模型不确定性下排队系统与供应链运营管理中的动态分布式鲁棒优化研究综述

    A Review of Dynamic Distributional Robust Optimization in Queueing Systems and Supply Chain Management under Model Uncertainty

    • 摘要: 在新一代信息技术和新型运营模式的推动下,现代供应链系统呈现出需求高度随机、系统结构复杂以及数据不完备等特征,传统依赖精确概率分布假设的运营管理模型在动态环境中的适用性日益受到挑战。上述问题的根源在于模型不确定性,即决策者对系统真实随机演化规律的认知存在偏差。近年来,分布式鲁棒优化作为应对模型不确定性的重要方法,通过构造分布不确定集并在最坏情形下进行优化,为信息不完备条件下的稳健决策提供了统一的分析框架。然而,现有研究主要集中于静态或离散时间决策问题,对于连续时间排队系统、动态定价以及多阶段运营决策的系统性研究仍相对有限。基于上述研究背景,本文系统回顾了模型不确定性下供应链与排队系统中的动态分布式鲁棒优化研究进展。从模型不确定性的来源与刻画方式出发,梳理了分布式鲁棒优化在连续时间随机控制问题中的主要建模范式,并重点总结了高负荷排队系统、动态定价与库存控制等典型应用场景下的代表性研究成果。综述结果表明,模型不确定性是动态供应链与运营管理决策中的核心特征,而分布式鲁棒优化在应对该问题中展现出显著优势,但其在连续时间建模、多产品与多阶段决策以及复杂系统结构下的系统性应用仍有待进一步深化。最后,本文总结了相关研究面临的共性挑战,并展望了若干具有潜在研究价值的未来研究方向。

       

      Abstract: Driven by the development of next-generation information technologies and emerging operational paradigms, modern supply chain systems are characterized by highly stochastic demand, complex system structures, and incomplete data, which increasingly challenge the applicability of traditional operations management models that rely on precisely specified probability distributions in dynamic environments. The root cause of this issue lies in model uncertainty, namely, decision makers’ imperfect knowledge of the true stochastic evolution of the system. In recent years, distributionally robust optimization has emerged as an important approach to addressing model uncertainty. By constructing ambiguity sets of probability distributions and optimizing system performance under worst-case scenarios, this approach provides a unified analytical framework for robust decision making under incomplete information. However, existing studies have largely focused on static or discrete-time decision problems, while systematic investigations of continuous-time queueing systems, dynamic pricing, and multi-stage operational decisions remain relatively limited. Motivated by this gap, this paper presents a systematic review of research on dynamic distributionally robust optimization in supply chain and queueing systems under model uncertainty. From the perspective of the sources and representations of model uncertainty, we summarize the main modeling paradigms of distributionally robust optimization in continuous-time stochastic control, with particular emphasis on representative studies in heavy-traffic queueing systems, dynamic pricing, and inventory control. The survey reveals that model uncertainty is a central feature of dynamic supply chain and operations management decisions, and that distributionally robust optimization offers significant advantages in addressing this challenge. Nevertheless, its systematic application to continuous-time modeling, multi-product and multi-stage decision problems, and complex system structures remains an open area for further research. Finally, we identify common challenges in the existing literature and outline several promising directions for future research.

       

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