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we learned something about Data Envolopment Analysis (DEA) and the different models at university today, but somehow I still don't quite understand the basic idea and the scale calculations, as well as the differences/advantages of the CCR/BCC and SBM models. Could someone explain this in a way that is easy to understand?

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If you are willing to know about DEA, there are lots of useful materials which can be found by googling. Some of the best ones are:

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Technical efficiency consists of the ability to maximize the quantity produced through the available production factors, i.e. the ability to minimize the amount of input required to produce a set quantity of output. In this sense, technical efficiency can be oriented towards increasing output (output approach) or reducing input (input approach). A fundamental aspect of the production process is the reference technology adopted, which remains to be determined. In parametric approaches, the frontier is in fact expressed with a known mathematical function; in non-parametric approaches, on the other hand, the possible production technologies are given by the set of observed data of which the frontier is the envelope. The techniques for making judgements about efficiency estimation are classified between so-called 'frontier' and 'non-frontier' approaches. The former measure the efficiency of the production units in the sample in relation to an 'optimal' reference, which may be given by the estimation of a frontier of production possibilities or by the best result achieved by the units considered in the analysis sample; the latter measure instead the efficiency with respect to the average results of the sample. The frontier approach bases the analysis on two types of function: the production function, which relates the quantity of individual inputs employed to the quantity of output obtained, and the cost function, which assesses, given the prices of inputs and outputs, the minimum sustainable cost of their production. Both functions share the frontier characteristic, maximum and minimum respectively, on which fully efficient firms are placed, given the state of technology. Underlying all parametric approaches is the ability to identify the frontier from observed data.

Non-parametric techniques, on the other hand, do not require the functional form (analytical expression) of the technology to be specified a priori: by means of linear programming, the belonging of the data to the frontier is assessed. The efficiency measure obtained for each observation is therefore relative. The non-parametric method is known as Data Envelopment Analysis (DEA), and was devised by Farrell in 1957.

DEA is a technique to assess the efficiency of a production unit (DMU - Decision Making Unit) relative to a given set of production units chosen for comparison. Unlike the 'statistical' approach that compares production units with a fictitious average production unit, DEA compares each DMU with the most efficient DMUs and evaluates their relative efficiency.

The first publication concerning the DEA methodology dates back to 1978, in the work entitled Measuring the efficiency of decision making units by Charnes, Cooper and Rhodes.The first model proposed for the analysis of technical efficiency was the CCR model (named after the creators Charnes, Cooper and Rhodes), which only measured efficiency under conditions of constant returns to scale (CRS).It was only around the 1980s that the BCC (Banker, Charnes, Cooper) method was introduced, which was also able to consider the scale effect in its formulation, admitting the evaluation of variable returns to scale (VRS).

The DEA methodology identifies a linear trait frontier, using linear programming techniques, and based on this determines whether the DMUs (Decision Making Units) in the analysis sample are efficient or not. In case a DMU is not efficient, there are two possible strategies to reach the frontier: 1) decrease the input level while keeping the output unchanged or 2) maximize the output with the same set of inputs.

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