Dawniej efektywność zakładów porównywano za pomocą prostych wskaźników statystycznych — średniej wydajności, kosztu jednostkowego czy wyników KPI — co wydawało się łatwe, ale prowadziło do ocen niesprawiedliwych i nietrafnych. Porównanie dwóch fabryk po średnich wynikach produkcji pomijało fakt, że jedna miała dostęp do lepszej technologii, a druga zużywała więcej surowca; lepsza technologia nie oznacza zaś wyższej efektywności, bo kosztuje. Podstawowym problemem była nieporównywalność jednostek: jedna mała, druga duża, jedna z nowoczesnymi maszynami, druga ze starymi i wolnymi. Autor ilustruje to dwoma gospodarstwami mlecznymi — analiza łącznej produkcji mleka wskazałaby większe jako efektywniejsze, pomijając, że mniejsze może lepiej wykorzystywać wodę, paszę i energię w przeliczeniu na krowę.
A Review of the Most Important DEA Methods for Assessing the Efficiency of Food Industry Processes
In the past, comparisons of the efficiency of different plants or units were often based on simple statistical indicators such as average productivity, cost per unit of production or KPI results. At first glance, these seemed useful and easy to apply. Their use, however, had serious drawbacks that made such comparisons unfair and inaccurate. Comparing two factories on the basis of average production results ignored the fact that one might have access to better technology while the other used more raw materials. In such cases, simple figures obscured differences in actual operating conditions.
Having better technology does not mean being more efficient. Remember that technology costs money. If high costs are not accompanied by high profits, the process is inefficient. One of the main problems was that units were not comparable. One unit was small and another large; one used modern technology and another old, slow machinery.
Imagine two dairy farms: one large, with hundreds of cows, and the other small and operated by one family. A simple analysis based on total milk output might show that the larger farm is more efficient. Such an assessment would fail to account for the fact that the smaller farm may use water, feed and energy better, achieving higher productivity per cow. Traditional methods based on the thoughtless use of simple indicators often overlook such nuances.
What is DEA methodology?
DEA methods were created to solve problems involved in comparing processes that are in fact incomparable—processes that can theoretically be compared, but whose comparison by traditional methods will be affected by errors. Their purpose is to compare units fairly and accurately while accounting for the diversity of resources, particularly production resources, and results—not only financial results but performance in general.
DEA enables multidimensional analysis, meaning that it considers different factors simultaneously, such as energy consumption, quantity of raw materials and final production results. This makes it possible not only to determine which unit is more efficient, but also to indicate where particular resources are wasted and how efficiency can be improved.
Real-life examples demonstrate why this approach is necessary. In the food industry, a jam factory may use substantially more raw materials and energy than a competing plant even though both achieve similar production results. DEA will not only identify the less efficient plant, but also indicate specific areas in which waste can be reduced—for example, fruit losses during processing. Similarly, in vegetable processing, where factories frequently lose part of their raw materials, DEA methods help find ways to minimize such losses.
Another important aspect is that DEA not only compares units, but also identifies leaders: the units achieving the best results. Other plants can consequently model themselves on their activities and implement proven methods for improving efficiency. In agriculture, for example, DEA analysis can show which farms manage water or feed resources most effectively.
To summarize, before DEA was invented, traditional statistical indicators were often unable to capture the complexity of different units’ operations. DEA methods arose from the need for a fairer and more accurate approach to efficiency analysis. They enable units to be compared while accounting for their diversity and allow leaders and areas for improvement to be identified. This makes them invaluable in many sectors, from food processing to agriculture, and helps managers make better decisions.
Review of comparative DEA methods
Over the years, many DEA methods have been developed—that is, algorithms based on Dantzig’s marginal optimization, or the simplex algorithm. The most important are: CCR—Charnes, Cooper and Rhodes; BCC—Banker, Charnes and Cooper; CEM (Cross-Efficiency Model)—Sexton, Silkman and Hogan; SE-CCR (Super-Efficiency CCR)—Andersen and Petersen; NR-DEA (Non-Radial DEA)—Thanassoulis, Dyson and Zhu; CEP (Cross-Efficiency Profiling)—Doyle, Green and Tofallis; SE-BCC (Super-Efficiency BCC)—Seiford and Zhu; and SE-SBM (Super-Efficiency Slack-Based Measure)—Tone. Each is discussed below.
CCR (Charnes, Cooper, Rhodes)
The CCR method was proposed in 1978 by Abraham Charnes, William Cooper and Edward Rhodes. It was the first Data Envelopment Analysis method and represented a breakthrough in assessing the efficiency of systems by comparing different decision-making units (DMUs) that transform input resources into outputs. CCR enables matrices of comparisons among units to be created, allowing benchmark units—leaders in their group in terms of efficiency—to be identified.
