Stem-cell transplantation is the last chance for patients of various blood-related diseases. Stem-cell donation centers admit patients in need of a stem-cell transplant and search for a perfect match between the patients and donors. The search process is time-consuming and requires expensive advanced equipments, in particular for DNA typing. In this study, we are concerned with a capacity planning problem in a network of stem-cell donation centers. The underlying optimization model integrates the operations for a donor search and aims to maximize the number of transplantations. A scenario-based stochastic programming approach is introduced to investigate the effect of the demand and service time variabilities into the capacity planning problem. We consider the maximum possible waiting time during the search process to obtain robust solutions against uncertainties. For this purpose, we approximate the maximum waiting time in the advanced blood testing with a robust queuing approach. The computational experiments are designed to illustrate the performance of the capacity planning model.