Chemotherapeutic treatment of cancer comes with side effects on the immune system, such as Chemotherapy-Induced Neutropenia (CIN). A recombinant form of Granulocyte Colony-Stimulating Factor (G-CSF) has been used to alleviate CIN. This is a challenging task due to the feedback complexity of the hematological system. A System Dynamics model is constructed to study this system and to derive practical insights for the management of CIN. Stimulation of neutrophil production via G-CSF is observed to propose crucial trade-offs. On one hand, production by stem cells and mobilization from bone marrow should be stimulated to compensate for the impairment caused by chemotherapy. On the other hand, it is important to avoid overstimulation, which reduces the regenerative capacity, as well as draining the much-needed bone-marrow reservoir. Our analysis supports the intuition that the response to G-CSF administration is conditional to patient characteristics, and "one for all" treatment protocols are impractical.