This paper contemplates how branch-price-and-cut solvers can be employed along with the robust optimization paradigm to address parametric uncertainty in the context of vehicle routing problems. In this setting, given postulated uncertainty sets for customer demands and vehicle travel times, one aims to identify a set of cost-effective routes for vehicles to traverse, such that the vehicle capacities and customer time window constraints are respected under any anticipated demand and travel time realization, respectively. To tackle such problems, we propose a novel approach that combines cutting-plane techniques with an advanced branch-price-and-cut algorithm. Specifically, we use deterministic pricing procedures to generate “partially robust” vehicle routes and then utilize robust versions of rounded capacity inequalities and infeasible path elimination constraints to guarantee complete robust feasibility of routing designs against demand and travel time uncertainty. In contrast to recent approaches that modify the pricing algorithm, our approach is both modular and versatile. It permits the use of advanced branch-price-and-cut technologies without significant modification, while it can admit a variety of uncertainty sets that are commonly used in robust optimization but could not be previously employed in a branch-price-and-cut setting.

本文考虑了如何使用分支价格和切割求解器以及稳健的优化范式来解决车辆路径问题背景下的参数不确定性。在这种情况下，给定客户需求和车辆行驶时间的假设不确定性集，我们旨在确定一组具有成本效益的车辆穿越路线，以便在任何预期需求和旅行下尊重车辆容量和客户时间窗口限制时间实现，分别。为了解决这些问题，我们提出了一种将切割平面技术与先进的分支价格和切割算法相结合的新方法。具体来说，我们使用确定性定价程序来生成“部分稳健”的车辆路线，然后利用圆形容量不等式和不可行路径消除约束的稳健版本来保证针对需求和旅行时间不确定性的路线设计的完全稳健可行性。与最近修改定价算法的方法相比，我们的方法既模块化又通用。它允许在不进行重大修改的情况下使用先进的分行定价和削减技术，同时它可以接受在稳健优化中常用但以前无法在分行定价和削减设置中使用的各种不确定性集. 与最近修改定价算法的方法相比，我们的方法既模块化又通用。它允许在不进行重大修改的情况下使用先进的分行定价和削减技术，同时它可以接受在稳健优化中常用但以前无法在分行定价和削减设置中使用的各种不确定性集. 与最近修改定价算法的方法相比，我们的方法既模块化又通用。它允许在不进行重大修改的情况下使用先进的分行定价和削减技术，同时它可以接受在稳健优化中常用但以前无法在分行定价和削减设置中使用的各种不确定性集.