In this study, we report our experience in commissioning a commercial treatment planning system (TPS) for fast-raster scanning of carbon-ion beams. This TPS uses an analytical dose calculation algorithm, a pencil-beam model with a triple Gaussian form for the lateral-dose distribution, and a beam splitting algorithm to consider lateral heterogeneity in a medium. We adopted the mixed beam model as the relative biological effectiveness (RBE) model for calculating the RBE values of the scanned carbon-ion beam. To validate the modeled physical dose, we compared the calculations with measurements of various relevant quantities as functions of the field size, range and width of the spread-out Bragg peak (SOBP), and depth-dose and lateral-dose profiles for a 6-mm SOBP in water. To model the biological dose, we compared the RBE calculated with the newly developed TPS to the RBE calculated with a previously validated TPS that is in clinical use and uses the same RBE model concept. We also performed patient-specific measurements to validate the dose model in clinical situations. The physical beam model reproduces the measured absolute dose at the center of the SOBP as a function of field size, range, and SOBP width and reproduces the dose profiles for a 6-mm SOBP in water. However, the profiles calculated for a heterogeneous phantom have some limitations in predicting the carbon-ion-beam dose, although the biological doses agreed well with the values calculated by the validated TPS. Using this dose model for fast-raster scanning, we successfully treated more than 900 patients from October 2018 to October 2020, with an acceptable agreement between the TPS-calculated and measured dose distributions. We conclude that the newly developed TPS can be used clinically with the understanding that it has limited accuracies for heterogeneous media.