CCR assumes constant returns to scale, meaning that a unit’s productivity remains unchanged regardless of its size. The method creates an efficiency frontier against which all units are assessed. Those on the frontier are called efficient; units outside it can seek improvement by following the benchmark units.
Imagine three processing plants:
- Plant A produces 100 tonnes of apple concentrate using 200 tonnes of apples and 5,000 kWh of energy.
- Plant B produces 80 tonnes of pear marmalade using 150 tonnes of pears and 4,000 kWh of energy.
- Plant C produces 120 tonnes of fruit juice using a mixture of 300 tonnes of fruit and 6,000 kWh of energy.
CCR creates a comparison matrix among these plants, identifying the most efficient benchmark units and showing how the others could improve efficiency by reducing resource consumption or increasing production.
BCC (Banker, Charnes, Cooper)
The BCC method was introduced in 1984 by Banker, Charnes and Cooper as an extension of CCR. It was inspired by the need to account for variable returns to scale in efficiency assessment. It has been widely applied in agriculture, where small farms may be more efficient than large ones for particular types of production.
BCC introduces an additional parameter accounting for changes in efficiency depending on operating scale. It permits fairer comparisons of differently sized units and is particularly useful when their sizes affect their ability to transform resources into results.
- Plant A is a small processing plant producing 50 tonnes of dried fruit from 80 tonnes of raw material. It uses 2,000 kWh of energy.
- Plant B is a large plant producing 300 tonnes of fruit syrups from 500 tonnes of fruit. It uses 10,000 kWh of energy.
The small plant may be more efficient on a small scale, while the large plant needs more resources to support mass production. BCC accounts for these differences and assesses efficiency proportionately to operating scale.
CEM (Cross-Efficiency Model)
CEM was proposed by Sexton, Silkman and Hogan in 1986 as an extension of classical DEA. The motivation was to create a tool that not only analyzes a unit’s efficiency, but also compares its results with other units, producing a more objective assessment.
CEM assesses units through mutual comparisons. Each unit is evaluated not only from its own data but also through the results of other units. This creates an efficiency matrix enabling detailed comparisons. Benchmark units are assessed both by their own efficiency and by their contribution to the group’s overall efficiency.
Consider three plants producing different products:
- Plant A produces 100 tonnes of fruit jam using 200 tonnes of raw material and 5,000 kWh of energy.
- Plant B produces 120 tonnes of tomato concentrate from 300 tonnes of tomatoes and uses 4,000 kWh of energy.
- Plant C produces 80 tonnes of citrus marmalade from 150 tonnes of fruit and uses 3,000 kWh of energy.
CEM creates a matrix of mutual comparisons in which units are assessed in relation to other plants. Plant A, for example, may receive a high rating for energy efficiency but a lower one for raw-material use, identifying potential areas for improvement.
SE-CCR (Super-Efficiency CCR)
SE-CCR was introduced by Andersen and Petersen in 1993 as an extension of CCR. It enables units on the efficiency frontier to be assessed in order to identify leaders even within a group considered efficient. It is particularly useful for identifying best practices in highly competitive industries.
SE-CCR assesses super-efficient units—those that not only reach the efficiency frontier but surpass it relative to other units. It permits more precise comparison of benchmark units and identifies models to follow.
- Plant A produces 200 tonnes of flour from 300 tonnes of wheat and uses 8,000 kWh of energy.
- Plant B produces 220 tonnes of flour from 320 tonnes of wheat and uses 7,000 kWh of energy.
- Plant C produces 180 tonnes of flour from 280 tonnes of wheat and uses 9,000 kWh of energy.
SE-CCR indicates that Plant B is super-efficient because it not only satisfies the efficiency criteria but also outperforms the other units in energy consumption relative to output.
NR-DEA (Non-Radial DEA)
NR-DEA was developed by Thanassoulis and Dyson in the 1990s to account for differing degrees of input-resource use. It analyzes situations in which not all resources are used fully proportionately, as is typical of diverse production processes.
NR-DEA evaluates efficiency while accounting for the disproportionate use of different resources. Unlike traditional DEA, it focuses on a detailed examination of waste in individual inputs such as raw materials, energy and labor time.
- Plant A uses 500 tonnes of potatoes to produce 300 tonnes of chips, but wastes 50 tonnes of raw material.
- Plant B processes 400 tonnes of potatoes into 280 tonnes of chips without wasting raw material, but consumes more energy than Plant A.
