@article {1432,
	title = {The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)},
	journal = {European Journal of Operational Research},
	volume = {272},
	year = {2019},
	pages = {372-388},
	abstract = {<p>The success of radiation therapy depends on the ability to deliver the proper amount of radiation to cancerous cells while protecting healthy tissues. As a natural consequence, any new treatment technology improves quality standards concerning primarily this issue. Similar to the widely used Intensity Modulated Radiation Therapy (IMRT), the radiation resource is outside of the patient{\textquoteright}s body and the beam is shaped by a multi-leaf collimator mounted on the linear accelerator{\textquoteright}s head during the state-of-the-art Volumetric Modulated Arc Therapy (VMAT) as well. However, unlike IMRT, the gantry of the accelerator may rotate along one or more arcs and deliver radiation continuously. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution; but the apertures are interdependent and optimal treatment planning problem cannot be decomposed into simpler independent subproblems as a consequence. In this work, we consider optimal treatment planning problem for VMAT. First, we formulate a mixed-integer linear program minimizing total radiation dose intensity subject to clinical requirements embedded within the constraints. Then, we develop efficient solution procedures combining Benders decomposition with certain acceleration strategies. We investigate their performance on a large set of test instances obtained from an anonymous real prostate cancer data.</p>},
	keywords = {algorithms, Benders decomposition, integer programming, Radiation therapy, VMAT},
	issn = {0377-2217},
	doi = {https://doi.org/10.1016/j.ejor.2018.06.023},
	url = {https://www.sciencedirect.com/science/article/pii/S0377221718305514},
	author = {P{\i}nar Dursun and Z C Ta{\c s}k{\i}n and I. Kuban Altinel}
}
@article {Hoermann;Derflinger:1993a,
	title = {A Portable Random Number Generator Well Suited for the Rejection Method},
	volume = {19},
	number = {4},
	year = {1993},
	pages = {489{\textendash}495},
	abstract = {<p>Up to now, all known efficient portable implementations of linear congruential random number generators with modulus $2^{31} - 1$ have worked only with multipliers that are small compared with the modulus. We show that for nonuniform distributions, the rejection method may generate random numbers of bad qualify if combined with a linear congruential generator with small multiplier. A method is described that works for any multiplier smaller than $2^{30}$. It uses the decomposition of multiplier and seed in high-order and low-order bits to compute the upper and lower half of the product. The sum of the two halves gives the product of multiplier and seed modulo $2^{21} - 1$. Coded in ANSI-C and FORTRAN77 the method results in a portable implementation of the linear congruential generator that is as fast or faster than other portable methods.</p>},
	keywords = {algorithms, linear congruential generator, portability, quality of nonuniform random numbers, rejection method, uniform random number generator},
	author = {Wolfgang H{\"o}rmann and Derflinger, Gerhard}
}
