Abstract. The paper develops an integrated mathematical framework for identifying and evaluating nearshoring and reshoring, two processes frequently associated in economic discourse, but analytically distinct. Nearshoring is treated as a redistribution of trade mass to partners located at shorter economic distances, and reshoring as an increase in the share of domestic supply in domestic absorption, conditional on the effective substitution of imports. Starting from a bilateral-sectoral-temporal tensor of flows, the analysis builds probability measures, proximity, concentration and entropy indicators, exact decompositions of the trade distance change, as well as a convex optimization problem of the supplier structure. Results are formulated and demonstrated regarding the monotony of trade transfer, the separation of geographical and sectoral effects, the necessary and sufficient conditions of reshoring and the uniqueness of the optimal solution. The framework is complemented by a PPML gravity specification, a dynamic adjustment model and a procedure for identifying structural breaks. The result is a quantitative architecture in which geographical proximity, production recovery, diversification and resilience are measured separately, but can be brought together in a formal decision rule.

Keywords: nearshoring, reshoring, commercial distance, optimal transport, entropy, convex optimization, PPML, structural ruptures.