In many settings, such as university admissions, the rationing of medical supplies, and the assignment of public housing, decision-makers use normative criteria (ethical, financial, legal, etc.) to justify who gets an allocation. These criteria can often be translated into quotas for the number of units available to particular demographics and priorities over agents who qualify in each demographic. Each agent may qualify in multiple categories at different priority levels, so many allocations may conform to a given set of quotas and priorities. Which of these allocations should be chosen? In this talk, I’ll formalize this reserve allocation problem and motivate Pareto efficiency as a natural desideratum. I’ll present an algorithm to locate efficient allocations that conform to the quota and priority constraints. This algorithm relies on beautiful techniques from integer and linear programming, and it is both faster and more straightforward than existing techniques in this space. Moreover, its clean formulation allows for further refinement, such as the secondary optimization of some heuristics for fairness.