Optimal Pooling, Batching, and Pasteurizing of Donor Human Milk

Human breast milk provides nutritional and medicinal benefits that are important to infants, particularly those who are premature or ill. Donor human milk, collected, processed, and dispensed via milk banks, is the standard of care for infants in need whose mothers cannot provide an adequate supply of milk. In this paper, we focus on streamlining donor human milk processing at nonprofit milk banks. On days that milk is processed, milk banks thaw frozen deposits, pool together milk from multiple donors to meet nutritional specifications of predefined milk types, bottle and divide the pools into batches, and pasteurize the batches using equipment with various degrees of labor requirements. Limitations in staffing and equipment and the need to follow strict healthcare protocols require productive, expedient, and frugal pooling strategies. We formulate integer programs that optimize the batching-pasteurizing decisions and the integrated poolingbatching-pasteurizing decisions by minimizing labor and meeting target production goals. We further strengthen these formulations by establishing valid inequalities for the integrated model. Numerical results demonstrate a reduction in the optimality gap through the strengthened formulation versus the basic integer programming formulation. A case study at Mothers' Milk Bank of North Texas demonstrates significant improvement in meeting milk type production targets and a modest reduction in labor compared with former practice. The model is in use at Mothers' Milk Bank of North Texas and has effectively improved their production balance across different milk types.