A modification of double frontier ideal point method for Malmquist productivity index in the investigation of eco-innovation in transportation industry

The Malmquist productivity index (MPI) is a well-known and widely used tool for evaluating performance over time in a variety of fields, including the transportation industry. There are flaws in the modelling and techniques that lead to inaccurate results and analyses. Although common weights (CW) based on the ideal point are used to achieve efficiencies relative to the best and worst frontiers, fractions of the MPI formula are computed inconsistently, i.e., the efficiency scores in the numerator and denominator of MPI fractions are calculated using different bases, and thus, the fractions do not accurately represent the amount of change. In this paper, we intend to present an innovative model to address the issues. Then, using the proposed model, we analyse Iran's freight transportation industry performance from 2014 to 2017. We observe that our method generates MPI with smaller variations among the decision-making units (DMUs), we further notice that although the results derived from our proposed method and the ones from Mavi et al. (2019a) are similar to a certain extent, there are significance differences in the results reported by these two methods in some cases.