School Families: A New Formulation of School District Planning Problem

Abstract

This paper makes a plan to introduce school families. School families refer to a hierarchical system where the junior high school district encompasses the elementary school district. School families have the advantage of promoting efficient cooperation between elementary and junior high schools. Therefore, we formulated a new school district planning problem to introduce school families and created an optimal plan under changing population situations. Our formulation achieves school families by exploiting the continuity constraints of the school district. We also compare two different methods of reorganizing school districts in the simulation experiments: changing school districts by transferring current students in a given year (school-year method) and switching new students' schools over a multi-year period (birth-year method). We examined the cost and computation time of plans obtained with both methods and showed that the method combining the two provides the most significant cost savings.