A new SBM-based global Malmquist productivity index and target setting

AbstractHighlights •Demonstrate that ignoring the slacks sometimes leads to misleading results.•Expand the global Malmquist Productivity Index (MPI) to consider all slacks.•Propose a new dynamic algorithm for target setting.•Propose a new mix integer linear programming to determine reference sets. AbstractThe global Malmquist productivity index is a tool for measuring productivity change. It has two advantages with respect to the conventional Malmquist productivity index: it is circular and the infeasibility of the mixed period models does not happen. One drawback of the global Malmquist productivity index is to ignore slacks in its computations. In this paper, we follow four main goals: (1) we show that ignoring the slacks sometimes leads to misleading results; (2) we introduce a new slack-based measure (SBM)-based global Malmquist productivity index to overcome this drawback; (3) we will use the new index to determine a target for each inefficient unit in a dynamic way so that the proposed target has the most progress in its productivity among all the observed possible targets; (4) we propose a new mix-integer linear programming model to determine all the observed possible targets. Finally, we apply the proposed approach to the dataset of eighteen Canadian power companies to demonstrate the applicability of the method.