In this thesis, we present multiple problems that arise in cancer treatment decision-making, and we analyze and implement methods used to solve them. The first problem is the selection of objectives that reflect latent clinical preferences during radiation therapy treatment. By connecting an inverse optimization formulation with greedy and regularized solution approaches, we show that sparse sets of objectives can be retrieved effectively. The development of the greedy forward selection approaches for objective selection leads to an in-depth exploration of the greedy algorithm's performance when the optimized set function is approximately submodular. In addition to the greedy algorithm, we study approximate submodularity in other areas in discrete optimization. The second cancer treatment problem is combination chemotherapy optimization, which requires merging differential equations that model dynamics together with discrete decision variables for complex operational constraints. We formulate this problem as a mixed-integer linear program and solve two models, one that focuses on tumor shrinkage and another that minimizes toxicity.