Weighted index of graph efficiency improvements for by-production technology and its application to the Indian coal-based thermal power sector

In contrast to conventional output-based efficiency indexes that hold input-levels fixed, a graph index of efficiency-improvements (EIs) is derived for a by-production technology by optimizing a weighted average of EIs in input and good and bad-output directions. Under the by-production approach, EIs in the input directions are non-positively related to EI in the good-output direction and non-negatively related to EI in the bad-output direction. The optimal configurations of EIs balances between the gains for the graph efficiency index from increase in EI in the emission direction and the loss from reduction in EI along the good-output direction when there are EIs in the input directions. A comprehensive classification of possible optimal configurations of EIs is provided. The optimal configuration that materializes depends crucially on the weights given to EIs in the input and output directions. Even with zero weights given to EIs in all the input directions, the optimal configuration can involve EIs in the directions of the emission-causing inputs. The optimal configurations of graph EIs for the plants in the Indian coal-based thermal power sector are studied.