Purpose: Fractionation in radiotherapy is the scheduled break up of a total treatment dose into individual doses. The goal of this thesis is to seek a mathematically optimal dose schedule, in the context of a biological tissue dose-response model, the linear-quadratic function. Methods: We examined the mathematical properties of the fractionation problem in the context of an arbitrary number of sensitive-structure constraints and determined the properties of the optima. We also implemented a numerical search technique to solve the problem. Results: On the theoretical side, we confirmed and extended the results in the literature. We showed the optima always occur at the intersection of two or more constraints or at the equal dose per fraction point (or at any arbitrary feasible point on the boundary, which includes the two points just mentioned). On the numerical side, we successfully implemented a simulated annealing algorithm to our problem.