In standard Data Envelopment Analysis (DEA) models it is as- sumed that the aggregate output (input) is a pure linear function of each output (input). But in real life situations linear pricing may not sufficiently reveal the differences in value which are created from one Decision Making Unit (DMU) to another. Thus for overcoming this difficulty a generalization of the? DEA methodology has been presented that incorporates piece- wise linear functions of factors. In this paper, considering the benefits of nonradial DEA models over that of radial ones, this subject has been expanded and new model have been presented. Also considering this situation the issue of efficiency assessment, finding targets and identifying reference set in presence of trade off technology has been discussed. Furthermore, the above-mentioned mode is compared to those obtained through radial ones and an example is provided for the sake of lucidity.