  Stereotactic radiosurgery is an effective technique to treat brain tumors for
which several inverse planning methods may be appropriate. We propose an
integer programming model to simultaneous sector duration and isocenter
optimization (SDIO) problem for Leksell Gamma Knife{\textregistered}
Icon{\texttrademark} (Elekta, Stockholm, Sweden) to tractably incorporate
treatment time. We devise a Benders decomposition scheme to solve the SDIO
problem to optimality. The performances of our approaches are assessed using
anonymized data from eight previously treated cases, and obtained treatment
plans are compared against each other and against the clinical plans. The plans
generated by our SDIO model all meet or exceed clinical guidelines while
demonstrating high conformity.
