In Japan, due to the shortage of healthcare workers, there has been a growing need to effectively allocate patients to different medical diagnoses or treatments in accordance with the severity of their illness and the capabilities of medical institutions. However, since these rules are often created manually by Japanese municipal authorities, their reasonableness is unclear and they require a lot of effort to create. In this paper, we propose a data-driven approach for designing patient allocation rules for medical diagnoses. Since patient allocation rules can be expressed as a flowchart-style diagram, our task of designing allocation rules is similar to a machine-learning problem of tree-based classification models. Due to its modeling capabilities, mixed-integer optimization has recently attracted attention for learning such tree-based models. Thus, we propose a mixed-integer optimization approach to obtain an effective decision diagram for allocating patients to medical diagnoses with practical constraints on medical resources. Specifically, this study focuses on chronic kidney disease (CKD) and allocating patients into three diagnostic classes: “See a diabetologist," “See a nephrologist," and “Do nothing." We first show that the current allocation rules can be summarized as a decision diagram. We then introduce practical constraints to consider (e.g., medical institutions’ capacity or medical cost constraints). Finally, we give a mixed-integer optimization formulation to find a decision diagram with high diagnosis effects and low medical costs. Our numerical experiments with synthetic data demonstrated that the proposed method could provide effective medical diagnosis allocations at a low cost.