A covering tour-based inventory routing framework for humanitarian logistics

Abstract In post-disaster situations, swiftly delivering humanitarian assistance to victims amid chaos and uncertainty poses a significant challenge in practice. Furthermore, efficient distribution of restricted resources, effective inventory control, and optimal resource allocation remain imperative priorities for humanitarian organizations that strive to meet urgent needs under adverse conditions. This study proposes a two-echelon Covering Inventory Routing Problem (CIRP) that integrates the Inventory Routing Problem (IRP) and the Covering Tour Problem (CTP) to support decision-making in the distribution of medical kits in post-disaster humanitarian logistics. A scenario-based probabilistic Mixed-Integer Linear Programming (MILP) model is introduced to decrease costs while adequately addressing unpredictable demand. The applicability of the model was assessed through scenario analysis and a case study. In addition, a three-phase matheuristic algorithm is proposed to solve the CIRP. The results demonstrate that integrating IRP and CTP in a two-echelon structure improves both cost efficiency and the reach of aid delivery under uncertainty. The use of a static-dynamic inventory approach, together with coordinated routing, effectively minimizes emergency shipments and adapts to fluctuating demand, providing valuable support for decision-making in real-time humanitarian contexts. The three-phase matheuristic achieved cost reductions of over 70% relative to the model’s incumbent solution within the first hour on large-scale instances, highlighting its practical use in accelerating decision-making amid post-disaster uncertainty.