Two-stage DEA models with fairness concern: Modelling and computational aspects

In a two-stage series system with two sub-stages connected, fairness concern between two sub-stages is critical. In order to evaluate system performance fairly and objectively, data envelopment analysis (DEA) has been widely applied for evaluating multi-input and multi-output two-stage series systems. Traditional two-stage evaluation DEA models ignore the behavioral factors between two sub-stages. This paper studies how one behavioral factor, fairness concern, impacts decision making unit (DMU) by proposing new utility-based two-stage DEA models to analyse the non-cooperative and cooperative modes. Two simple algorithms are proposed to solve our nonlinear models and one simple algorithm is proposed to determine the parameters of fairness concern. Further, theorems are proposed to better understand the impacts of fairness concern on DMUs. Finally, a numerical example and an application of fairness concern between sub-stages in non-life insurance companies are given to illustrate the proposed approach and to compare it in different scenarios, respectively. The results from two examples show that acknowledging fairness concern in two-stage system is imperative to achieve its best performance.