@article {1441,
	title = {Exact solution algorithms for the maximum flow problem with additional conflict constraints},
	journal = {European Journal of Operational Research},
	volume = {287},
	year = {2020},
	pages = {410-437},
	abstract = {<p>We consider a variant of the maximum flow problem on a given directed graph where some arc pairs are incompatible or conflicting; in other words, they are not allowed to carry positive flow simultaneously. This problem, called the maximum flow problem with conflicts, is known to be strongly NP-hard. In this paper, we present mixed-integer linear programming formulations for the problem and develop exact solution methods based on Benders decomposition, branch-and-bound, and Russian Doll Search over the conflict graph which represents the conflict relations. The effectiveness of the proposed algorithms is tested on a large number of randomly generated instances. The results reveal that their performances are superior to solving the mixed-integer linear programming formulations with a commercial software.</p>},
	keywords = {Benders decomposition, Branch-and-bound, Combinatorial optimization, Conflict, Maximum flow, Russian doll search},
	issn = {0377-2217},
	doi = {https://doi.org/10.1016/j.ejor.2020.04.001},
	url = {https://www.sciencedirect.com/science/article/pii/S0377221720303192},
	author = {Zeynep {\c S}uvak and I. Kuban Altinel and Necati Aras}
}
@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}
}
