In this paper, we address the problem of optimal thyroid hormone replacement strategy development for hypothyroid patients. This is challenging for the following reasons. First, it is difficult to determine the correct dosage leading to normalized serum thyroid hormone concentrations of a patient. Second, it remains unclear whether a levothyroxine L-T4) monotherapy or a liothyronine/levothyroxine (L-T3/L-T4) combined therapy is more suitable to treat hypothyroidism. Third, the optimal intake frequency of L-T3/L-T4 is unclear. We address these issues by extending a mathematical model of the pituitary-thyroid feedback loop to be able to consider an oral intake of L-T3/L-T4. A model predictive controller (MPC) is employed to determine optimal dosages with respect to the thyroid hormone concentrations for each type of therapy. The results indicate that the L-T3/L-T4 combined therapy is slightly better (in terms of the achieved hormone concentrations) to treat hypothyroidism than the L-T4 monotherapy. In case of a specific genetic variant, namely genotype CC in polymorphism rs2235544 of gene DIO1, the simulation results suggest that the L-T4 monotherapy is better to treat hypothyroidism. In turn, when genotype AA is considered, the L-T3/L-T4 combined therapy is better to treat hypothyroidism. Furthermore, when genotype CC of polymorphism rs225014 (also referred to as c.274A>G or p.Thr92Ala) in the DIO2 gene is considered, the outcome of the L-T3/L-T4 combined therapy is better in terms of the steady-state hormone concentrations (for a triiodothyronine setpoint at the upper limit of the reference range of healthy individuals). Finally, the results suggest that two daily intakes of L-T3 could be the best trade-off between stable hormone concentrations and inconveniences for the patient. Copyright © 2022 Wolff, Dietrich and Müller.