Bi-level programming for emergency blood transshipment-allocation considering substitution against public health events

. The emergence of major public health crises, such as the Covid-19 pandemic, has significantly impacted the blood supply chain. We developed a bi-level programming model for emergency blood transshipment-allocation under this scenario, based on a cross-regional blood transshipment allocation network with a hierarchical structure. Our model considers emergency allocation, blood acceptability limits, blood type substitution relationships, hierarchical relationships among scheduling networks, and cross-regional and multi-modal transportation. The upper-level objective of our model is to minimize the total system cost, which includes shortage and substitution penalties. The lowerlevel objective is to maximize blood allocation satisfaction while considering demand urgency and blood type substitution. A primal-dual algorithm based on complementary relaxation conditions is established to solve the transformed model. The efficacy of our proposed model and solution strategy is validated through numerical calculations.