We propose a parallel algorithm for computing exact solutions to the problem of minimizing the number of multileaf collimator apertures needed in step-and-shoot intensity modulated radiotherapy. These problems are very challenging particularly as the problem size increases. Here, we investigate...

In this paper, we introduce five classes of new valid cutting planes for the precedence-constrained (PC) and/or time-window-constrained (TW) Asymmetric Travelling Salesman Problems (ATSPs) and directed Vehicle Routing Problems (VRPs). We show that all five classes of new inequalities are...