Student assignment algorithms have far reaching implications for families, the education system, and for society as a whole. Motivated by operational challenges faced by the San Francisco Unified School District (SFUSD), we use a mechanism design framework to develop, operationalize, and streamline algorithmic student matching policies in San Francisco. From 2018-2020, we worked with the SFUSD to design a new policy for student assignment system that meets the district's goals of diversity, predictability, and proximity. We used optimization techniques to investigate the district's proposal of restricting choice to zones and suggested additional classical school choice policies from the literature. We find that appropriately-designed zones with minority reserves can achieve all the district's goals, at the expense of choice. Using predictive choice models, we show that a zone-based policy can decrease the percentage of racial minorities in high-poverty schools from 29% to 11%, decrease the average travel distance from 1.39 miles to 1.29 miles, and improve predictability, but reduce the percentage of students assigned to one of their top 3 programs from 80% to 59%. Traditional district-wide choice approaches can improve diversity and choice at the expense of proximity. Our work informed the design and approval of a zone-based policy for use starting the 2026-27 school year. Building off the potential of zone-based policies, we also investigate more rigorous methods of zone optimization. To address challenges in zone design, we propose a framework for computationally difficult and highly constrained multi-objective optimization. We generate an ensemble of potential zone maps using a multi-lens integer programming approach, narrow in on a smaller set of viable solutions, then simulate the student assignment process to understand the interactions between zones and choice patterns. Using tools inspired by the literature on human-computer interaction, we learn the optimization model specifications from district stakeholders and elicit value trade-offs to help select the final map for implementation. Another challenge faced by San Francisco is that nearly 20% of applicants take an outside option during the student assignment process, opting out of SFUSD. Overbooking schools in the first round of assignment can mitigate costly student shuffling in the presence of cancellations. In a more general setting, we consider the problem of overbooking when assigning agents to items, and agents have priorities for each item. The goal is to determine how much to overbook or "inflate" capacities for each item to minimize reassignment costs. Reassignment based on a priority ordering arises in several applications beyond school choice, including allocating airplane seats and medical appointments, and college placement. We provide a Greedy heuristic that approximates the optimal capacities when reassignment must respect these priorities. Using the heuristic, we show that the presence of priorities generates a bullwhip effect, where less popular items face higher yield uncertainty and incur higher costs due to externalities created by more popular items. Simulations using data from a school district validate our theoretical results on the structure of the greedy solution, and the resulting capacities informed overbooking in the district for the 2023-24 school year. [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.]