Prioritization model for decision making units in Data Envelopment Analysis from uncertain cross-evaluation values by the eigenvalue method

This paper proposes two-stage model for prioritizating decision making units (DMU) where each unit has multiple inputs and outputs. The rst stage model is a noncooperative game where each optimal input-output weight set of DMU is de ned by the Data Envelopment Analysis (DEA) and each DMU evaluates other DMUs by its own weights. The equilibrium state obtained from the rst stage motivates none of DMUs to change its optimal input-output weights from the current ones. In the second stage, the cross-evaluation matrix xed by the equilibrium weights of the rst stage is utilized to rank DMUs by the eigenvalue method in Analytical Hierarchy Process (AHP). The theoretical contribution of this paper is to show a duality theorem for a certain class of multifractional programming problems. Specially, the noncooperative game model of the rst stage is equivalent to nding an optimal eigenvalue of a positive matrix whose column vectors are included in compact sets such as polytopes. This paper also reports the numerical example of application of the two-stage analysis to the R&D project selection problem.