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An Assignment Problem Algorithm Using Minimum Cost Moving Method

  • Lee, Sang-Un (Dept. of Multimedia Engineering, Gangneung-Wonju National University)
  • 투고 : 2015.05.19
  • 심사 : 2015.06.19
  • 발행 : 2015.08.31

초록

Generally, the optimal solution of assignment problem has been obtained by Hungarian algorithm with O($n^3$) time complexity. This paper proposes more simple algorithm with O($n^2$) time complexity than Hungarian algorithm. The proposed algorithm simply selects minimum cost in each row, and classified into set S, H, and T. Then, the minimum cost is moved from S to T and $S{\rightarrow}H$, $H{\rightarrow}T$. The proposed algorithm can be obtain the same optimal solution as well-known algorithms and improve the optimal solution of partial unbalanced assignment problems.

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참고문헌

  1. R. Burkard, M. Dell'Amico, and S. Martello, "Assignment Problems," SIAM., ISBN: 978-1-61197-222-1, 2012.
  2. H. W. Kuhn, "The Hungarian Method for the Assignment Problem," Naval Research Logistics Quarterly, Vol. 2, No. 1-2, pp. 83-97, Mar. 1955. https://doi.org/10.1002/nav.3800020109
  3. L. Ntaimo, "Introduction to Mathematical Programming: Operations Research: Transportation and Assignment Problems", Vol. 1, 4th edition, by W. L. Winston and M. Venkataramanan, 2005.
  4. K. Kinahan and J. Pryor, "Algorithm Animations for Practical Optimization: A Gentle Introduction," http://optlab-server.sce.carleton.ca/POAnimations2007/Default.html, 2007.
  5. D. N. Kumar, "Optimization Methods," http://www.nptel.iitm.ac.in/Courses/Webcourse-contents/IISc-BANG/OPTIMIZATIONMETHODS/pdf/Module_4/M4L3_LN.pdf, IISc, Bangalore, 2008.
  6. S. U. Lee, "Assignment Problem Algorithm Based on the First Selection Method of the Minimum Cost," Journal of the IIBC, Vol. 13, No. 5, pp. 163-171, Oct. 2013.
  7. S. U. Lee, "A Reverse-delete Algorithm for Assignment Problem," Journal of the KIIT, Vol. 10, No. 8, pp. 117-126, Aug. 2012.
  8. S. U. Lee, "The Optimal Algorithm for Assignment Problem," Journal of the KSCI, Vol. 17, No. 9, pp. 139-147, Sep. 2012.
  9. S. U. Lee, "The Simplified Solution for Assignment Problem," Journal of the IIBC, Vol. 12, No. 5, pp. 141-151, Oct. 2012.
  10. Rai Foundation Colleges, "Information Research," Bachelor of Business Administration, Business Administration, 2008.
  11. S. Noble, "Lectures 15: The Assignment Problem," Department of Mathematical Sciences, Brunel University, 2000.
  12. A. Dimitrios, P. Konstantinos, S. Nikolaos, and S. Angelo, "Applications of a New Network-enabled Solver for the Assignment Problem in Computer-aided Education," Journal of Computer Science, Vol. 1, No. 1, pp. 19-23, 2005. https://doi.org/10.3844/jcssp.2005.19.23
  13. R. M. Berka, "A Tutorial on Network Optimization," http://home.eunet.cz/berka/o/English/networks/node8.html, 1997.
  14. M. S. Radhakrishnan, "AAOC C222: Optimization," Birla Institute of Technology & Science, 2006.
  15. R. Burkard, M. D. Amico, and S. Martello, "Assignment Problems, SIAM Monographs on Discrete Mathematics and Applications, 2006.
  16. S. C. Niu, "Introduction to Operations Research," School of Management, The University of Texas at Dallas, 2004.
  17. W. Snyder, "The Linear Assignment Problem," Department of Electrical and Computer Engineering, North Carolina State University, 2005.
  18. M. E. Salassi, "AGEC 7123: Operations Research Methods in Agricultural Economics: Standard LP Form of the Generalized Assignment Problem," Department of Agricultural Economics and Agribusiness, Louisiana State University, 2005.
  19. K. Wayne, "Algorithm Design," http://www.cs.princeton.edu/-wayne/kleinberg-tardos/07assignment.pdf, 2005.
  20. J. Havlicek, "Introduction to Management Science and Operation Research," http://orms.czu.cz/text/transproblem.html, 2007.
  21. R. Sedgewick and K. Wayne, " Computer Science 226: Data Structures and Algorithms, Princeton University, 2002.
  22. J. E. Beasley, "Operations Research and Management Science: OR-Notes," Department of Mathematical Sciences, Brunel University, West London, 2004.
  23. D. Doty, "Munkres' Assignment Algorithm: Modified for Rectangular Matrices," KCVU, Murray State University, Dept. of Computer Science and Information Systems, 2008.
  24. G. B. Dantzig, "Linear Programming and Extensions," USAF Project RAND, R-366-PR, The RAND Corporation, Santa Monica, California, U.S., 1963.
  25. Optimalon Software, "Transportation Problem (Minimal Cost)," http://www.optimalon.com/examples/transport.htm, 2008.