A multi-objective distance friction minimization model for performance assessment through data envelopment analysis

Abstract

The distance friction minimization (DFM) model proposed by Suzuki, Nijkamp, Rietveld, & Pels (2010) is an important data envelopment analysis (DEA) model for performance improvement. This model has been widely applied to improve the performance of government, finance and transportation sectors and energy-environment management. The DFM model is constructed to set input and output improvements based on the optimal weight vector of the traditional CCR model. However, non-unique optimal weight vectors of the CCR model may be obtained when different linear programming solvers are used. Thus, different values for the two distance friction (DF) objectives may be obtained. Furthermore, the DF values obtained using one optimal weight vector may be dominated by those obtained using another optimal vector. To address this issue, we propose an improved DFM model that considers all the possible optimal weight vectors of the CCR model to determine a set of non-dominated DF values definitively. Our DFM model is a multi-objective, quadratic and nonlinear programming model that is solvable by an augmented ɛ-constraint method that ensures all solutions are Pareto efficient. We demonstrate the applicability of our new model by using it to analyse China's transportation sectors.