In Chapter 1, we study the allocation of homogeneous positions under affirmative action policies where some positions are reserved for underrepresented groups on a "minimum guarantee" basis. Each individual has a merit-based score and may be eligible for multiple reserves. When an individual counts towards each of the reserves that she is eligible for upon admission, we propose a choice function that satisfies three properties: the minimum guarantee requirement, non-wastefulness, and a stronger fairness notion than the one introduced by Sonmez and Yenmez (2019). Moreover, our proposed choice function is the unique one that produces an assignment achieving the maximal cutoff score among all non-wasteful assignments satisfying the minimum guarantee requirement. Furthermore, we show that the outcome of this choice function is not score-wise dominated by any other assignment that satisfies the minimum guarantee requirement. In Chapter 2, we study high school admission in China that is implemented through a centralized mechanism in each city independently. To better achieve equality in education, within the last decade, many provinces have adopted a reservation system where elite high school seats are reserved for reserve-eligible students from designated middle schools. To maintain the quality of students at elite schools, in some cities, students become qualified for reserves if their exam scores satisfy certain constraints. We study two types of widely used score constraints under reserve systems: fixed and dynamic score constraints. We first show that the reserve system with fixed reserve score constraints does not have any fundamental failure, but the precedence order of different types of seats can affect the representation of reserve-eligible students. On the other hand, the reserve system with dynamic reserve score constraints suffers from major deficiencies. Motivated by this flawed practice, we propose a new choice function that can be applied to the student-proposing deferred acceptance mechanism while preserving its desired features such as stability and strategy-proofness. In Chapter 3, we investigate the assignment system of government positions in Imperial China by building upon the previous research by Bo and Chen (2021). The system assigned a set of heterogeneous jobs to a set of candidates and was subject to two distributional constraints, namely job category eligibility and location restrictions. The primary objectives of policy makers were to assign high-level candidates to as many suitable jobs as possible while minimizing the number of unassigned jobs. However, to handle the two goals well, previous assignment systems did not ask candidates to submit their preferences. We construct a model in which candidates are allowed to submit their preferences over all jobs. Our focus is to assign candidates to jobs while satisfying the constraints and goals of policy makers and incorporating candidates' preferences. We propose a sequential implementation of deferred acceptance algorithm to achieve a more efficient outcome. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]