The widespread adoption of digital distribution channels both enables and forces more and more logistical service providers to manage booking processes actively to maintain competitiveness. As a result, their operational planning is no longer limited to solving vehicle routing problems. Instead, demand management decisions and vehicle routing decisions are optimized integratively with the aim of maximizing revenue and minimizing fulfillment cost. The resulting integrated demand management and vehicle routing problems (i-DMVRPs) can be formulated as Markov decision process models and, theoretically, can be solved via the well-known Bellman equation. Unfortunately, the Bellman equation is intractable for realistic-sized instances. Thus, in the literature, i-DMVRPs are often addressed via decomposition-based solution approaches involving an opportunity cost approximation as a key component. Despite its importance, to the best of our knowledge, there is neither a technique to systematically analyze how the accuracy of the opportunity cost approximation translates into overall solution quality nor are there general guidelines on when to apply which class of approximation approach. In this work, we address this research gap by proposing an explainability technique that quantifies and visualizes the magnitude of approximation errors, their immediate impact, and their relevance in specific regions of the state space. Exploiting reward decomposition, it further yields a characterization of different types of approximation errors. Applying the technique to a generic i-DMVRP in a full-factorial computational study and comparing the results with observations in existing literature, we show that the technique contributes to better explaining algorithmic performance and provides guidance for the algorithm selection and development process.

翻译：数字分销渠道的广泛采用既推动也迫使越来越多的物流服务提供商主动管理预订流程以保持竞争力。因此，其运营规划不再局限于解决车辆路径问题。相反，需求管理决策与车辆路径决策被集成优化，旨在最大化收入并最小化履约成本。由此产生的集成需求管理与车辆路径规划问题（i-DMVRPs）可建模为马尔可夫决策过程，理论上可通过著名的贝尔曼方程求解。然而，对于实际规模的问题实例，贝尔曼方程难以处理。因此，在现有文献中，i-DMVRPs通常通过基于分解的求解方法处理，其中机会成本近似是关键组成部分。尽管其重要性，据我们所知，目前既没有系统分析机会成本近似精度如何转化为整体解质量的技术，也没有关于何时应用哪类近似方法的通用指导原则。在本工作中，我们通过提出一种可解释性技术来填补这一研究空白，该技术量化并可视化近似误差的大小、其直接影响及其在状态空间特定区域的相关性。利用奖励分解，该技术进一步刻画了不同类型的近似误差。通过将该技术应用于通用i-DMVRP进行全因子计算研究，并将结果与现有文献中的观察进行比较，我们证明该技术有助于更好地解释算法性能，并为算法选择与开发过程提供指导。