Endogenous uncertainty concerns uncertainty which is dependent of decisions such as link failure in the retrofitting planning application. We propose a marginal-based distributionally robust optimization framework for integer stochastic optimization with decision-dependent discrete distributions that can be applied for the retrofitting planning application. We show that the resulting model can be formulated as a mixed-integer linear optimization problem. In order to solve the problem, we develop a constraint generation algorithm given the exponentially large number of constraints. Numerical results for the retrofitting planning application show that the proposed algorithm once tailored can solve the problem efficiently.

内生不确定性涉及依赖于决策的不确定性，例如改造规划应用中的链路故障。我们提出了一个基于边际的分布鲁棒优化框架，用于整数随机优化，具有决策相关的离散分布，可应用于改造规划应用。我们表明，所得模型可以表述为混合整数线性优化问题。为了解决这个问题，我们开发了一种约束生成算法，给定指数级的大量约束。改造计划应用的数值结果表明，所提出的算法一旦定制就可以有效地解决问题。