Granulocyte-colony stimulating factor (G-CSF) is used clinically for treating chemotherapy-induced neutropenia (low neutrophil levels). Here we present a delay differential equation model for the regulation of neutrophil production that accounts for the effects of G-CSF. Using a combination of analysis and numerical simulations, we use this model to study the effects of delaying G-CSF treatment following chemotherapy for two recombinant forms of G-CSF (filgrastim and pegfilgrastim). We also examine the consequences of varying the duration of filgrastim treatment. We found that varying the starting day or the duration of G-CSF treatment can lead to different qualitative responses in the neutrophil count. These changes can be explained by the coexistence of two stable solutions in the mathematical model.