NR-DEA shows that Plant B uses raw material efficiently but has scope to optimize energy use, while Plant A should focus on reducing raw-material losses.
CEP (Cross-Efficiency Profiling)
CEP was proposed by Doyle and Green in the 1990s and later developed by Tofallis. It responded to the need for a more comprehensive approach to analyzing efficiency in groups of diverse units. CEP not only identifies efficient units, but also assesses their contribution to improving the efficiency of the entire group.
CEP compares units’ efficiency with one another while accounting for their individual results and influence on the group. It adds profiling, showing how individual units affect overall efficiency and identifying their strengths and weaknesses. Detailed efficiency profiles can therefore be created for every unit.
- Plant A processes 600 tonnes of carrots into 350 tonnes of juice and uses 10,000 kWh of energy.
- Plant B produces 500 tonnes of mashed potato from 700 tonnes of raw material and uses 12,000 kWh of energy.
- Plant C processes 800 tonnes of beet into 400 tonnes of sugar and uses 15,000 kWh of energy.
CEP analyzes each unit’s contribution to overall efficiency. Plant A, for example, may receive a high rating for energy efficiency but a low one for raw-material use, allowing specific areas for improvement to be identified.
SE-BCC (Super-Efficiency BCC)
SE-BCC was introduced by Seiford and Zhu in the 1990s as an extension of classical BCC. Its purpose was to distinguish more precisely among units that had already reached the efficiency frontier. It permits super-efficient units to be assessed where operating scales differ greatly.
SE-BCC combines BCC and super-efficiency, identifying leaders even among units considered efficient. It accounts for variable returns to scale, making it more flexible in assessing diverse production processes. Unlike standard BCC, it enables comparisons among efficient units, which is particularly useful in highly competitive sectors.
- Plant A produces 300 tonnes of tomato concentrate from 400 tonnes of tomatoes and uses 9,000 kWh of energy.
- Plant B produces 250 tonnes of purée from 350 tonnes of tomatoes and uses 8,000 kWh of energy.
- Plant C processes 280 tonnes of tomatoes into 260 tonnes of purée and uses 7,500 kWh of energy.
SE-BCC indicates that Plant A is super-efficient relative to the other units because of its better balance of raw material and energy against output. At the same time, the method may identify areas for improvement at Plant C even though it operates on a smaller scale.
SE-SBM (Super-Efficiency Slack-Based Measure)
SE-SBM was developed by Tone in the 1990s as an extension of classical DEA. It was designed to account for unused resources, or slack, when assessing units and to introduce a mechanism for assessing super-efficient units. It is applied where efficiency depends not only on the quantity of resources and outputs, but also on imperfect resource use.
SE-SBM focuses on detailed analysis of input and output use in DMUs. It enables super-efficiency to be assessed and identifies which efficient units can serve as models for minimizing resource waste. Accounting for losses and reserves in resource use permits a more precise efficiency assessment.
- Plant A produces 100 tonnes of fruit jam using 150 tonnes of fruit and 5,000 kWh of energy, leaving 10% of the fruit unused.
- Plant B produces 120 tonnes of tomato concentrate from 200 tonnes of tomatoes and uses 8,000 kWh of energy, wasting 5% of the raw material.
- Plant C processes 80 tonnes of beet into 60 tonnes of sugar, uses 7,000 kWh of energy and leaves no raw-material losses.
SE-SBM indicates that Plant C is super-efficient because it generates no raw-material loss, while Plants A and B have scope to reduce raw-material losses and optimize energy consumption.
| Method | Main objective (specialization) | Weaknesses |
|---|---|---|
| BCC | Comparing units of different operating scales while accounting for variable returns to scale. | Difficulty distinguishing efficient units in large datasets; requires homogeneous inputs and outputs. |
| CEM | Creating mutual efficiency assessments and detailed rankings. | Complexity increases with the number of units; requires advanced software and more data. |
| SE-CCR | Identifying efficiency leaders even among units already considered efficient. | Requires very detailed input and output data; less effective for inefficient units. |
| NR-DEA | Detailed resource-use analysis accounting for waste and reserves. | May be difficult to implement for large datasets; mainly focused on reducing resource losses. |
| CEP | Profiling units’ efficiency and contribution to group efficiency. | Focuses more on profiles than rankings; complexity grows with unit diversity. |
| SE-BCC | Combining super-efficiency analysis with variable returns to scale. | Best for efficient units; less effective at identifying improvements for weaker units. |
| SE-SBM | Accounting for unused resources and indicating areas for improvement. | Requires detailed slack data; difficult with limited input data. |
Summary
DEA stands for Data Envelopment Analysis. It is a method of efficiency analysis that makes it possible to compare units.