Goal-Programming-Based Procedure for Calculating Positive Multipliers Under a Multiple Criteria Data Envelopment Analysis Framework: An Application to UEFA EURO 2012

Abstract

One of the motivations for the arise of the multiple criteria data envelopment analysis (MCDEA) model was the need to yield more reasonable input-output multipliers than those derived from standard data envelopment analysis (DEA), without using priori information. The problem of unreasonable multipliers occurs when some production units are efficient in standard DEA simply because the optimization problem allows those units to select few inputs/outputs to attach positive multipliers, discarding all of the others. Notwithstanding, MCDEA may fail in providing multipliers schemes free of non-null values. Therefore, in this paper, we propose an alternative procedure, based on goal programming, for calculating positive multipliers within a MCDEA framework. This procedure is applied to a previously reported problem, concerning the performance evaluation of national teams that participated in the 2012 UEFA European Football Championship (UEFA EURO 2012), where the MCDEA model has not succeeded in providing strictly positive multipliers schemes. The results derived by the proposed procedure indicate that, to assure non-null multipliers, it is necessary a mild detachment of non-dominated solutions.