A Malmquist Productivity Index with Directional Distance Function and Uncertain Data

Document Type: Article

Authors

1 Department of Mathematics Ardabil Branch, Islamic Azad University, Ardabil, Iran

2 bBusiness Systems and Analytics Department Lindback Distinguished Chair of Information Systems and Decision Sciences La Salle University, Philadelphia, PA 19141, USA

3 aDepartment of Mathematics Ardabil Branch, Islamic Azad University, Ardabil, Iran

Abstract

We present an integrated data envelopment analysis (DEA) and Malmquist productivity index (MPI) to evaluate the performance of decision making units (DMUs) by using a directional distance function with undesirable interval outputs. The MPI calculation is performed to compare the efficiency of the DMUs in distinct time periods. The uncertainty inherent in real-world problems is considered by using the best and worst-case scenarios, defining an interval for the MPI and reflecting the DMUs’ advancement or regress. The optimal solution of the robust model lies in the efficiency interval, i.e., it is always equal to or less than the optimal solution in the optimistic case and equal to or greater than the optimal solution in the pessimistic case. We also present a case study in the banking industry to demonstrate applicability and efficacy of the proposed integrated approach.

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