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Parliament seating assignment problems

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Abstract
Motivated by evidence that parliament seatings are relevant for decision making, we consider the problem to assign seats in a parliament to members of parliament. We prove that the resulting seating assignment problem is strongly NP-hard in several restricted settings. We present a Mixed Integer Programming formulation of the problem, we describe two families of valid inequalities and we discuss symmetry-breaking constraints. Further, we design a heuristic. Finally, we compare the outcomes of the Mixed Integer Programming formulation with the outcomes of the heuristic in a computational study.
Keywords
Information Systems and Management, Management Science and Operations Research, Modelling and Simulation, General Computer Science, Industrial and Manufacturing Engineering, Combinatorial optimization, Complexity theory, Heuristics, Valid inequalities

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Please use this url to cite or link to this publication:

MLA
Vangerven, Bart, et al. “Parliament Seating Assignment Problems.” EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, vol. 296, no. 3, 2022, pp. 914–26, doi:10.1016/j.ejor.2021.08.002.
APA
Vangerven, B., Briskorn, D., Goossens, D., & Spieksma, F. C. R. (2022). Parliament seating assignment problems. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 296(3), 914–926. https://doi.org/10.1016/j.ejor.2021.08.002
Chicago author-date
Vangerven, Bart, Dirk Briskorn, Dries Goossens, and Frits C.R. Spieksma. 2022. “Parliament Seating Assignment Problems.” EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 296 (3): 914–26. https://doi.org/10.1016/j.ejor.2021.08.002.
Chicago author-date (all authors)
Vangerven, Bart, Dirk Briskorn, Dries Goossens, and Frits C.R. Spieksma. 2022. “Parliament Seating Assignment Problems.” EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 296 (3): 914–926. doi:10.1016/j.ejor.2021.08.002.
Vancouver
1.
Vangerven B, Briskorn D, Goossens D, Spieksma FCR. Parliament seating assignment problems. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. 2022;296(3):914–26.
IEEE
[1]
B. Vangerven, D. Briskorn, D. Goossens, and F. C. R. Spieksma, “Parliament seating assignment problems,” EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, vol. 296, no. 3, pp. 914–926, 2022.
@article{8723438,
  abstract     = {{Motivated by evidence that parliament seatings are relevant for decision making, we consider the problem to assign seats in a parliament to members of parliament. We prove that the resulting seating assignment problem is strongly NP-hard in several restricted settings. We present a Mixed Integer Programming formulation of the problem, we describe two families of valid inequalities and we discuss symmetry-breaking constraints. Further, we design a heuristic. Finally, we compare the outcomes of the Mixed Integer Programming formulation with the outcomes of the heuristic in a computational study.}},
  author       = {{Vangerven, Bart and Briskorn, Dirk and Goossens, Dries and Spieksma, Frits C.R.}},
  issn         = {{0377-2217}},
  journal      = {{EUROPEAN JOURNAL OF OPERATIONAL RESEARCH}},
  keywords     = {{Information Systems and Management,Management Science and Operations Research,Modelling and Simulation,General Computer Science,Industrial and Manufacturing Engineering,Combinatorial optimization,Complexity theory,Heuristics,Valid inequalities}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{914--926}},
  title        = {{Parliament seating assignment problems}},
  url          = {{http://dx.doi.org/10.1016/j.ejor.2021.08.002}},
  volume       = {{296}},
  year         = {{2022}},
}

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