Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations

In this paper, for evaluating the efficiency in a three-stage DEA structure we use additive and multiplicative cooperative models that comply with cooperation paradigm organizations, where improving of system, stages cooperate together. Since overall from may not be unique consequently stages’ efficiencies, then combine them Nash bargaining game approach besides maximizing scores whole provides fair decomposition. Second order programming relaxation proposed nonlinear are given contrast to parametric linear literature. Finally, effectiveness illustrated two numerical examples.