Common weights data envelopment analysis with uncertain data: A robust optimization approach

• The paper introduces a robust model to find out common weights in DEA with uncertain data.
• The proposed model considers two important issues of data uncertainty and common weights for inputs and outputs.
• The paper uses the goal programming technique to develop the suitable robust counterpart of the common weight DEA model.

One of the primary issues on data envelopment analysis (DEA) models is the reduction of weights flexibility. There are literally several studies to determine common weights in DEA but none of them considers uncertainty in data. This paper introduces a robust optimization approach to find common weights in DEA with uncertain data. The uncertainty is considered in both inputs and outputs and a suitable robust counterpart of DEA model is developed. The proposed robust DEA model is solved and the ideal solution is found for each decision making units (DMUs). Then, the common weights are found for all DMUs by utilizing the goal programming technique. To illustrate the performance of the proposed model, a numerical example is solved. Also, the proposed model of this paper is implemented by using some actual data from provincial gas companies in Iran.