From Trees to Closed Loops: Inventory Management in Treewidth-Bounded Supply Chain Networks

51 Pages Posted: 5 Feb 2025 Last revised: 18 Mar 2025

See all articles by Philippe Blaettchen

Philippe Blaettchen

Bayes Business School (formerly Cass)

Andre Calmon

Georgia Institute of Technology - Operations Management Area

Georgina Hall

INSEAD - Decision Sciences

Mohit Tawarmalani

affiliation not provided to SSRN

Date Written: March 10, 2025

Abstract

We propose a new linear programming (LP) framework for the Guaranteed Service Model (GSM), one of the most widely applied approaches for optimizing safety stock placement in supply chain networks. Unlike existing approaches, our framework optimizes the GSM on any acyclic supply chain network of bounded treewidth  a graph-theoretic measure quantifying how "tree-like" a network is. The framework uses an exact LP reformulation of the GSM with size exponential in the network's treewidth but polynomial in other network parameters, such as the number of nodes. This makes it tractable for real-world supply chains, which typically exhibit low treewidth, and allows for the use of standard LP optimization software, unlike previous GSM optimization strategies, which rely on specialized algorithms or heuristics. It also enables new results and insights for the GSM, such as duality-based sensitivity analysis, principled upper and lower bounds, and the ability to incorporate operational constraints. We extend this framework to handle closed-loop supply chains with reverse flows, demonstrating that individual reverse flows only marginally increase computational complexity. This closed-loop GSM facilitates the analysis of how reverse flows impact safety stock placement in supply chains that involve recycling, remanufacturing, and product returns. Overall, our framework provides new theoretical foundations and practical tools for managing safety stock in complex modern supply chain networks. 

Keywords: supply chain management, inventory management, algorithms, computational complexity, circular economy

Suggested Citation

Blaettchen, Philippe and Calmon, Andre and Hall, Georgina and Tawarmalani, Mohit, From Trees to Closed Loops: Inventory Management in Treewidth-Bounded Supply Chain Networks (March 10, 2025). Available at SSRN: https://ssrn.com/abstract=5125427 or http://dx.doi.org/10.2139/ssrn.5125427

Philippe Blaettchen (Contact Author)

Bayes Business School (formerly Cass) ( email )

United Kingdom

Andre Calmon

Georgia Institute of Technology - Operations Management Area ( email )

800 West Peachtree St.
Atlanta, GA 30308
United States

Georgina Hall

INSEAD - Decision Sciences ( email )

United States

Mohit Tawarmalani

affiliation not provided to SSRN

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