Fairness based unique common equilibrium efficient frontier for evaluating decision-making units with fixed-sum outputs

Data envelopment analysis, a non-parametric programming approach, has been extended to situations in which all total decision-making unit (DMU) outputs are fixed, and a secondary goal approach based on a minimum reduction strategy proposed to achieve an equilibrium efficient frontier to evaluate these fixed-sum output DMUs. However, the non-uniqueness of the equilibrium efficient frontier and the calculation burden of the iterative procedure have reduced the practicability of these approaches. Therefore, to address these problems, this paper developed a fairness based common equilibrium efficient frontier data envelopment analysis approach (CEEFDEA) that can guarantee the uniqueness of the common equilibrium efficient frontier and achieve such a frontier in only one step. Fairness is also included into the proposed CEEFDEA approach and the price of fairness is defined. One numerical example from previous studies and one case study focused on an efficiency evaluation of the Chinese appliance industry in 2019 are given to illustrate the effectiveness of the proposed approach. The results from the numerical example showed that the proposed CEEFDEA approach was able to achieve a fairer common equilibrium efficient frontier at the expense of a 5.85% increase in the adjustment proportion.