This chapter provides a critical review on the DEA method with a focus on its contribution to assess the performance of healthcare organizations around the world and specifically in Tunisia. To start with, we shed light upon the efficient border-based methods to help to systematically pinpoint the DEA among its counterparts. Afterwards, main key features of the DEA are discussed, and information on their theories, their corroborative evidence in the literature as well as directions for further enhancements are provided. Focusing on the healthcare field, this chapter also sketches the contributions of the DEA as an aid decision tool. In particular, we highlight the existence of two research strands, namely cross-sectional and overall based performance assessment of healthcare centers. Additionally, relevant gaps that need to be filled are stressed, most notably for studies dealing with the assessment of units within one healthcare center. Particular attention is also paid to the experiences of using DEA-based approach to assess cross-efficiency healthcare organization in Tunisia. Case studies as well as the lessons learned are reported.

This work investigates a new hybrid data envelopment analysis (DEA) and grey relational analysis (GRA) for a macro-level evaluation of healthcare organizations. Once similar processes and decision-making units (DMUs) are identified, the DEA is used to extract the efficient DMUs and introduce potential improvements. Then, the identified DMUs and inputs are scanned by the GRA to highlight their preference order and thus retrieve the benchmarked DMUs and the most influencing variables to prioritize. An empirical analysis evolving 63 DMUs across four departments of a Tunisian teaching hospital was conducted to provide useful guidance to policymakers to better allocate available resources.

Our purpose in this paper is to present a fixed point result for multivalued mappings satisfying nonlinear quasi-contractive condition only on related points. Moreover, we provide a qualitative study of well-posedness, limit shadowing property and Ulam-Hyers stability of our fixed point problem. As application, we discuss the existence of a unique solution for a class of differential inclusions.