Deterministic Data Envelopment Analysis Models Research Articles

Stochastic efficiency measures for production units with correlated data

While the real world is stochastic in nature, in many cases deterministic data envelopment analysis (DEA) models are used to measure the relative efficiency of a set of production units for simplicity. However, deterministic DEA models are not able to differentiate efficient units. More seriously, the decision maker will be over-confident with the presumably uncertain and probably misleading results. By applying a standard normal transformation, this paper develops a stochastic DEA model which is able to take the correlation between the input/output factors of each production unit to be evaluated into account to obtain the distribution of the stochastic efficiency. The efficiency distribution is more discriminative and informative than the single-valued efficiency, in that the probability that the stochastic efficiency of a unit is greater than that of another unit can be calculated. The case of twenty-five Taiwanese commercial banks discussed in a previous study that assumed the input/output factors to be independent is used to illustrate the characteristics of different models. The data is shown to be correlated, and the results confirm that ignoring the correlations between the input/output factors in measuring efficiency obtains misleading rankings.

Satisficing data envelopment analysis: a Bayesian approach for peer mining in the banking sector

Over the past few decades, the banking sectors in Latin America have undergone rapid structural changes to improve the efficiency and resilience of their financial systems. The up-to-date literature shows that all the research studies conducted to analyze the above-mentioned efficiency are based on a deterministic data envelopment analysis (DEA) model or econometric frontier approach. Nevertheless, the deterministic DEA model suffers from a possible lack of statistical power, especially in a small sample. As such, the current research paper develops the technique of satisficing DEA to examine the still less explored case of Peru. We propose a Satisficing DEA model applied to 14 banks operating in Peru to evaluate the bank-level efficiency under a stochastic environment, which is free from any theoretical distributional assumption. The proposed model does not only report the bank efficiency, but also proposes a new framework for peer mining based on the Bayesian analysis and potential improvements with the bias-corrected and accelerated confidence interval. Our study is the first of its kind in the literature to perform a peer analysis based on a probabilistic approach.

Chance Constrained Data Envelopment Analysis for Efficiency Analysis: An Application to Turkish Manufacture of Iron and Steel Sector

This study aims to determine the technical efficiency levels of the enterprises active in the “Manufacture of Basic Iron and Steel and of Ferro-Alloys” sector in Turkey. The inputs and outputs are deterministic in classical Data Envelopment Analysis, so the changes in exchange rate, inflation rate, etc. aren’t considered, and the precautions for future inconsistencies are not foreseen. This leads to critics of deterministic Data Envelopment Analysis models. In this paper, the additive model developed depending on the Banker, Charnes and Cooper (BCC) model was extended by chance constrained programming formulations in order to overcome the insufficiencies in deterministic Data Envelopment Analysis, and the technical analysis of “Manufacture of Basic Iron and Steel and of Ferro-Alloys” sector was performed.

Monte Carlo Data Envelopment Analysis with Genetic Algorithm for Knowledge Management performance measurement

The paper targets to devise a genuine Knowledge Management (KM) performance measurement model in a stochastic setting based on Data Envelopment Analysis (DEA), Monte Carlo simulation and Genetic Algorithm (GA). The proposed model evaluates KM using a set of proxy measures correlated with the major KM processes. Data Collection Budget Allocation (DCBA) that maximizes the model accuracy is determined using GA. Additional data are generated and analyzed using a Monte-Carlo-enhanced DEA model to obtain the overall KM efficiency and KM processes’ efficiency scores. An application of the model has been carried out to evaluate KM performance in higher educational institutions. It is found that with GA, the accuracy of the model has been greatly improved. Lastly, comparing with a conventional deterministic DEA model, the results from the proposed model would be more useful for managers to determine future strategies to improve their KM.

An input relaxation measure of efficiency in stochastic data envelopment analysis

We introduce stochastic version of an input relaxation model in data envelopment analysis (DEA). The input relaxation model, recently developed in DEA, is useful to resource management [e.g. G.R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion, Appl. Math. Comput. 151(1) (2004) 263–273]. This model allows more changes in the input combinations of decision making units than those in the observed inputs of evaluating decision making units. Using this extra flexibility in input combinations we can find better outputs. We obtain a non-linear deterministic equivalent to this stochastic model. It is shown that under fairly general conditions this non-linear model can be replaced by an ordinary deterministic DEA model. The model is illustrated using a real data set.

Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on “joint chance constraints.” An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present.