![]() ![]() 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. 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)).
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