Facility location decision is strategic: the construction of a new facility is typically costly and the impact of the decision is long-lasting. Environmental changes, such as population shift and natural disasters, may cause today’s optimal location decision to perform poorly in the future. Thus, it is important to consider potential uncertainties in the design phase, while explicitly taking into account the possible customer reassignments as recourse decisions in the execution phase. This paper studies a robust fixed-charge location problem under uncertain demand and facility disruptions. To model this problem, we adopt a two-stage robust optimization framework, where the first-stage location decision is made here-and-now and the second-stage allocation decision can be deferred until the uncertainty information is revealed. We develop a column-and-constraint generation (C&CG) algorithm to solve the models exactly and benchmark it with the other C&CG algorithm in the literature. We further extend our modeling and solution schemes to facility fortification problems under uncertainties, where investment decisions are made for already existing supply chain systems to protect facilities from disruptions and against uncertain demand. We conduct extensive numerical tests to study the differences in solutions produced by the three robust models and the impacts of uncertainties on solution configuration. Results show that our C&CG algorithm can solve more instances to optimality and consume less computing time on average, compared to the benchmark algorithm. Several managerial insights are also drawn from our numerical experiments.

设施选址决策具有战略意义：新设施的建设通常成本很高，而且决策的影响是持久的。人口迁移和自然灾害等环境变化可能会导致当今的最佳位置决策在未来表现不佳。因此，重要的是要在设计阶段考虑潜在的不确定性，同时在执行阶段明确考虑将可能的客户重新分配作为追索决定。本文研究了不确定需求和设施中断下的鲁棒固定收费地点问题。为了对此问题建模，我们采用了两阶段鲁棒性优化框架，其中第一阶段的位置决策是从现在到现在进行的第二阶段的分配决策可以推迟到不确定性信息被揭示出来。我们开发了一种列约束生成（C＆CG）算法，以精确地求解模型，并与文献中的其他C＆CG算法进行基准测试。我们进一步将建模和解决方案扩展到不确定性下的设施设防问题，在这些问题上，将为现有的供应链系统制定投资决策，以保护设施不受干扰并应对不确定的需求。我们进行了广泛的数值测试，以研究由三个鲁棒模型产生的解的差异以及不确定性对解配置的影响。结果表明，与基准算法相比，我们的C＆CG算法可以解决更多实例达到最佳状态，平均减少计算时间。