Designing a blood supply chain network with temporary mobile facilities in natural disasters by a relax-and-fix approach: a case study

Natural disasters severely disrupt blood availability, as surging emergency demand coincides with constrained collection, testing, and distribution capacities. This study develops a dynamic disaster-responsive blood supply chain (BSC) planning framework that integrates mobile blood collection facilities with permanent blood centres. The proposed multi-period network incorporates a dual-channel donation structure that allows donors to donate either at temporary mobile sites or directly at fixed centres, while enabling the dynamic relocation of mobile facilities across planning periods. A bi-objective mixed-integer linear programming (MILP) location-allocation model is formulated to simultaneously minimise the maximum blood shortage across locations and periods – improving distributional equity – and minimise total operational cost, including transportation, relocation, and inventory holding. The minimax equity objective is reformulated through linearisation to maintain tractability within the MILP structure. To efficiently solve the large-scale model, a hybrid solution approach combining the augmented ϵ-constraint method with a relax-and-fix heuristic is developed to generate Pareto-efficient solutions. The framework is validated through a real-world case study of the emergency blood collection network in Tehran. Results show that dynamically relocating mobile units and enabling dual-channel donations significantly reduce maximum shortages while maintaining comparable costs.