Multistage network data envelopment analysis: Semidefinite programming approach

Additive efficiency aggregation is one of the important techniques measuring the relative efficiency of decision-making units under network data envelopment analysis (DEA). However, the modelling of additive network DEA is limited to parametric methods to approximate optimal solutions in previous literature. Under multistage network structure, if some outputs leave the system from a given stage while others become inputs to the next stage and some new inputs enter at any stage, the additive network models become extremely nonlinear and are impossible to be solved by linear program. The current paper proposes to solve general additive two-stage models by using semidefinite programming, which is known as effective as linear program. We then extend the methodology to general multistage network structures (including serial processes, parallel processes, multistage processes with non-immediate successor flows, and multistage processes with feedbacks). A numerical data set and the case of regional R&D processes in China are revisited by using the newly developed approach.