  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.
