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Random assignment problems

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  • Krokhmal, Pavlo A.
  • Pardalos, Panos M.

Abstract

Analysis of random instances of optimization problems provides valuable insights into the behavior and properties of problem's solutions, feasible region, and optimal values, especially in large-scale cases. A class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems, and many important problems in operations research and computer science can be formulated as assignment problems. This paper presents an overview of the recent results and developments in the area of probabilistic assignment problems, including the linear and multidimensional assignment problems, quadratic assignment problem, etc.

Suggested Citation

  • Krokhmal, Pavlo A. & Pardalos, Panos M., 2009. "Random assignment problems," European Journal of Operational Research, Elsevier, vol. 194(1), pages 1-17, April.
    • Handle: RePEc:eee:ejores:v:194:y:2009:i:1:p:1-17
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    References listed on IDEAS

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    1. Renata M. Aiex & Mauricio G. C. Resende & Panos M. Pardalos & Gerardo Toraldo, 2005. "GRASP with Path Relinking for Three-Index Assignment," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 224-247, May.
    2. Burkard, Rainer E., 1984. "Quadratic assignment problems," European Journal of Operational Research, Elsevier, vol. 15(3), pages 283-289, March.
    3. Egon Balas & Matthew J. Saltzman, 1991. "An Algorithm for the Three-Index Assignment Problem," Operations Research, INFORMS, vol. 39(1), pages 150-161, February.
    4. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    5. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    6. Mavridou, T. & Pardalos, P.M. & Pitsoulis, L.S. & Resende, Mauricio G.C., 1998. "A GRASP for the biquadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 105(3), pages 613-621, March.
    7. Bonomi, Ernesto & Lutton, Jean-Luc, 1986. "The asymptotic behaviour of quadratic sum assignment problems: A statistical mechanics approach," European Journal of Operational Research, Elsevier, vol. 26(2), pages 295-300, August.
    8. Terry Jones & Stephanie Forrest, 1995. "Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms," Working Papers 95-02-022, Santa Fe Institute.
    9. Burkard, Rainer E. & Cela, Eranda & Woeginger, Gerhard J., 1995. "A minimax assignment problem in treelike communication networks," European Journal of Operational Research, Elsevier, vol. 87(3), pages 670-684, December.
    10. Richard M. Karp & Alexander H. G. Rinnooy Kan & Rakesh V. Vohra, 1994. "Average Case Analysis of a Heuristic for the Assignment Problem," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 513-522, August.
    11. J. B. G. Frenk & M. van Houweninge & A. H. G. Rinnooy Kan, 1985. "Asymptotic Properties of the Quadratic Assignment Problem," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 100-116, February.
    12. Thomas E. Vollmann & Elwood S. Buffa, 1966. "The Facilities Layout Problem in Perspective," Management Science, INFORMS, vol. 12(10), pages 450-468, June.
    13. Wansoo T. Rhee, 1991. "Stochastic Analysis of the Quadratic Assignment Problem," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 223-239, May.
    14. D. A. Grundel & C. A. S. Oliveira & P. M. Pardalos, 2004. "Asymptotic Properties of Random Multidimensional Assignment Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 487-500, September.
    15. Burkard, R. E. & Karisch, S. & Rendl, F., 1991. "QAPLIB-A quadratic assignment problem library," European Journal of Operational Research, Elsevier, vol. 55(1), pages 115-119, November.
    16. Frenk, J.B.G. & van Houweninge, M. & Rinnooy Kan, A.H.G., 1987. "Order statistics and the linear assignment problem," Econometric Institute Research Papers 11690, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Burkard, Rainer E. & Cela, Eranda, 1995. "Heuristics for biquadratic assignment problems and their computational comparison," European Journal of Operational Research, Elsevier, vol. 83(2), pages 283-300, June.
    18. Don A. Grundel & Pavlo A. Krokhmal & Carlos A. S. Oliveira & Panos M. Pardalos, 2007. "On the number of local minima for the multidimensional assignment problem," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 1-18, January.
    19. Carraresi, P. & Gallo, G., 1984. "A multi-level bottleneck assignment approach to the bus drivers' rostering problem," European Journal of Operational Research, Elsevier, vol. 16(2), pages 163-173, May.
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    3. Panayotis Mertikopoulos & Heinrich H. Nax & Bary S. R. Pradelski, 2019. "Quick or Cheap? Breaking Points in Dynamic Markets," Cowles Foundation Discussion Papers 2217, Cowles Foundation for Research in Economics, Yale University.
    4. Helena Gaspars-Wieloch, 2021. "The Assignment Problem in Human Resource Project Management under Uncertainty," Risks, MDPI, vol. 9(1), pages 1-17, January.
    5. Kammerdiner, A.R. & Pasiliao, E.L., 2014. "In and out forests on combinatorial landscapes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 78-84.
    6. Ortega, Josue & Klein, Thilo, 2022. "Improving efficiency and equality in school choice," ZEW Discussion Papers 22-046, ZEW - Leibniz Centre for European Economic Research.
    7. Panayotis Mertikopoulos & Heinrich H. Nax & Bary S. R. Pradelski, 2019. "Quick or cheap? Breaking points in dynamic markets," ECON - Working Papers 338, Department of Economics - University of Zurich.
    8. Mădălina M. Drugan, 2015. "Generating QAP instances with known optimum solution and additively decomposable cost function," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1138-1172, November.
    9. Li, Xiaobo & Natarajan, Karthik & Teo, Chung-Piaw & Zheng, Zhichao, 2014. "Distributionally robust mixed integer linear programs: Persistency models with applications," European Journal of Operational Research, Elsevier, vol. 233(3), pages 459-473.
    10. Chrétien, Stéphane & Corset, Franck, 2016. "A lower bound on the expected optimal value of certain random linear programs and application to shortest paths in Directed Acyclic Graphs and reliability," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 221-230.
    11. Mordant, Gilles & Segers, Johan, 2021. "Maxima and near-maxima of a Gaussian random assignment field," Statistics & Probability Letters, Elsevier, vol. 173(C).
    12. Sana Bouajaja & Najoua Dridi, 2017. "A survey on human resource allocation problem and its applications," Operational Research, Springer, vol. 17(2), pages 339-369, July.
    13. Mordant, Gilles & Segers, Johan, 2021. "Maxima and near-maxima of a Gaussian random assignment field," LIDAM Discussion Papers ISBA 2021008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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