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We propose a novel variant of the value-based additive data envelopment analysis model. It conducts a comprehensive robustness analysis of efficiency outcomes for all feasible input and output weights using mathematical programming and the Monte Carlo simulation. We also introduce the original procedures for selecting a common vector of weights and an approach for investigating the stability of results in a multiscenario setting. The presented framework is applied to evaluate the performance of emergency department physicians using data from the Children's Hospital of Eastern Ontario in Ottawa. Our focus is on the physicians' performance when dealing with groups of patients' complaints related to abdominal pain and constipation, fever, extremity injury, head injury, and laceration/puncture. The obtained results emphasize the strong dependence of the physicians' performances on the selected weight vectors. However, they prove helpful in pointing out overall good performers who can serve as universal benchmarks or niche performers being markedly better in providing care to a given complaint group. They also offer a basis for developing an improvement plan for the underperforming physicians, identifying the priorities for a practice-oriented model, and recognizing the most challenging patients' complaints.

We introduce a novel methodological framework based on additive value-based efficiency analysis. It considers inputs and outputs organized in a hierarchical structure. Such an approach allows us to decompose the problem into manageable pieces and determine the analyzed units’ strengths and weaknesses. We provide robust outcomes by analyzing all feasible weight vectors at different hierarchy levels. The analysis concerns three complementary points of view: distances to the efficient unit, ranks, and pairwise preference relations. For each of them, we determine the exact extreme results and the distribution of probabilistic results. We apply the proposed method to a case study concerning the performance of healthcare systems in sixteen Polish voivodeships (provinces). We discuss the results based on the entire set of factors (the root of the hierarchy) and three subcategories. They concern health improvement of inhabitants, efficient financial management, and consumer satisfaction. Finally, we show the practical conclusions that can be derived from the hierarchical decomposition of the problem and robustness analysis.

We consider the problem of measuring the efficiency of decision-making units with a ratio-based model. In this perspective, we introduce a framework for robustness analysis that admits both interval and ordinal performances on inputs and outputs. The proposed methodology exploits the uncertainty related to the imprecise data and all feasible input/output weight vectors delimited through linear constraints. We offer methods for verifying the robustness of three types of outcomes: efficiency scores, efficiency preference relations, and efficiency ranks. On the one hand, we formulate mathematical programming models to compute the extreme, necessary, and possible results. On the other hand, we incorporate the stochastic analysis driven by the Monte Carlo simulations to derive the probability distribution of different outcomes. The framework is implemented in R and made available on open-source software. Its use is illustrated in two case studies concerning Chinese ports or industrial robots.