Modified piecewise linear DEA model

Recently, Cook and Zhu have proposed the Piecewise Linear Data Envelopment Analysis (PL-DEA) model, a situation in which a generalization of the DEA methodology which incorporates piecewise linear functions of factors is considered. Standard DEA models provide an efficiency score and targets for an inefficient unit, but the PL-DEA model fails to produce acceptable targets. Thus, this issue has been considered in the piecewise linear CCR model, in which a non-increasing set of multipliers describe the weight function. Also, the piecewise linear CCR model has been enhanced by introducing two MIP models for a two-stage procedure in order to set targets precisely. Furthermore as it follows, the above-mentioned models are compared with each other and an example is provided for the sake of lucidity.     

Computation of efficient targets in DEA models with production trade-offs and weight restrictions

Recently new models of data envelopment analysis (DEA) were introduced that incorporate production trade-offs between inputs and outputs or based on them weight restrictions. In this paper, we develop a computational procedure suitable for the practical application of such models. We show that the standard two-stage optimisation procedure used in DEA to test the full efficiency of units and identify their efficient targets may work incorrectly in the new models. The modified procedure consists of three stages: the first evaluates the radial efficiency of the unit, the second identifies its efficient target, and the third its reference set of efficient peers. Each stage requires solving one linear program for each unit.