The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. We also explore a number of variants where additional constraints are imposed on the first-stage decisions, specifically matroid and multi-knapsack constraints. Our eventual goal is to provide results for supplier problems in the most general distributional setting, where there is only black-box access to the underlying distribution. To that end, we follow a two-step approach. First, we develop algorithms for a restricted version of each problem, in which all possible scenarios are explicitly provided; second, we employ a novel \emph{scenario-discarding} variant of the standard \emph{Sample Average Approximation (SAA)} method, in which we crucially exploit properties of the restricted-case algorithms. We finally note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.

翻译：本文的主要重点是以半径(供应商)为主,在两阶段随机集成中采用追索方法,模型固有的随机性以预算限制的形式出现。 我们还探索了对第一阶段决定施加额外限制的若干变式,具体地说,是类固醇和多形形形形色色限制。我们最终的目标是在最普遍的分布环境中为供应商问题提供结果,因为在最普遍的分布环境中,只有黑盒可以进入基本分布。为此,我们采取两步方法。首先,我们为每个问题的一个限制性版本制定算法,其中明确提供了所有可能的假想;第二,我们采用了标准的 emph{Sample 平均应用吸附(SAA)} 方法的变式,其中我们关键地利用了有限量算法的特性。我们最后指出,为了在半径上实现最佳化,有必要对SAA方法进行假想式分解。