High-grade serous tubo-ovarian carcinoma (HGSC) is a major cause of cancer-related death. Treatment is not uniform, with some patients undergoing primary debulking surgery followed by chemotherapy (PDS) and others being treated directly with chemotherapy and only having surgery after three to four cycles (NACT). Which strategy is optimal remains controversial. We developed a mathematical framework that simulates hierarchical or stochastic models of tumor initiation and reproduces the clinical course of HGSC. After estimating parameter values, we infer that most patients harbor chemoresistant HGSC cells at diagnosis and that, if the tumor burden is not too large and complete debulking can be achieved, PDS is superior to NACT due to better depletion of resistant cells. We further predict that earlier diagnosis of primary HGSC, followed by complete debulking, could improve survival, but its benefit in relapsed patients is likely to be limited. These predictions are supported by primary clinical data from multiple cohorts. Our results have clear implications for these key issues in HGSC management.