A computational method is developed for solving time consistent distributionally robust multistage stochastic linear programs with discrete distribution. The stochastic structure of the uncertain parameters is described by a scenario tree. At each node of this tree, an ambiguity set is defined by conditional moment constraints to guarantee time consistency. This method employs the idea of nested Benders decomposition that incorporates forward and backward steps. The backward steps solve some conic programming problems to approximate the cost-to-go function at each node, while the forward steps are used to generate additional trial points. A new framework of convergence analysis is developed to establish the global convergence of the approximation procedure, which does not depend on the assumption of polyhedral structure of the original problem. Numerical results of a practical inventory model are reported to demonstrate the effectiveness of the proposed method.

开发了一种计算方法，用于求解具有离散分布的时间一致的分布鲁棒多级随机线性程序。不确定参数的随机结构由情景树描述。在该树的每个节点上，通过条件矩约束来定义歧义集以保证时间一致性。该方法采用了嵌套Benders分解的思想，该思想结合了向前和向后的步骤。后退步骤解决了一些圆锥编程问题，以逼近每个节点处的成本函数，而前退步骤用于生成其他试验点。开发了一种新的收敛性分析框架来建立逼近过程的全局收敛性，它不依赖于原始问题的多面体结构的假设。