Data Enabled Analytics

Data Envelopment Analysis (DEA) should be viewed as a method (or tool) for data-oriented analytics. DEA is a data-oriented tool for performance evaluation & benchmarking. DEA generates a composite index. DEA identifies an envelopment of the data. DEA is a classification tool. DEA measures efficiency & productivity.

Let's discover the new uses and potentials of DEA under big data research.

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Let the Data Speak for Themsleves

The user does not impose any assumptions. DEA is used to identify best-practices when multiple performance metrics or measures are present for organizations. Although DEA has a strong link to production theory in economics, the tool is also used for benchmarking in operations management, where a set of measures is selected to benchmark the performance of manufacturing and service operations. In the circumstance of benchmarking, the efficient DMUs, as defined by DEA, may not necessarily form a "production frontier", but rather lead to a "best-practice frontier".
*Cook, W.D., Tone, K., and Zhu, Joe, Data envelopment analysis: Prior to choosing a model, OMEGA, Vol. 44 (2014), 1-4.

Data Science Tool

We know DEA stands for Data Envelopment Analysis. As OR/MS is moving into the area of Operations Analytics, DEA is evolving into Data Envelopment Analytics. DEA is big Data Enabled Analytics. DEA is a data-oriented data science tool for productivity analytics, benchmarking, performance evaluation, and composite index construction, among other new uses, in addition to the traditional uses such as, production efficiency and productivity measurement.

Numerious Posibilities

Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries. These DEA applications have used DMUs of various forms to evaluate the performance of entities, such as hospitals, US Air Force wings, universities, cities, courts, business firms, and others, including the performance of countries, regions, etc. Because it requires very few assumptions, DEA has also opened up possibilities for use in cases which have been resistant to other approaches because of the complex (often unknown) nature of the relations between the multiple metrics labled as inputs and multiple outputs involved in DMUs.

Network DEA is data enabled analysis of information hidden in big data.

Network DEA is based upon DEA ratios, but can behave very differently from the standard (or traditional) DEA. Network DEA may not be able to be converted into linear programming problems. Depending on the specific network structures of the decision making units (DMUs), network DEA can be solved via parametric linear programming and most recently by using second-order cone programming techniques.

There are many new research opportunities within the network DEA modeling. Convex optimization techniques need to be employed and adopted for solving non-convex network DEA mdoels.


Read a (draft) paper by Joe Zhu.

Note that the standard DEA models can be presented in either envelopment or multiplier form. However, under network DEA, such a duality no longer exists. In the dual to the multiplier DEA model (namely, the envelopment model), researchers discover the "convexity" and established a link between DEA and production function. This indicates that returns to scale (RTS) assumptions when applied to the network DEA need to be investigated.

Under the DEA ratio, the assumptions of constrant RTS (CRS) and variable RTS (VRS) represent two different shapes of the DEA best-practice frontier. Under the standard DEA, a CRS score cannot exceed the corresponding VRS score. However, under network DEA, this observarion may not hold.

Network DEA ≠ Standard DEA

although it bears with the name of "DEA".

Ratio Data

We can use ratio data to define a new composite measure. The DEA multiplier model implies the "convexity" because of the duality to the envelopment model. However, this does not necessary mean that "convexity" is required in the multiplier DEA model. However caution should be paid when ratio data are used. See, e.g., Cook, W.D., Tone, K., and Zhu, J., Data envelopment analysis: Prior to choosing a model, OMEGA, Vol. 44 (2014), 1-4.
Zhang, Q., Koutmos, D., Chen, K., and Zhu, J., Using operational and stock analytics to measure airline performance: network DEA approach, Decision Sciences, in press.

Negative Data

Negative data (or undesirable measurs) can be treated and modelled in DEA. These modeling techniques are useful in addressing eco-efficiency or benchmarking with the presence of wastes. See, e.g., Seiford, L.M., and Zhu, J., Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, Vol. 142, Issue 1 (2002), 16-20.

Production Technology

Standard DEA model generates a composite index or measure and "efficiency" does not necessarily mean "production efficiency" in many DEA application. "Efficiency" is a standard terminology in DEA to represent the optimal value to the DEA model. Therefore, the standard DEA model is not necessarily a model of "production" or "technology".

Inputs-Outputs

Performance measures are "classified" as Inputs and Outputs in DEA. Inputs and outputs do not necessarily represent the actual resources and products in a production process. Under the network DEA, some performance metrics are called intermdiate measures or links that require coordination between two network components.

Sample Size

DEA is an optimization tool. Sample size or the number of DMUs vs the number of inputs/outputs is not very important. However, there are cases where many DMUs are rated as "efficient" if there are too many performance measures used compared to the number of DMUs under consideration. However, this is not a problem of DEA; rather it is an issue the user has to address. There are DEA methods that can address such an issue. See, e.g., 5. Charles, V., Aparicio, J., and Zhu, J. (2019), The curse of dimensionality of decision-making units: A simple approach to increase the discriminatory power of data envelopment analysis, European Journal of Operational Research (in press) and Khezrimotlagh, D., Cook, W.D., and Zhu, J., Increasing the discrimination power of data envelopment analysis as number of input-output Increases or number of decision making units decreases.

Returns-to-Scale

Returns to Scale (RTS) in DEA can only refer to the shape of the DEA best-practice frontier. The term constant RTS (CRS) or variable RTS (VRS) only bears the economic meaning if DEA is used under production technology.

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