@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 {1439,
	title = {Assignment problem with conflicts},
	journal = {Computers \& Operations Research},
	volume = {111},
	year = {2019},
	pages = {214-229},
	abstract = {<p>We focus on an extension of the assignment problem with additional conflict (pair) constraints in conjunction with the assignment constraints and binary restrictions. Given a bipartite graph with a cost associated with each edge and a conflict set of edge pairs, the assignment problem with conflict constraints corresponds to finding a minimum weight perfect matching without any conflicting edge pair. For example, some chemicals cannot be processed on close processors, food and toxic products cannot be stored neighboring locations at the same storage area, and machines cannot be sent to process jobs without satisfying some spatial constraints. Unlike the well-known assignment problem, this problem is NP-hard. We first introduce a realistic special class and demonstrate its polynomial solvability. Then, we propose a Branch-and-Bound algorithm and a Russian Doll Search algorithm using the assignment problem relaxations for lower bound computations, and introduce combinatorial branching rules based on the conflicting edges in an optimal solution of the relaxations. According to the extensive computational experiments we can say that the proposed algorithms are very efficient.</p>},
	keywords = {Assignment problem, Branch-and-bound, Conflicts, integer programming},
	issn = {0305-0548},
	doi = {https://doi.org/10.1016/j.cor.2019.07.001},
	url = {https://www.sciencedirect.com/science/article/pii/S0305054819301777},
	author = {Temel {\"O}ncan and Zeynep {\c S}uvak and M. Hakan Aky{\"u}z and I. Kuban Altinel}
}
