Abstract

We introduce a new class of two-stage stochastic uncapacitated facility location problems under system nervousness considerations. The location and allocation decisions are made under uncertainty, while the allocation decisions may be altered in response to the realizations of the uncertain parameters. A practical concern is that the uncertainty-adaptive second-stage allocation decisions might substantially deviate from the corresponding pre-determined first-stage allocation decisions, resulting in a high level of nervousness in the system. To this end, we develop two-stage stochastic programming models with restricted recourse that hedge against undesirable values of a dispersion measure quantifying such deviations. In particular, we control the robustness between the corresponding first-stage and scenario-dependent recourse decisions by enforcing an upper bound on the Conditional Value-at-Risk (CVaR) measure of the random CVaR-norm associated with the scenario-dependent deviations of the recourse decisions. We devise exact Benders-type decomposition algorithms to solve the problems of interest. To enhance the computational performance, we also develop efficient combinatorial algorithms to construct optimal solutions of the Benders cut generation subproblems, as an alternative to using an off-the-shelf solver. The results of our computational study demonstrate the value of the proposed modeling approaches and the effectiveness of our solution methods.

摘要

我们在系统紧张考虑下引入了一类新的两阶段随机无容量设施位置问题。位置和分配决定是在不确定的情况下做出的，而分配决定可以响应于不确定参数的实现而改变。一个实际问题是，不确定性自适应的第二阶段分配决策可能会大大偏离相应的预先确定的第一阶段分配决策，从而导致系统高度紧张。为此，我们开发了具有有限追索权的两阶段随机规划模型，以对冲量化此类偏差的离散度量的不良值。特别是，我们通过对与情景相关的追索决策的偏差相关联的随机 CVaR 范数的条件风险价值 (CVaR) 度量实施上限来控制相应的第一阶段和情景相关的追索决策之间的稳健性. 我们设计了精确的 Benders 型分解算法来解决感兴趣的问题。为了提高计算性能，我们还开发了高效的组合算法来构建 Benders 切割生成子问题的最佳解决方案，作为使用现成求解器的替代方法。我们的计算研究结果证明了所提出的建模方法的价值和我们的解决方案方法的有效性。