithm work to assign students?
The Belmont-Redwood Shores School District assigns students to schools using an algorithm. The school assignment algorithm developed by the District is based on a linear optimization (also known as linear programming) function known as minimum-cost flow formula. Companies use similar linear optimization functions to make important business decisions. For example, airlines use a linear optimization function to determine flight routes that are most direct and minimize fuel costs, and shipping companies use a similar method to move packages from warehouses to stores to customers most efficiently.
In our case, the District uses a linear optimization method to assign incoming students to schools close to their homes and within the limits of the enrollment capacity at each school. The assignment algorithm allows the District to find the optimal solution to minimize the total distance traveled by all students to their schools. One way to think about the District’s goal is to imagine a pedometer attached to every student for one morning’s walk to school; the optimal assignment would minimize the sum of the distances of all students’ walks to their schools. Instead of pedometers, however, the walking distance for all students is determined by querying the same Web-based mapping service, such as Bing Maps.
The Belmont-Redwood Shores School District assigns students to schools using the algorithm to minimize total walking distance traveled collectively by all students being assigned in that calculation. The calculation consists of two distinct phases. In the first phase, the distance from each student’s home to each of the six elementary schools is calculated. In the second phase, which can be run repeatedly with different parameters, these distances are used, along with minimum and maximum capacity of each school, to perform an assignment that minimizes the total distance travelled.
In the current implementation, the Bing Maps service is used to transform the addresses of each student to a latitude and longitude, and this location is then used to calculate the walking distance to each school entrance. When calculating distances to each of the six schools, there are two schools that have multiple entrances, and for those schools, the distance used for assignment is the minimum distance to any of the school’s entrances.
Once the distances are calculated for each student, the assignment is performed according to the capacity constraints provided by the program operator. In order to perform the actual assignment to minimize the total distance travelled by all students being assigned to schools while respecting the capacity constraints at each school, the Microsoft Solver Foundation package is used.
Statistics and Examples
For the 2013-2014 school year, 98% of new, non-sibling, incoming kindergarteners who enrolled during the first enrollment period were assigned to either their first or second closest schools.
Consider the following two extremely simple examples to illustrate the process. In each example, there are two families each having one child and two schools each having space for one child. With six schools and several hundred incoming Kindergarteners, the actual calculation is more complicated, but the idea is the same: we want to find the lowest aggregate distance. When enrollment falls a reasonable amount below the capacity of the incoming classrooms, all students would be assigned to their closest school. These examples use meters as the distance unit because the actual calculation is done in meters, but the units don't impact the results in any way.
In the first example, Family 1 lives 500 meters from School A and 1,000 meters from School B. Family 2 lives 1,200 meters from School A and 300 meters from School B. There are two possible assignments. If Family 1 is assigned to School A and Family 2 is assigned to School B, the total distance travelled will be 800 meters. If Family 1 is assigned to School B and Family 2 is assigned to School A, the total distance travelled will be 2,200 meters. Since the assignment with a total distance travelled of 800 meters is the minimum, that will be the assignment chosen by this process.
In the second example, Family 1 lives 300 meters from School A and 1,200 meters from School B. Family 2 lives 500 meters from School A and 1,700 meters from School B. As before there are two possible assignments for this example. If Family 1 is assigned to School A and Family 2 is assigned to School B, the total distance travelled will be 2,000 meters. If Family 1 is assigned to School B and Family 2 is assigned to School A, the total distance travelled will be 1,700 meters. Since the assignment with a total distance travelled of 1,700 meters is the minimum, that will be the assignment chosen by this process. Note that while Family 1 is not assigned to their closest school, the assignment that is chosen minimizes the distance travelled by all of the students assigned. As a reminder, these examples are contrived to demonstrate how the assignment process functions.
If you would like to calculate the distance to each of the six elementary schools in the district in the same manner as the district does at assignment time, please enter a complete address within the BRSSD school district. As an example, the address for the district office should be entered as 2960 Hallmark Drive and Belmont should be selected as the city.