Data driven approach for weight restricted data envelopment analysis models with single output

Data Envelopment Analysis (DEA) models with weight restrictions (WRs) have proven valuable for benchmarking and target setting. Although the DEA literature has explored the incorporation of managerial preferences and value judgments regarding the relative worth of inputs and outputs, as well as the establishment of targets in benchmarking contexts, little attention has been devoted to target setting under restricted DEA models. Moreover, despite the significant advances offered by minimum distance models for target establishment, limited research has addressed benchmarking improvement plans that integrate expert opinions and prior knowledge. Some studies have examined minimum distance models constrained to the efficient Assurance Region (AR) frontier, primarily by extending the concept of closest targets under WR. In contrast, this paper develops improvement plans that deviate minimally from the closest target projection obtained from the original, unrestricted DEA model—termed the reference target. This reference target is considered an acceptable “peer” since it requires the least effort for a decision making unit (DMU) to reach optimal performance before incorporating WR. To this end, we developed a mixed-integer linear programming (MILP) model under the assumption of Variable Returns to Scale in DEA. The proposed approach is illustrated through an application to benchmarking the tourism performance of localities in Córdoba, Argentina. The results reveal realistic and achievable improvement plans for the analyzed localities, ensuring that both global efforts are managed and expert-imposed restrictions are satisfied.

Relevance. Public health effectiveness is crucial for population health, especially in the face of global challenges like the COVID-19 pandemic. The study applies the Data Envelopment Analysis (DEA) model to measure the efficiency of operating costs in the health care system across various regions of Kazakhstan from 2017 to 2021. Existing methods for assessing healthcare effectiveness often overlook the system's complexity, which turns DEA into a valuable tool to identify inequalities in healthcare availability and quality. Research objective. This study aims to employ the DEA model to measure the efficiency of operating costs in the health care system across regions of Kazakhstan in 2017-2021. Data and methods. The DEA model was chosen for its ability to analyze the efficiency of operating costs. Data were collected from the Agency for Strategic Planning and Reforms of the Republic of Kazakhstan. Results. Our findings indicate the need for increased healthcare financing in specific regions, emphasizing the importance of transparent spending. The study concludes that the DEA model can regularly assess health financing, ensuring resources are directed where most needed. The novelty lies in establishing a link between financing and health outcomes. Conclusions. The study's results and methodology can be used by public health authorities in assessing operating costs' effectiveness, allocating resources judiciously, and making informed decisions to enhance the healthcare system.

Data Envelopment Analysis (DEA) models and Free Disposal Hull (FDH) models were proposed almost simultaneously in the scientific literature. In DEA models, the constraints generate a convex set. For this reason, optimization methods and software are widely used for modeling and computations for these models. Non-convexity of production possibility set of FDH models refrained significantly the development of these models. In this paper, two methods are proposed for two-and three-dimensional frontier visualization for DEA and FDH models. Computational experiments using real-life datasets documented reliability and effectiveness of proposed methods.

A generalized model for data envelopment analysis with interval data

The appreciative democratic voice of DEA: A case of faculty academic performance evaluation

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

Cross-efficiency aggregation in DEA models using the evidential-reasoning approach

Analysis of Beijing’s environmental efficiency and related factors using a DEA model that considers undesirable outputs

Objectives: This paper aims to assess the agricultural ecological and economic efficiency of the Yangtze River Economic Belt by using the data envelopment analysis (DEA) model to evaluate the regional agricultural level. Methods: Relevant data from 11 provinces and cities in the Yangtze River Economic Belt from 2010 to 2020 was collected from statistical yearbooks. Then, the agricultural eco-efficiency and economic efficiency were evaluated using the slack-based measure (SBM) model in the DEA model. Findings: The evaluation result of agricultural eco-efficiency was consistently higher than that of ecological efficiency. From a regional perspective, the eco-efficiency of the downstream area was higher than that of the middle and upper reaches. From the perspective of group division, only Guizhou and Chongqing had a high eco-efficiency. Improvement: The findings suggest that the overall agricultural eco-efficiency in the Yangtze River Economic Belt is low, and there is still a large space for development. It is necessary to further reduce agricultural carbon emissions and non-point source pollution and improve agriculture through technological innovation and other means.

In models of data envelopment analysis (DEA), an optimal set of input and output weights is generally assumed to represent the assessed decision making unit (DMU) in the best light in comparison to all the other DMUs. The paper shows that this may not be correct if absolute weight bounds or some other weight restrictions are added to the model. A consequence may be that the model will underestimate the relative efficiency of DMUs. The incorporation of weight restrictions in a maximin DEA model is suggested. This model can be further converted to more operational forms, which are similar to the classical DEA models.

