Vaccine delivery in under-resourced locations with security risks is not just challenging but also life threatening. The current COVID pandemic and the need to vaccinate have added even more urgency to this issue. Motivated by this problem, we propose a general framework to set-up limited temporary (vaccination) centers that balance physical security and desired (vaccine) service coverage with limited resources. We set-up the problem as a Stackelberg game between the centers operator (defender) and an adversary, where the set of centers is not fixed a priori but is part of the decision output. This results in a mixed combinatorial and continuous optimization problem. As part of our scalable approximation of this problem, we provide a fundamental contribution by identifying general duality conditions of switching max and min when both discrete and continuous variables are involved. We perform detailed experiments to show that the solution proposed is scalable in practice.

翻译：由于这个问题,我们提出了一个总框架,以有限的资源来建立有限的临时(疫苗接种)中心,以平衡人身安全和理想(疫苗)服务范围。我们把这个问题作为中心操作员(defender)和对手之间的斯塔克伯格游戏来设置,中心组合并非先验固定,而是决策产出的一部分。这导致了混合组合和连续优化问题。作为这一问题可伸缩近似的一部分,我们提出一个基本贡献,在涉及离散和连续变数时,确定一般的双重条件,即最大和最小转换。我们进行了详细的实验,以表明所提议的解决办法在实践中是可以伸缩的。