We provide a novel analysis of the
Guaranteed Service Model (GSM), one of the most widely applied models for multi-echelon inventory management.
In particular, we develop a procedure to solve the GSM in time exponential in the
treewidth of the underlying supply chain network graph, but linear in the number of nodes n of the graph.
The treewidth of a graph describes the graph's similarity to a tree — it is one for a tree graph, and n-1 for a fully connected graph.
Our procedure is based on solving a linear program, so it can easily be implemented with standard solvers.
This allows solving the GSM for large and highly complex supply chain networks, as long as the underlying network's treewidth is relatively small — which, recent literature has identified, is the case for supply chain networks encountered in practice.
We then extend the GSM and our procedure to closed-loop supply chain networks, that is, networks with reverse flows.
We show that individual reverse flows do not significantly affect the solution time.
This opens the door to analyzing inventory management in the circular economy and evaluating the viability of different circular business models.
With Andre Calmon (Georgia Tech), Georgina Hall (INSEAD), & Mohit Tawarmalani (Daniels School of Business).
Analysis in progress.
A draft with the core analytical results only is available here.