Background. Low-and-middle-income countries (LMICs) have higher mortality-to-incidence ratio for breast cancer compared to high-income countries (HICs) because of late-stage diagnosis. Mammography screening is recommended for early diagnosis, however, the infrastructure capacity in LMICs are far below that needed for adopting current screening guidelines. Current guidelines are extrapolations from HICs, as limited data had restricted model development specific to LMICs, and thus, economic analysis of screening schedules specific to infrastructure capacities are unavailable. Methods. We applied a new Markov process method for developing cancer progression models and a Markov decision process model to identify optimal screening schedules under a varying number of lifetime screenings per person, a proxy for infrastructure capacity. We modeled Peru, a middle-income country, as a case study and the United States, an HIC, for validation. Results. Implementing 2, 5, 10, and 15 lifetime screens would require about 55, 135, 280, and 405 mammography machines, respectively, and would save 31, 62, 95, and 112 life-years per 1000 women, respectively. Current guidelines recommend 15 lifetime screens, but Peru has only 55 mammography machines nationally. With this capacity, the best strategy is 2 lifetime screenings at age 50 and 56 years. As infrastructure is scaled up to accommodate 5 and 10 lifetime screens, screening between the ages of 44-61 and 41-64 years, respectively, would have the best impact. Our results for the United States are consistent with other models and current guidelines. Limitations. The scope of our model is limited to analysis of national-level guidelines. We did not model heterogeneity across the country. Conclusions. Country-specific optimal screening schedules under varying infrastructure capacities can systematically guide development of cancer control programs and planning of health investments.