With ‘good health and well-being’ being set as one of the targets of the Sustainable Development Goal (SDG), this paper proposes the application of Pinch Analysis, a quantitative method originally applied to conserve scarce resources in source-demand allocation networks, for identifying gaps in health care service delivery. This method is also found to be useful for health care infrastructure capacity planning and policy testing. The major contribution of this method in this context is identification of marginalized sections and testing specific policies targeted towards them, which will justify release of financial aid and infrastructure development for appropriate sections. We explored this concept for investigating the in-patient health care delivery system in the context of developing nations, where the health care facilities (both public and private) thrive by offering services at drastically different prices. A novel framework is developed in this paper, supported by a case study of Kolkata, India where both the gaps and surplus faced by different sections of population are identified. In order to offset these gaps, we offer recommendations for possible policy implementation. A few hypothetical scenarios are also examined in order to understand the importance of Pinch Analysis for policy testing. We conclude by proving that Pinch Analysis can be a robust integrated decision-making framework for the health care sector, especially in resource-constrained communities.