Nash decomposition for process efficiency in multistage production systems

• DEA models in which each DMU is organized internally as a sequence of processes or stages are considered.
• Nash bargaining theory is used to obtain a decomposition of the overall efficiency in the multistage production system.
• A explicit formula for the Nash decomposition is obtained.
• Interpretations of the results are provided.

Many production systems consist of a sequence of processes or stages. For these systems, relational network DEA can be used and an overall system efficiency (equal to the efficiency of the different processes) can be computed. However, there can be alternative solutions that give different estimations of the process efficiencies and therefore lead to different decompositions of the overall system efficiency. It is not obvious which efficiency decomposition to use. In this paper, it is shown how a Nash bargaining game can be used to compute point estimates of the efficiency of the processes for multistage systems. The proposed approach extends and improves over existing approaches for production systems with just two stages. The rationality principles behind the proposed solution approach are presented and an interesting interpretation of the resulting efficiency decomposition is provided. The fact that this rigorous solution approach leads to such a simple and elegant efficiency decomposition should facilitate its adoption by Expert and Intelligent Systems practitioners.