An Uncertain Allocation Models in Data Envelopment Analysis: A Case in the Iranian Stock Market

Abstract

Data envelopment analysis (DEA) can be employed for investigating operation and evaluation of units as one of the most important concerns of managers. DEA is a linear programming technique for calculating relative performance of decision-making units (DMUs) with multiple inputs and outputs. Although all inputs and outputs are considered as certain items in these models, there are uncertain items in the real word and existing interference between these two concepts will result in uncertain models. Allocation models were studied in an uncertain environment with belief degree based uncertain input costs and output prices. Belief degree based uncertainty is useful for cases where there is no historical information on an uncertain event. Utilizing the uncertain entropy model as a second objective function, the cost and revenue models showed an optimal performance with a maximum dispersion rate in their constituent components. As a solution methodology, the uncertain allocation models were separately converted into crisp models by expect value (EV) and expected value and chance-constrained (EVCC) methods. A practical example from the Iranian Stock Market was also presented to evaluate the performance of the new model.