Optimal Partition of the Compulsory Education Period

Abstract

In the United States, the K-12 school system is implemented in compulsory education, but the educational system varies from country to country and from era to era. In this paper, we propose a mathematical model for optimally partitioning the education period based on the facility location problem. In simulation experiments using a dataset from Nara City, the ancient capital of Japan, we show that a parameter set that increases the school commuting cost for younger students can successfully explain the current number of schools. Then, we show that under that parameter set, changing the school-age partition has the potential to reduce the total commuting cost and operation cost. We also find the property that when the commuting costs are uniform, the optimal solution is to integrate all education periods into a single school.