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、消息和客户)的流动。在经济活动的各个领域都会遇到多阶段系统：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；以及在通信网络中，信息从一个节点传送到下一个节点。由于这类系统的复杂性，许多公司(如果不是大多数公司)仍然难以有效地控制库存，特别是在存在多个产品流动的情况下。这项由探索性研究资助的早期概念资助研究旨在推进在这种多阶段系统中优化管理库存的方法，从而降低供应链运营的成本。该项目还将为博士生和硕士研究生提供教育机会，并有助于扩大代表不足的群体在研究和商业教育方面的参与。复杂供应链研究的主要数学挑战在于对应的随机优化问题可行域边界的多维性。不同于经典的只有规则产品流的多级库存问题，具有多个产品流的多阶段系统不允许归结到可行域的一维边界。本研究的一个主要目的是在建立目标成本函数的弱分解的基础上，探索一种新的求解多阶段系统的数学框架。通过在凸分析中发展与最小化下保持这种弱分解有关的新结果，本研究将致力于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稳健的算法来优化控制这类系统和评估实现的节省成为可能。

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.