A new efficiency evaluation approach with rough data: An application to Indian fertilizer

In the world of chaos, nothing is certain. In such an unpredictable world, measuring the efficiency of any individual is inevitable. In a conventional data envelopment analysis (DEA) model, exact input and output quantity data are needed to measure the relative efficiencies of homogeneous decision-making units (DMUs). However, in many real-world applications, the exact knowledge of data might not be available. The rough set theory allows for handling this type of situation. This paper tries to construct a rough DEA model by combining conventional DEA and rough set theory using optimistic and pessimistic confidence values of rough variables, all of which help provide a way to quantify uncertainty. In the proposed method, the same set of constraints (production possibility sets) is employed to build a unified production frontier for all DMUs that can be used to properly assess each DMU's performance in the presence of rough input and output data. Besides, a ranking system is presented based on the approaches that have been proposed. In the presence of uncertain conditions, this article investigates the efficiency of the Indian fertilizer supply chain for over a decade. The results of the proposed models are compared to the existing DEA models, demonstrating how decision-makers can increase the supply chain performance of Indian fertilizer industries.