Performance Maps for Distribution Network Configuration: Multidimensional Analysis with the Buckingham Theorem

Optimizing Distribution Networks (DNs) is vital for retailers' profitability, impacting supply chain performance in terms of service levels and costs. A key decision in DN configuration is the stock deployment policy, which involves choosing between centralized, decentralized, and hybrid DNs for each Stock Keeping Unit (SKU). This decision is challenging since many variables influence the choice of the optimal (cost-effective) stock deployment policy, and they must be considered simultaneously (e.g., number of customers served, number of distribution centers, SKU unitary cost, SKU backorder cost, etc.). Moreover, retailers can manage thousands of SKUs, therefore the decision on the optimal stock deployment policy must be repeated several times. To simplify this decision, retailers seek support tools that guide in associating SKUs with optimal deployment policies. To address this need, Dimensional Analysis (DA) and, particularly, the Buckingham Theorem (BT) offer promising methodologies. Indeed, after modeling the DN configuration problem in a mathematical form, BT checks the meaningfulness of its governing equations, identifies influential variables, extracts knowledge on how they mutually when influencing the optimal stock deployment policies, and facilitates informed decisions about the option to select. Accordingly, BT allows for comparing different DN configurations, creating performance maps which suggest similar stock deployment decisions for similar (scaled) SKUs, suppliers, distributors, etc. Despite the potential usefulness of these maps, no study has explored the capabilities of BT to address stock deployment decisions. This paper addresses this gap by leveraging BT to develop supporting maps for multidimensional scaling, similarity analysis, and economic performance prediction of centralized, decentralized, and hybrid DNs. The achieved maps will constitute the main results of this study, providing retailers with decision support tools for associating similar DNs with optimal stock deployment policies. These maps offer a visual aid for retailers to make informed decisions on DN configuration, ultimately enhancing supply chain performance.