Evaluation of system efficiency using the Monte Carlo DEA: The case of small health areas

• Monte Carlo-DEA assessed the Small Health Areas (SHA) efficiency.
• Expert knowledge assigned statistical distributions for the variables.
• Input/output combinations analysed different perspectives of SHA efficiency.
• Best combinations were used for benchmarking.
• k-means analysis validated a panel of experts’ classification.

This paper uses Monte Carlo Data Envelopment Analysis (Monte Carlo DEA) to evaluate the relative technical efficiency of small health care areas in probabilistic terms with respect to both mental health care as well as the efficiency of the whole system. Taking into account that the number of areas did not permit maximum discrimination to be achieved, all the scenarios of non-correlated inputs and outputs of a specific size were designed using Monte Carlo Pearson to maximize the discrimination of Monte Carlo DEA and the information included in the models. A knowledge base was included in the simulation engine in order to guide the dynamic interpretation of non-standard inputs and outputs. Results show the probability that all DMU and the whole system have of being efficient, as well as the specific inputs and outputs that make the areas or the system efficient or inefficient, along with a classification of the areas into four groups according to their efficiency (k-means cluster analysis). This final classification was compared with an expert-based classification to validate both the knowledge base and the Monte Carlo DEA model. Both classifications showed results that were very similar although not exactly the same, basically due to the difficulty experts experience in recognizing “intermediately-inefficient” DMU. We propose this methodology as an instrument that could help health care managers to assess relative technical efficiency in complex systems under uncertainty.