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The inverse Data Envelopment Analysis (DEA) method is primarily used to analyze the changing relationship between the inputs and outputs of production units while preserving efficiency levels. This paper aims to perform an efficiency and post-efficiency analysis of 130 public hospitals in Iran. However, we faced with some hospital data that are only available in form of ratios. This motivates us to develop a novel and proper inverse DEA methodology capable of dealing with such cases. We develop the theoretical foundation of the inverse DEA-R model as a post-efficiency analysis approach. Both input-oriented and output-oriented inverse models are developed. In the end, we apply the proposed models for efficiency assessment and moreover inverse analysis of 130 public hospitals in Iran. • In this paper, data envelopment analysis models for ratio data are presented. • Using the concept of inverse data envelopment analysis, models are proposed to estimate ratio inputs and/or ratio outputs. • The feasibility and performance of the proposed models have been proven. • The proposed models are used to estimate the criteria of 130 hospitals in Iran. [ABSTRACT FROM AUTHOR]