Malmquist productivity index for network production systems

The conventional Malmquist productivity index (MPI) measures the performance improvement of a production system between two periods, where the system is treated as a black box, ignoring the internal operations of the component processes. Based on a relational model of the data envelopment analysis (DEA) for measuring the system and process efficiencies, this paper develops a methodology for calculating the system and process MPIs in one model. Moreover, relationships between the system and process MPIs are derived. By defining the ratio of the inefficiencies of a unit in two periods as complementary MPIs, this paper finds that the system complementary MPI is a linear combination of the process complementary MPIs, and the former is also close to a weighted average of the latter. Knowing the relationship between the system and process MPIs helps identify the processes that deter the improvement of the system; amendments to them will improve the system performance in the future.