Abstract:

Data envelopment analysis is one of the most important methods for organization performance assessment. The conventional data envelopment analysis method assumes that the output level can be changed freely for each decision-making unit， while the fixed-sum constraint which is common in many managerial applications invalids the independence assumption， implying that the output level cannot be changed freely for decision-making units. Although it has attracted much attention on evaluating decision-making units with fixed-sum outputs， there has been few previous studies in the environment with network production structures. Alternatively， a two-stage network structure with fixed-sum shared outputs is considered， where the first stage uses inputs to generate intermediate outputs and a proportion of shared outputs， while the second stage uses intermediate outputs and some additional inputs to produce another proportion of shared outputs and other final outputs. To address the fixed-sum shared outputs， a two-stage data envelopment analysis approach is proposed for evaluating decision-making units with fixed-sum shared outputs. Furthermore， models are develiped to decompose the two-stage overall efficiency into sub-stage efficiency scores. Finally， the proposed approach is illustrated with an empirical study of energy generation-utilization activities for 30 provincial regions in China by considering the carbon peak policy.

Key words: data envelopment analysis, fixed-sum constraint, two-stage structure, share outputs