Browse > Article
http://dx.doi.org/10.7236/JIIBC.2013.13.6.211

Linear Bottleneck Assignment Problem Based on Reverse-delete Algorithm  

Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.13, no.6, 2013 , pp. 211-220 More about this Journal
Abstract
This paper proposes an algorithm that easily finds an optimal solution for linear bottleneck assignment problems. It is either threshold or augmenting path algorithm that is generally used to solve the bottleneck assignment problem. This paper proposes a reverse-delete algorithm that follows 2 steps. Firstly, the algorithm deletes the maximum cost in a given matrix until it renders a single row or column. Next, the algorithm improves any solution that contains a cost exceeding the threshold value $c^*_{ij}$. Upon its application to 28 balanced assignment problems and 7 unbalanced problems, the algorithm is found to be both successful and simple.
Keywords
Threshold value; Bottleneck; Bottleneck assignment problem; Threshold value;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 B. Rainer, M. Dell'Amico, and S. Martello, "Assignment Problems," SIAM, 2009.
2 H. W. Kuhn, "The Hungarian Method for the Assignment Problem," Naval Research Logistics Quarterly, Vol. 2, pp. 83-97, 1955.   DOI
3 L. Ntaimo, "Introduction to Mathematical Programming: Operations Research: Transportation and Assignment Problems", Vol. 1, 4th edition, 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 R. Sedgewick and K. Wayne, " Computer Science 226: Data Structures and Algorithms, Princeton University, 2002.
6 J. E. Beasley, "Operations Research and Management Science: OR-Notes," Department of Mathematical Sciences, Brunel University, West London, 2004.
7 D. Doty, "Munkres' Assignment Algorithm: Modified for Rectangular Matrices," KCVU, Murray State University, Dept. of Computer Science and Information Systems, 2008.
8 M. A. Trick, "Network Optimizations for Consultants," http://mat.gsia.cmu.edu/mstc/ networks/ networks.html, 1996.
9 Optimalon Software, "Transportation Problem (Minimal Cost)," http://www.optimalon.com/ examples/transport.htm, 2008.
10 F. D. Croce, V. T. Paschos, and A. Tsoukias, "An Improved General Procedure for Lexigraphic Bottleneck Problems," Operations Research Letters, Vol. 24, No. 4, pp. 187-194, May 1999.   DOI   ScienceOn
11 H. W. Corley and H. Golnabi, "Technical Note: A Generalized Bottleneck Assignment Problem," Journal of Optimization Theory and Applications, Vol. 36, No. 1, pp. 135-138, Jan 1982.   DOI
12 R. Burkard, M. Dell'Amico, and S. Martello, "Linear Assignment Problems, Section 6.6 Lexicographic Bottleneck Assignment Problem," pp. 198-202, SIAM, 2008.
13 R. S. Garfinkel, "An Improved Algorithm for the Bottleneck Assignment Problem," Operations Research, Vol. 19, No. 7, pp. 1747-1751, Jul 1971.   DOI   ScienceOn
14 R. E. Burkard, "Optimierung und Kontrolle: Selected Topics on Assignment Problems," Karl-Franzens-Universitat Graz & Technische Universitat Graz, 1999.
15 O. Gross, "The Bottleneck Assignment Problem," Report No. P-1620, The Rand Corporation, Santa Monica, California, 1959.
16 R. Fulkerson, I. Glickberg, and O. Gross, "A Production Line Assignment Problem," Technical Report RM-1102, The Rand Corporation, Santa Monica, California, 1953.
17 H. N. Gabow and R. E. Tarjan, "Algorithms for two Bottleneck Optimization Problems," Journal of Algorithms, Vol. 9, No. 3, pp. 411-417, Sep 1988.   DOI
18 Sang-Un Lee, "The Simplified Solution for Assignment Problem," Journal of the Institute of Internet, Broadcasting and Communication, Vol. 12, No. 5, pp. 141-151, 2012.   과학기술학회마을   DOI   ScienceOn
19 D. N. Kumar, "Optimization Methods," IISc, Bangalore, 2008.
20 Sang-Un Lee, "The Assignment Problem Algorithm Based on the First Selection Method of the Minimum Cost," Journal of the Institute of Internet, Broadcasting and Communication, Vol. 13, No. 5, pp. 163-171, 2013.   과학기술학회마을   DOI   ScienceOn
21 Rai Foundation Colleges, "Information Research," Bachelor of Business Administration, Business Administration, 2008.
22 S. Noble, "Lectures 15: The Assignment Problem," Department of Mathematical Sciences, Brunel University, 2000.
23 R. M. Berka, "A Tutorial on Network Optimization," http://home.eunet.cz/berka/o/English/networks/node8.html, 1997.
24 M. S. Radhakrishnan, "AAOC C222: Optimization," Birla Institute of Technology & Science, 2006.
25 R. Burkard, M. D. Amico, and S. Martello, "Assignment Problems," SIAM Monographs on Discrete Mathematics and Applications, 2006.
26 S. C. Niu, "Introduction to Operations Research," School of Management, The University of Texas at Dallas, 2004.
27 W. Snyder, "The Linear Assignment Problem," Department of Electrical and Computer Engineering, North Carolina State University, 2005.
28 K. Wayne, "Algorithm Design," http://www.cs.princeton.edu/-wayne/kleinberg-tardos/07assignment.pdf, 2005.
29 J. Havlicek, "Introduction to Management Science and Operation Research," http://orms.czu.cz/text/transproblem.html, 2007.
30 E. S. Page, "A Note on Assignment Problems," The Computer Journal, Vol. 6, No. 3, pp. 241-243, 1963.   DOI
31 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.
32 U. Derigs, "Alternate Strategies for Solving Bottleneck Assignment Problems-Analysis and Computational Results," Computing, Vol. 33, No. 2, pp. 95-106, Feb 1984.   DOI
33 U. Pfershy, "The Random Linear Bottleneck Assignment Problem," RAIRO Operations Research, Vol. 30, No. 2, pp. 127-142, Feb 1996.   DOI
34 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, Jan 2005.   DOI