Optimizing the Assignment of Students to Classes in an Elementary School

Every summer, the Salanter Akiba Riverdale SAR Academy must create class placements for their elementary school students. Each grade of 80 to 100 students must be divided into four classes. In assigning students to classes, the school administration aims to foster a positive social and educational environment for students while satisfying placement requests and recommendations from parents, teachers, and school therapists. The school must satisfy several constraints such as not placing certain pairs of students in the same class or keeping boy/girl ratios balanced. The process of creating optimal class placements by hand can be laborious and difficult, especially for grades with many constraints to satisfy. This paper describes a model that is being used to assist SAR Academy with creating class placements. Following the constraints and objectives given by administrators at the school, we describe an integer-programming model for satisfying placement constraints and heuristics to further improve on the outputs of the integer-programming model. The results of this process were successfully used to assist administrators in assigning students in one grade for the 2012--13 school year, and SAR Academy plans to use the model for help with future class placements.