A Nash bargaining game data envelopment analysis model for measuring efficiency of dynamic multi-period network structures

Abstract
Purpose – A Nash bargaining game data envelopment analysis (NBG-DEA) model is proposed to measure the efficiency of dynamic multi-period network structures. This paper aims to propose NBG-DEA model to measure the performance of decision-making units with complicated network structures.

Design/methodology/approach – As the proposed NBG-DEA model is a non-linear mathematical programming, finding its global optimum solution is hard. Therefore, meta-heuristic algorithms are used to solve non-linear optimization problems. Fortunately, the NBG-DEA model optimizes the well-formed problem, so that it can be solved by different non-linear methods including meta-heuristic algorithms. Hence, a metaheuristic algorithm, called particle swarm optimization (PSO) is proposed to solve the NBG-DEA model in this paper. The case study is Industrial Management Institute (IMI), which is a leading organization in providing consulting management, publication and educational services in Iran. The sub-processes of IMI are
considered as players where their pay-off is defined as the efficiency of sub-processes. The network structure
of IMI is studied during multiple periods.

Findings – The proposed NBG-DEA model is applied to measure the efficiency scores in the IMI case study. The solution found by the PSO algorithm, which is implemented in MATLAB software, is compared with that generated by a classic non-linear method called gradient descent implemented in LINGO software. Originality/value – The experiments proved that suitable and feasible solutions could be found by solving the NBG-DEA model and shows that PSO algorithm solves this model in reasonable central process unit time.

Keywords Network data envelopment analysis, Nash bargaining game, Particle swarm optimization, Performance assessment