考虑决策单元竞争合作动态变化的DEA博弈交叉效率方法

利用DEA方法进行相对效率评估时,决策单元通常需要考虑多重目标,且随着目标的变化,决策单元间竞争合作状态也会发生动态变化。传统竞合模型虽然考虑了决策单元间竞争与合作同时存在的现象,但忽视了竞争合作关系动态变化的过程。本文以竞争合作对策为切入点,将多目标规划中的优先因子引入传统DEA博弈交叉效率模型中,提出了带有优先等级的多目标DEA博弈交叉效率模型,即动态竞合博弈交叉效率模型。该模型充分体现了不同目标下决策单元间竞争合作关系的动态变化,其焦点由传统竞合模型对多重最优权重现象的改善,转向对最优效率得分的直接寻找。利用DEA动态竞合博弈交叉效率模型,本文对环境污染约束下2014年长三角地区制造业投入产出绩效进行了客观的评估。分析结果表明:DEA动态竞合博弈交叉效率模型收敛速度优于传统DEA博弈交叉效率模型,其交叉效率得分收敛于唯一的纳什均衡点;不同目标重要性的差异程度,对最终排名结果不产生明显影响,不需要确切指出。

DEA Game Cross Efficiency Method for Dynamic Change of Competitive and Cooperative between Decision Making Units

Using DEA to evaluate relative efficiency, DMUs (decision making units) often needs to consider multiple objectives. The competitive and cooperative relationships between DMUs will also change with the change of objectives. Although the traditional competitive and cooperative model considers the situation that competition and cooperation between DMUs occur simultaneously, it ignores the dynamic change of competition and cooperation. Regarding the competitive and cooperative strategy as the breakthrough point, we introduce the priorities of multi-objective programming into the traditional game cross efficiency model, developing a multi-objective DEA game cross efficiency model, that is the DEA game cross efficiency model for dynamic change of competitive and cooperative relationships between decision making units. This model fully reflects the dynamic change of competition and cooperation between DMUs. Its focus is to find the optimal cross efficiency score directly rather than improve the problem of multiple optimal weights. Using this model, we evaluate the input-output efficiency of manufacturing in Yangtze River Delta region in 2014 under the constraints of environmental pollution. The analysis indicates that the DEA game cross efficiency model for dynamic change of competitive and cooperative converges more quickly than the traditional DEA game cross efficiency model, and its cross efficiency scores converge to a unique Nash equilibrium. Our model implicitly incorporates the relative importance of different objectives without the need for specifying the exact assurance regions.