Robust two-stage DEA models under discrete uncertain data

Abstract

Data envelopment analysis (DEA) is a well-known non-parametric technique for evaluating the relative efficiency of decision-making units (DMUs). One of the most important issues associated with DEA is the uncertainty related to input data. When all the input data are uncertain, it is practically impossible to use traditional methods to handle the uncertainty. In this paper, by using Stackelberg (leader–follower) and centralized game theory approaches, two robust DEA models are proposed for the performance measurement of two-stage processes. The developed models calculate the efficiency scores for DMUs that contain discrete uncertain data on output and input parameters. The methods are based on a robust optimization approach developed by Mulvey in 1995 and utilize probable scenarios. The two proposed robust models are applied to a real world data-set related to 20 bank branches in the State of East Virginia.

Keywords:

• Data envelopment analysis
• uncertainty
• robust
• Stackelberg game theory
• centralized model

JEL classification:

• C02
• C44
• C61
• C71
• C72

Notes

1. Charnes, Cooper, & Rhodes.