A bi-criteria GTSP-based MILP model for the human milk supply chain: A two-tier Hub-and-Spoke framework with one Hub per Taluk

The Human Milk Supply Chain (HMSC) comprises the collection, processing, storage, and distribution of donor milk. Human Milk Banks (HMBs) serve as central hubs. Efficient management is essential in India, where Preterm Birth (PTB) rates are the highest globally. Its limited availability and logistical barriers limit the effectiveness of HMBs. This study proposes a hybrid two-tier Hub-and-Spoke (H&S) approach that integrates facility selection and routing optimization through the Generalized Traveling Salesman Problem (GTSP) formulated as a Mixed-Integer Linear Programming (MILP) model. The model ensures equitable selection of Collection Hubs (CHs), one per zone, to consolidate milk from widely distributed Collection Centers (CCs), minimizing direct transportation from all CCs and optimizing logistics. Real-time traffic data from the Google Maps Distance Matrix API is used to adjust routing dynamically for efficiency. Sensitivity and robustness analyses are performed to validate the model, testing its stability under variations in travel time and route configurations. The model is applied to Ernakulam district in Kerala, India, and demonstrates improved logistical efficiency, accessibility, and scalability. It reduces transportation costs, optimizes resource use, and fosters a culture of milk donation, contributing to a more equitable and effective HMB network in India.

کلیدواژه ها:

Human Milk Supply Chain ، Human Milk Banks ، Two-tier Hub-and-Spoke approach ، Generalized Traveling Salesman Problem ، Mixed-Integer Linear Programming ، Google maps distance matrix