In this paper, a possibilistic bi-objective bi-level programming model is proposed to optimize the management of scarce drugs supply and rationing under difficult situations such as COVID-19 outbreak. Multiple followers and single leader exist in the proposed Stackelberg model in which the followers are divided into two groups, manufacturers and suppliers. The first group has priority over the latter. The competition between these two groups is addressed using a lexicographical procedure. Moreover, the interaction between the individuals in each group is incorporated through a normalized Nash equilibrium. To avoid the discriminative allocations, the disability-adjusted life years (DALY) index is employed to improve the rationing process. Due to the significance of uncertainty in such a problem, a novel risk-based possibilistic expected value approach is devised to control the mean and risk values of the objective functions. Finally, to validate the proposed solution method, the model is solved by applying Karush–Kuhn–Tucker (KKT) conditions and using the data extracted from a real case study. The results reveal the applicability and usefulness of the proposed possibilistic model compared to the conventional possibilistic approach

在本文中，提出了一种可能的双目标双层规划模型，以优化在 COVID-19 爆发等困难情况下稀缺药物供应和配给的管理。在提出的 Stackelberg 模型中存在多个追随者和单个领导者，其中追随者分为两组，制造商和供应商。第一组优先于后者。这两个群体之间的竞争是使用字典程序来解决的。此外，每个组中的个体之间的相互作用是通过标准化的纳什均衡结合起来的。为了避免歧视性分配，伤残调整生命年（DALY）指数被用来改进配给过程。由于在这样一个问题中不确定性的重要性，设计了一种新的基于风险的可能性期望值方法来控制目标函数的均值和风险值。最后，为了验证所提出的求解方法，通过应用 Karush-Kuhn-Tucker (KKT) 条件并使用从真实案例研究中提取的数据来求解模型。结果揭示了与传统的可能性方法相比，所提出的可能性模型的适用性和有用性