Linganisha mbinu

	Malmquist Productivity Index	Uchambuzi wa Bahasha ya Data ya Mtandao (Network DEA)
Nyanja	Uchanganuzi wa Ufanisi	Uchanganuzi wa Ufanisi
Familia	Regression model	Regression model
Mwaka wa asili	1994	2000
Mwanzilishi	Färe, Grosskopf, Norris & Zhang	Färe & Grosskopf
Aina	Non-parametric productivity index	Multi-stage nonparametric efficiency model
Chanzo asilia	Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review, 84(1), 66–83.	Färe, R., & Grosskopf, S. (2000). Network DEA. Socio-Economic Planning Sciences, 34(1), 35–49.
Majina mbadala	MPI, Malmquist Index, Malmquist DEA Productivity Index, Malmquist Verimlilik Endeksi	Network Data Envelopment Analysis, Network Efficiency Analysis, Multi-Stage DEA, Ağ Veri Zarflama Analizi
Zinazohusiana	1	2
Muhtasari	The Malmquist Productivity Index (MPI) is a non-parametric measure of total factor productivity (TFP) change over time. Formally grounded in distance functions by Caves, Christensen, and Diewert (1982) and operationalized using Data Envelopment Analysis by Färe, Grosskopf, Norris, and Zhang (1994), MPI decomposes productivity growth into two components: efficiency change (catching-up to the frontier) and technical change (shift of the frontier itself).	Network Data Envelopment Analysis (Network DEA) is a nonparametric efficiency measurement framework introduced by Färe and Grosskopf (2000) that extends classical DEA to multi-stage or multi-division production processes. Rather than treating a decision-making unit as a black box, it explicitly models the internal structure — the divisions and the intermediate products that flow between them — enabling stage-level and overall efficiency scores to be estimated simultaneously within a single coherent model.