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Patients taking warfarin for long-term anticoagulation require frequent clinic visits to monitor the prothrombin time ratio (PTR), a measure of blood clotting. A dynamic stochastic model using nonlinear optimization was developed to select follow-up visit intervals that minimize the overall costs of patient care. Assuming that fluctuations in a patient's PTR behave as a random diffusion process, future PTR fluctuations are unknown, except as revealed by past PTRs. To determine the incidence and costs of complications in relation to PTR, the authors reviewed the charts of 216 patients who had 719 patient-years of follow-up with 695 trivial, significant, life-threatening, or fatal complications. They modeled the relationship between costs of complications and deviation of the PTR from the therapeutic target as a fourth-order convex polynomial. The model is used to compute the interval to the next follow-up visit to minimize accumulated potential costs. Variables in the optimization are the cost of a monitoring visit and the expected costs of complications. The latter are derived from the current PTR, the variability of the patient's past PTR values, the number of past PTRs available, and the target PTR for the patient. No attempt is made to predict the level of the next PTR or suggest adjustments in the warfarin dose. Shorter follow-up is recommended for patients who have histories of large fluctuations in past PTRs and for patients with few prior PTR determinations. As visits accumulate, the patient's degree of variability can be estimated more accurately and visit intervals adjusted accordingly. The scheduling method balances costs to the health care system of monitoring each patient against the expected costs of complications. This approach has the potential to reduce the number of monitoring visits necessary for safe management of anticoagulated patients with stable PTRs and to improve control among unstable patients.