Composite network data envelopment analysis model

This paper extends the DEA model to considering the decision-making unit (DMU) with the network structure. We define the network DMU and its network DEA efficiency based on the postulate system. On the series structure of the DMU, we further discuss a sequential optimization model originally proposed by Sexton and Lewis.1,2Based on their work, we extend to the DMU with general network of k stages and propose a composite network DEA model which evaluate the network DEA efficiency by solving only one linear programming. We show that the network efficiency obtained from the composite model is equivalent to that obtained by the sequential optimization model. We show that a network DMU is network-efficient if and only if it is efficient at all stages. That is, the network-efficient DMU follows the "Bellman Optimal Principle." Our model shows that if a network DMU is not DEA-efficient, then it is not efficient at one stage at least. We also define the projection of the network DMU on the corresponding production possibility set of network DMUs. Finally, we discuss other basic structures of the network DMU and show that the overall network DEA model can be extended to the general network DMU.