Evaluation of Financial Ratios in DEA-R model with production trade–offs and weight restrictions

Data envelopment analysis (DEA) is one of the best tools for evaluating units with multiple inputs and multiple outputs. In mul-tiplier models of DEA sometimes data on inputs or outputs is available, and/or some assumptions are imposed to the model that result in some conditions on weights vectors, in addition to non-negative conditions of the weight vectors of u and v. These conditions are called weights re- strictions. Applying weights restrictions on the multiplier model creates new variables in its corresponding DEA model. Thus, applying weights restrictions on the multiplier model leads to the development of tech- nology model in the envelopment form. This makes the projection of an inefficient unit that is on the efficiency frontier of the developed tech- nology not to be necessarily producible. Therefore, applying weights restrictions on multiplier models will enjoy this defect. To solve this problem weights restrictions are applied through the trade-off matrix that is a simultaneous change in inputs and outputs. Applying these restrictions is mathematically equivalent to applying weights restrictions in conventional methods such as assurance region and the difference is in the technological interpretation of its equivalent envelopment model, which resolves the above-mentioned defect. Applying weights restric-tions in DEA model helps us keep under control the significance of one output to other output or the significance of one input to other input and/or the significance of one output to one input. DEA-R model is a model for evaluating the performance of decision-making units (DMUs) that can analyse the role of each input in relation to each output. The specific feature of this model is to evaluate DMUs without imposing redundant weights restrictions that lead to the unreasonable decrease of the efficiency value. In this article, the tradeoff matrix has been uti-lized in order to impose weight restrictions on the weights of DEA-R models and using the proposed model an efficient method for evaluating business enterprises have been provided based on financial ratios.