Integration of Two Types of School Districts

Abstract

In Japan, compulsory education consists of six years in elementary school and three years in junior high school. But recently, the government has pushed to introduce integrated schools for nine years that combine the functions of elementary and junior high schools. Becuase the current elementary and junior high school districts are so intricate that it is not easy to determine which schools should be converted to integrated schools. Moreover, to make it easier for residents to agree, school districts similar to both elementary and junior high school districts should be created for integrated schools. Therefore, we first propose to use Adjusted Rand Index (ARI) as a measure of similarity of two partitions of districts. Then, we formulate the problem of deciding which schools should be converted to integrated elementary and junior high schools as a linear programming problem and propose a procedure for creating a school district reorganization plan. In a simulation experiment using the Nara City dataset, we confirm that the proposed method creates school districts for integrated schools that are similar to those of existing elementary and junior high schools.