Daycare Matching in Japan: Transfers and Siblings

TL;DR

This paper introduces a new centralized algorithm for daycare matching in Japan that accounts for transfers and sibling preferences, demonstrating its effectiveness and stability through experiments on real data.

Contribution

The paper develops a novel integer programming-based algorithm for daycare matching that handles transfers and family preferences, extending classical matching theory.

Findings

Algorithm performs as well as current methods in matching children.

It finds stable outcomes in all tested instances.

Experimental validation on real data sets supports its practical utility.

Abstract

In this paper, we study a daycare matching problem in Japan and report the design and implementation of a new centralized algorithm, which is going to be deployed in one municipality in the Tokyo metropolis. There are two features that make this market different from the classical hospital-doctor matching problem: i) some children are initially enrolled and prefer to be transferred to other daycare centers; ii) one family may be associated with two or more children and is allowed to submit preferences over combinations of daycare centers. We revisit some well-studied properties including individual rationality, non-wastefulness, as well as stability, and generalize them to this new setting. We design an algorithm based on integer programming (IP) that captures these properties and conduct experiments on five real-life data sets provided by three municipalities. Experimental results show that i) our algorithm performs at least as well as currently used methods in terms of numbers of matched children and blocking coalition; ii) we can find a stable outcome for all instances, although the existence of such an outcome is not guaranteed in theory.