Split-plot designs are commonly used in industrial experiments when there are hard-to-change and easy-to-change factors. Due to the number of factors and resource limitations, it is more practical to run a fractional factorial split-plot (FFSP) design. These designs are variations of the fractional factorial (FF) design, with the restricted randomisation structure to account for the whole plots and subplots. We discuss the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions and variations on this criterion.