In this paper, we solve a combinatorial optimization problem that arises from the treatment planning of a type of radiotherapy where intensity is modulated by multileaf collimators in a step-and-shoot manner. In Ernst et al. [INFORMS Journal on Computing 21:4 (2009) 562–574], we proposed an exact method for minimizing the number of multileaf collimator apertures needed for a treatment. Our meth...