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

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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.