In this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second-stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal ones. It is shown that the robust two-stage versions of basic network optimization and selection problems are NP-hard, even in a very restrictive cases. Some exact and approximation algorithms for the general problem are constructed. Polynomial and approximation algorithms for the robust two-stage versions of basic problems, such as the selection and shortest path problems, are also provided.

中文翻译：

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凸第二阶段成本不确定性下的鲁棒两阶段组合优化问题

本文讨论了一类鲁棒的两阶段组合优化问题。假设不确定的第二阶段成本以凸不确定集的形式指定，特别是多面体或椭圆体。结果表明，即使在非常严格的情况下，基本网络优化和选择问题的鲁棒两阶段版本也是 NP 难的。为一般问题构造了一些精确算法和近似算法。还提供了用于基本问题（例如选择和最短路径问题）的稳健两阶段版本的多项式和近似算法。