Estimation of inputs and outputs in the general production possibility set with negative data based on the inverse DEA

The primary models in data envelopment analysis (DEA), consider the inputs and outputs of the decision-making units (DMUs) as non-negative. However, in the real world, we face many cases where the data is negative. In this paper, we investigate the inverse DEA models to estimate the optimal level of inputs and outputs of DMUs based on target efficiency scores. We also assume that some input and output components are negative. In this way, we propose three different models in variable returns to scale (VRS) to determine optimal levels. In order to solve each model, we determine the counterpart DMU corresponding to the DMUs under evaluation. This DMU is obtain based on the additive model, and then we get the level of the target and the observed outputs corresponding to the DMU under evaluation to determine which of these three models to use to measure the efficiency of the DMU under evaluation. We apply the proposed approach with a numerical example and consider it to measure the optimal levels of inputs and outputs of bank branches. Also we propose the results of paper.