Managing blood donations is a challenging problem due to the perishability of blood, limited donor pool, deferral time restrictions, and demand uncertainty. The problem addressed here combines two important aspects of blood supply chain management: the inventory control of blood products and the donation schedule. We propose a stochastic scenario-based reformulation of the blood donation management problem that adopts multicomponent apheresis and utilizes donor pool segmentation into here-and-now and wait-and-see donors. We propose a flexible donation scheme that is resilient against demand uncertainty. This scheme enables more flexible donation schedules because wait-and-see donors may adjust their donation schedules according to the realized values of demand over time. We propose a column generation\bl{-based} approach to solve the associated multi-stage stochastic donation tailoring problem. The numerical results show the effectiveness of the proposed optimization model, which provides solutions with less than a 7% optimality gap on average with respect to a lower bound. It also improves the operational cost of the standard donation scheme that does not use wait-and-see donors by more than 18% on average. Utilizing multicomponent apheresis and flexible wait-and-see donations are suggested for donation organizations because they yield significant cost reductions and resilient donation schedules.