Blood donation centers face challenges in matching supply with demand while managing donor availability. Although targeted outreach is important, it can cause donor fatigue via over-solicitation. Effective recruitment requires targeting the right donors at the right time, balancing constraints with donor convenience and eligibility. Despite extensive work on blood supply chain optimization and growing interest in algorithmic donor recruitment, the operational problem of assigning donors to sessions across a multi-site network, taking into account eligibility, capacity, blood-type demand targets, geographic convenience, and donor safety, remains unaddressed. We address this gap with an optimization framework for donor invitation scheduling incorporating donor eligibility, travel convenience, blood-type demand targets, and penalties. We evaluate two strategies: (i) a binary integer linear programming (BILP) formulation and (ii) an efficient greedy heuristic. Evaluation uses the registry from Instituto Português do Sangue e da Transplantação (IPST) for invite planning in the Lisbon operational region using 4-month windows. A prospective pipeline integrates organic attendance forecasting, quantile-based demand targets, and residual capacity estimation for forward-looking invitation plans. Results reveal its key role in closing the supply-demand gap in the Lisbon operational region. A controlled comparison shows that the greedy heuristic achieves results comparable to the BILP, with 188x less peak memory and 115x faster runtime; trade-offs include 3.9 pp lower demand fulfillment (86.1% vs. 90.0%), larger donor-session distance, higher adverse-reaction donor exposure, and greater invitation burden per non-high-frequency donor, reflecting local versus global optimization. Experiments assess how constraint-aware scheduling can close gaps by mobilizing eligible inactive/lapsing donors.