A maximum-tolerated dose (MTD) reduces the drug-sensitive cell population, though it may result in the competitive release of drug resistance. Alternative treatment strategies such as adaptive therapy (AT) or dose modulation aim to impose competitive stress on drug-resistant cell populations by maintaining a sufficient number of drug-sensitive cells. However, given the heterogeneous treatment response and tolerable tumor burden level of individual patients, determining an effective dose that can fine-tune competitive stress remains challenging. This study presents a mathematical model-driven approach that determines the plausible existence of an effective dose window (EDW) as a range of doses that conserve sufficient sensitive cells while maintaining the tumor volume below a threshold tolerable tumor volume (TTV). We use a mathematical model that explains intratumor cell competition. Analyzing the model, we derive an EDW determined by TTV and the competitive strength. By applying a fixed endpoint optimal control model, we determine the minimal dose to contain cancer at a TTV. As a proof of concept, we study the existence of EDW for a small cohort of melanoma patients by fitting the model to longitudinal tumor response data. We performed identifiability analysis, and for the patients with uniquely identifiable parameters, we deduced patient-specific EDW and minimal dose. The tumor volume for a patient could be theoretically contained at the TTV either using continuous dose or AT strategy with doses belonging to EDW. Further, we conclude that the lower bound of the EDW approximates the minimum effective dose (MED) for containing tumor volume at the TTV.