A generalized cost Malmquist index to compare the productivities of units with negative data in DEA

In some data envelopment analysis (DEA) applications, some inputs of DMUs have negative values with positive cost. This paper generalizes the global cost Malmquist productivity index to compare the productivity of dierent DMUs with negative inputs in any two periods of times under variable returns to scale (VRS) technology, and then the generalized index is decomposed to several components. The obtained components are computed using the nonparametric linear programming models, known as DEA. To illustrate the generalized index and its components, a numerical example at three successive periods of time is given.