We study the Japanese Residency Matching Program (JRMP) in which hospitals are partitioned into disjoint regions and both hospitals and regions are subject to quotas. To achieve a balanced distribution of doctors across regions, hard bounds are imposed by the government to limit the number of doctors who can be placed in each region. However, such hard bounds lead to inefficiency in terms of wasted vacant positions. In this paper, we propose two suitable algorithms to reduce waste with minimal modification to the current system and show that they are superior to the algorithm currently deployed in JRMP by comparing them theoretically and empirically.