This particular constraint is responsible for enveloping the data and identifying the efficient frontier. This constraint specifies that the set of weights assigned to DMU O and used with any other DMU’s values, must be lower or equal to 1. As illustrated by the first constraint, the set of weights used in the objective function (the ‘max’ line) will be used with each of the other DMU’s values as per illustrated by the first constraint. The formulation above measures the efficiency of DMU O. The input and output vectors are said to be semi-positive. Some inputs are allowed to be equal to 0 although at least one input (or output) will need to have a positive value per input vector (or output vector). The last two constraints restrict all the inputs and outputs to be non-negative. The first constraint ensures that the maximum possible value for the ratio is 1.

Linear programming optimisation techniques are used to find the optimal solutions (e.g. Because the above model formulation only measures DMU O’s efficiency, the problem will have to be solved n times to measure all the DMUs’ efficiency. The notation in the CCR paper (‘s’ as number of outputs, ‘m’ as number of inputs, ‘n’ DMUs and DMU O as the DMU under examination) is generally accepted and used in DEA’s literature. The model was expressed in a sum (Σ) notation in the CCR paper although for clarity purposes the formulation has here been expanded. This process is experimental and the keywords may be updated as the learning algorithm improves.The variables of this fractional problem are ‘u’ and ‘v’ which are respectively the output and input weight vectors (u=(u 1,u 2,…,u s ) while v=(v 1,v 2,…,v m)). These keywords were added by machine and not by the authors. With the capacity of Excel Solver, the DEAFrontier can deal with large sized performance evaluation tasks. The DEAFrontier does not set limit on the number of units, inputs or outputs. Chapter 4 introduces a ready-to-use Excel Solver-based DEA software called DEAFrontier. In addition, chapter 5 describes a variety of models to adapt DEA for particular applications and circumstances to enable users to employ the most appropriate models for their organization. The following chapter illustrates the power of DEA with multiple inputs and outputs. We have described the basic DEA model, the insights it provides in a simple example where similar insight could be gained from observation and where the linear programming calculations could easily be done without a computer.

Data envelopment analysis example excel