EAGER: An Exploratory Approach for Managing Multiple Flows in Serial Supply Systems

现代全球供应链的成功在很大程度上取决于如何通过多阶段、相互连接的节点/位置管理物品（例如，产品、信息和客户）的流动。多阶段系统在经济活动领域中随处可见：在制造系统中，生产经过不同的阶段进行；在物流网络中，货物从一个地点运输到另一个地点；在通信网络中，信息从一个节点传输到下一个节点。由于这种系统的复杂性，即使不是大多数公司，也有许多公司仍在努力有效地控制库存，特别是在存在多种产品流动的情况下。这项早期概念探索性研究基金（EAGER）支持的研究旨在推进在这种多级系统中优化管理库存的方法，从而降低供应链运营成本。该项目还将为博士生和硕士生提供教育机会，并帮助扩大代表性不足的群体在研究和商业教育中的参与。复杂供应链研究的主要数学挑战在于相应的随机优化问题可行域边界的多维性。与只有规则产品流的经典多级库存问题不同，具有多个产品流的多级系统不允许简化到可行区域的一维边界。本研究的主要目标是在建立目标成本函数弱分解的基础上，探索求解多阶段系统的新数学框架。通过在凸分析中开发与最小化下保存这种弱分解有关的新结果，本研究将旨在提供有效和可操作的策略来管理具有多个产品流的多阶段系统。这些控制策略将使设计快速和鲁棒的算法成为可能，以优化控制这些系统并评估实现的节省。

The success of a modern global supply chains is determined to a large extent by how flows of items (e.g., products, messages, and customers) are managed through multi-stage, inter-connected nodes/locations. Multi-stage systems are encountered throughout the realm of economic activity: in manufacturing systems where production proceeds through distinct stages; in logistics networks in which goods are transported from one location to another; and in communication networks in which messages are transmitted from one node to the next. Because of the complexity of such systems, many if not most firms still struggle to effectively control inventory, especially in the presence of multiple flows of product. This EArly-concept Grant for Exploratory Research (EAGER) supported research aims to advance methods to optimally manage inventory in such multi-stage systems, and thus reduce the cost of supply chain operations. This project will also provide educational opportunities for doctoral and master's students and help broaden participation of underrepresented groups in research and business education. The main mathematical challenge for the study of complex supply chains lies in the multi-dimensional nature of the boundary of the feasible region for corresponding stochastic optimization problems. Unlike classical multi-echelon inventory problems with only the regular flow of product, multi-stage systems with multiple flows of product do not admit a reduction to a single-dimensional boundary of the feasible region. A main goal of this research is explore a new mathematical framework for solving multi-stage systems, based on establishing a weak decomposition of the objective cost function. By developing new results in convex analysis that pertain to the preservation of this weak decomposition under minimization, this research will then aim to provide effective and actionable policies to manage multi-stage systems with multiple flows of product. These control policies will make it possible to design fast and robust algorithms to optimally control such systems and evaluate the realized savings.