Abstract

Cooperation is an important strategy to improve companies’ profitability. As a data-driven tool for performance evaluation, data envelopment analysis (DEA) is often used to measure the benefits from cooperation between independent decision making units (DMUs) or systems, but few involve the internal cooperation in a network structure system. For a double-level system that consists of an upper- and multiple lower-level processes, prior to cooperation, its internal processes are independent and fail to yield profit. Once the upper-level process cooperates with at least one lower-level process, the system can operate to obtain profit. At present, no research explores the internal cooperation in a double-level system from the perspective of relative performance, considering such dependency between upper- and lower-level processes. To fill this gap, we propose a double-level DEA game by integrating network DEA and cooperative game theory, and prove this new game is monotone, super-additive, and has non-empty core. We use an example of 15 supply chains including one supplier and three retailers to validate our approach and provide an example as a real-life application. Results show the Shapley value and nucleolus have the best performance in allocating the total profit in terms of fairness and stability, respectively.

摘要

合作是提高企业盈利能力的重要战略。作为绩效评估的数据驱动工具，数据包络分析（DEA）通常用于衡量独立决策单元（DMU）或系统之间的合作收益，但很少涉及网络结构系统中的内部合作。对于一个由一个上层流程和多个下层流程组成的双层系统，在合作之前，其内部流程是独立的，无法产生利润。一旦上级流程与至少一个下级流程合作，系统就可以运行以获取利润。目前，没有研究从相对性能的角度探讨双层系统中的内部协作，考虑到上下级流程之间的这种依赖关系。为了填补这个空白，我们将网络DEA和合作博弈论相结合，提出了一个双层DEA博弈，证明了这个新博弈是单调的、超可加的、非空核的。我们使用 15 个供应链的示例（包括一个供应商和三个零售商）来验证我们的方法并提供一个实际应用示例。结果表明，沙普利值和核仁在分配总利润的公平性和稳定性方面分别表现最好。