Semi-Additive Integer-Valued Production Technology for Analyzing Public Hospitals in Mashhad

Conventional Data Envelopment Analysis (DEA) models assume real-valued input-output data and ignore the collaboration among decision-making units (DMUs) in the analysis of efficiency. This paper proposes a novel DEA production technology that is capable of dealing with the collaboration concept and resource sharing for both integer and real-valued data in the efficiency measurement and target setting. This is accomplished by way of a mixed integer linear programming (MILP) efficiency analysis model. We also deal with the computational aspect of the proposed model and invent a MILP with the computational complexity of O(n + m - p) rather than O(2(n) + m - p). We explain the proposed models by numerical examples and graphical illustrations. We apply our models for efficiency analysis of 15 governmental (public) hospitals in Mashhad City in Iran and demonstrate the practical relevance and advanced future of the proposed methods.