Development of a bi-objective stochastic location-allocation model for a blood supply chain considering reliability under the uncertainty of the main centers capacities

Authors
Yosra Aali 1
Sayyed Ehsan Monabbati 1
Zohreh Alipour 2
1 Alzahra University
2 Khatam University
Abstract
Blood supply is a vital component of human health, and managing it effectively under all conditions is a significant challenge for health systems. This study presents a bi-objective mixed-integer linear programming model designed to optimize the blood supply chain, considering the uncertainty in the capacity of the main blood donation centers. The model aims to minimize total costs and maximize the reliability of the blood supply chain.

The research introduces a novel model for defining the reliability of the blood supply chain based on the capacity of donation centers. The uncertainty of the model is converted into a deterministic form using stochastic programming with chance constraints.The bi-objective model is then transformed into a single-objective model using the Lp-metric method. A Relax & Fix heuristic algorithm is implemented to obtain feasible solutions, and these results are compared with those from the CPLEX solve.

The study determines the optimal locations of main and temporary centers, the allocation of donors to main and temporary centers and allocation of temporary centers to main centers and the optimal blood flow in the supply chain. The Relax & Fix heuristic algorithm provides a feasible solution with a small relative gap from the optimal solution.

This research concludes that the developed mathematical model can effectively address the challenges of blood supply chain management by optimizing costs and ensuring the availability of blood products. The model's implementation in Julia and its comparison with CPLEX demonstrate its reliability and efficiency. The findings suggest that this approach can improve the decision-making process in blood supply chain management, ensuring a more reliable and cost-effective system.
Keywords
Blood supply chain
Location-Allocation
Reliability
Uncertainty
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