Data Envelopment Analysis – Comparing Efficiency in Operations

It is practically impossible to ignore the importance of indicators that measure the company's performance. It is necessary to measure how much was produced, sold, how many customers were served, that is, the effectiveness of its operations. However, we also need to understand what resources were used to achieve the objectives, to guarantee the health and competitiveness of the organization. It is also necessary to evaluate the efficiency of the processes.

A common practice in the market is the comparisons that companies, or their productive and operational units, make among themselves to find out if they are being more, or less, efficient than the others. Or even, if there is a path to be followed for maximum efficiency. In theory, it would be easy to do this analysis with simple calculations, but the differences in the operational characteristics of the analyzed units make a fair comparison enormously difficult. For example, one can think of calculating productivity by the area covered by an operation, but we could also think of measuring it by the number of customers served. Each of these options could indicate one or another operation as the most efficient, but what would be the correct criterion? How, then, can these different forms of measurement be combined to make fair comparisons between units?

Data Envelopment Analysis (DEA) is a mathematical method based on linear programming logic that allows this comparison of efficiency between different productive units (called DMU), using multiple input criteria, which would be the resources (inputs); and outputs or results achieved (outputs). Through this model, it is possible to arrive at a single percentage of efficiency for each of the units analyzed in the comparison, and thus understand which of them are parameters (benchmarks) and which still have points of improvement.

Unlike parametric models, such as linear regression and AHP, the DEA allows assigning different weights to each input and output criterion in order to maximize the efficiency of each DMU, ​​which provides a fair comparison between different operations. DEA models can be oriented either to inputs as for outputs. In other words, we can think “how much of my resources should I be spending to achieve a result” or “how much should I be producing with the resources I have”. It is important to choose the appropriate model, based on the variables that are controllable by the managers of the analyzed operations.

Once the orientation model is chosen, a linear programming problem (LPL), which assigns different weights to inputs e outputs of each unit, seeking to maximize its efficiency. Thus, we arrive at the efficiency of each DMU. With these values ​​in hand, we can still calculate how much the less efficient DMUs should improve, setting a goal of reducing inputs or increase of outputs, depending on the guidance model chosen. Thus, we can in some cases show the DEA graphically, building the so-called efficiency frontiers. Companies that are 100% efficient are at the limit of this region, and companies that are not 100% efficient are in the “interior” of the region, as shown in Figure 1.

Figure 1 – Source of AED efficiency

Source: ILOS

This was a brief introduction to Data Envelopment Analysis, very useful in the logistics area to compare operations with different characteristics (eg DCs and Logistics Operators operating in different regions of the country) and, in a fair and adequate manner, identify opportunities for improvement operating on the way to the efficiency frontier. In the references below, you can check a more detailed presentation, in addition to the formulation of logical problems and tools that help to solve them.

References

SOARES DE MELLO, JCCB et al. DATA ENVELOPMENT ANALYSIS COURSE. XXXVIII Brazilian Symposium on Operational Research, 2005

ANGULO MEZA, L.; BIONDI NETO, L.; SOARES DE MELLO, JCCB; GOMES, EG ISYDS – Integrated System for Decision Support (SIAD – Integrated Decision Support System): a software package for data envelopment analysis model. Operational Research, v. 25, (3), p. 493-503, 2005

ANGULO MEZA, L.; BIONDI NETO, L.; SOARES DE MELLO, JCCB; GOMES, EG; COELHO, PHG Free software for decision analysis: a software package for data envelopment models. In: 7th International Conference on Enterprise Information Systems – ICEIS 2005, v. 2, p. 207-212.