A NETWORK EXTENDED-DIRECTIONAL MIX-EFFICIENCY MEASURE IN THE PRESENCE OF UNCONTROLLABLE INPUT AND UNDESIRABLE OUTPUT
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In conventional data envelopment analysis, decision making units are considered as a whole, that is, internal stages are generally ignored. In real life, most systems are composed of many divisions operating interdependently via the intermediate products that are created by some divisions and consumed by some others within the system. The aim of the study was to develop a formalized network mix efficiency model that can deal with both controllable and uncontrollable inputs as well as desirable and undesirable outputs by considering the internal structures of systems. A linear programming approach of data envelopment analysis was used by taking the ratio of slack based measure and directional distance function to measure the eco-efficiency of 54 African countries. The inputs into the system were classified as controllable and uncontrollable while the output as desirable and undesirable. Stage one captured agricultural production efficiency, while stage two evaluated the environmental impact of carrying out agricultural activities. The network efficiency model identified sources of inefficiencies from the components of a complex system rather than looking at the system as a black box. Controllable inputs and undesirable outputs were minimized while the desirable outputs were maximized. The approach provided policymakers with robust benchmarks for enhancing agricultural productivity while mitigating environmental degradation.
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