Estimating multi-period global cost efficiency and productivity change of systems with network structures

The current paper develops three different ways to measure the multi-period global cost efficiency for homogeneous networks of processes when the prices of exogenous inputs are known at all time periods. A multi-period network data envelopment analysis model is presented to measure the minimum cost of the network system based on the global production possibility set. We show that there is a relationship between the multi-period global cost efficiency of network system and its subsystems, and also its processes. The proposed model is applied to compute the global cost Malmquist productivity index for measuring the productivity changes of network system and each of its process between two time periods. This index is circular. Furthermore, we show that the productivity changes of network system can be defined as a weighted average of the process productivity changes. Finally, a numerical example will be presented to illustrate the proposed approach.