Running any dairy enterprise is a risky activity: the profitability of the enterprise is affected by the price fluctuation of feed and animal health products from inputs, as well as by the fluctuation of end-product prices. Under these circumstances, it is essential for the cattle breeders, in order to survive, to harness the reserves in management as effectively as possible. In this research the efficiency and risk of 32 sample dairy farms were analysed in the Northern Great Plain Region from the Farm Accountancy Data Network (FADN) by applying classical Data Envelopment Analysis (DEA) and stochastic DEA models. The choice of this method is justified by the fact that there was not such an available reliable database by which production functions could have been defined, and DEA makes possible to manage simultaneously some inputs and outputs, i.e. complex decision problems. By using DEA, the sources that cause shortfall on inefficient farms can be identified, analysed and quantified, so corporate decision support can be reinforced successfully. A disadvantage of the classical DEA model is that the stochastic factors of farming cannot be treated either on the side of inputs or outputs; therefore, their results can be adopted with reservations, especially in agricultural models. This may have been because we could not discover that many agricultural applications. Considering the price of inputs and outputs as probability variables, 5000 simulation runs have been done in this research. As a result, it can be stated that at which intervals of the input and output factors can become competitive and the fluctuation of these factors can cause what level of risk at each farm.

This study employs four data envelopment analysis (DEA) models to evaluate the performance efficiency of 21 OECD countries and assess whether the undesirable outputs are over-produced relative to desirable outputs. In evaluating the performance of OECD countries via super-efficiency models, this study focuses on two aspects. First, employing the concept of the Sharpe ratio, we propose another method to deal with undesirable outputs (the unemployment rate, inflation, and air pollution) in DEA. This approach can reveal the relative importance of desirable outputs and undesirable outputs, detect whether undesirable outputs are over-produced, and obtain more accurate efficiency scores. Second, we examine whether knowledge capital can improve a country’s efficiency scores. Our empirical results support the above arguments. In addition, research and development (R&D) expenditures, the proxy variable for knowledge capital, can indeed improve countries’ efficiency scores, implying that the endogenous growth theory is supported in OECD countries. Evidently, whether the undesirable outputs are included in the DEA models and are properly treated is crucial in the evaluation of efficiency values.

An efficiency measurement model of a university faculty is proposed with additional new sub-functions that produce new output variables, based on the network Data Envelopment Analysis (DEA) model for systems with a hierarchical structure.For production systems composed of hierarchical processes, the system efficiency is well represented as the aggregated performance of the components involved in the system. It is identified that the conventional DEA model ignores internal process activities in a university. Therefore, an improved DEA model based on a network structure that accounts for more activities in a university is proposed to measure its overall efficiency. The impact of major functions of a university are taken into account to represent the output variables in assessing the efficiency. Currently, collaboration activities have been given more attention, so, this variable is suggested as a new output for the hierarchical production system. In order to show the practicality of the model, a hypothetical set of data of 14 faculties has been used as a numerical example. The results show that none of the faculties is relatively efficient since its functions were found to be inefficient. The proposed model enables to help the management of university faculties to identify weaknesses of each function and thus to plan for suitable actions on improving the overall performance of the university.

It has become a more and more concerned issue of optimising the scientific & technical (S&T) resources configuration to improve its input-output efficiency. By applying data envelopment analysis (DEA) model, the thesis evaluates the S&T resources input-output efficiency of 45 major enterprises and 8 leading industries of region A. The result of data analysis shows, over half enterprises didn't reach S&T input-output efficiency in a DEA analysis, and 2 of the 8 leading industries didn't reach efficiency. The thesis analyzes the reasons of inefficiency enterprises and industries, as well bring forward the improving strategy based on the evaluation result accordingly.

Data envelopment analysis (DEA) is one of the best tools for evaluating units with multiple inputs and multiple outputs. In multiplier models of DEA sometimes data on inputs or outputs is available, and/or some assumptions are imposed to the model that result in some conditions on weights vectors, in addition to non-negative conditions of the weight vectors of u and v. These conditions are called weights restrictions. Applying weights restrictions on the multiplier model creates new variables in its corresponding DEA model. Thus, applying weights restrictions on the multiplier model leads to the development of technology model in the envelopment form. This makes the projection of an inefficient unit that is on the efficiency frontier of the developed technology not to be necessarily producible. Therefore, applying weights restrictions on multiplier models will enjoy this defect. To solve this problem weights restrictions are applied through the trade-off matrix that is a simultaneous change in inputs and outputs. Applying weights restrictions in DEA model helps us keep under control the significance of one output to other output or the significance of one input to other input and/or the significance of one output to one input.