Browse > Article
http://dx.doi.org/10.7737/JKORMS.2014.39.1.013

A New Mixed-Integer Programming Modeling for the Steiner Ring Star Problem  

Yuh, Junsang (Division of Industrial Management Engineering, Korea University)
Lee, Youngho (Division of Industrial Management Engineering, Korea University)
Park, Gigyoung (Division of Industrial Management Engineering, Korea University)
Publication Information
Journal of the Korean Operations Research and Management Science Society / v.39, no.1, 2014 , pp. 13-27 More about this Journal
Abstract
In this paper, we deal with a Steiner Ring Star (SRS) problem arising from the design of survivable telecommunication networks. We develop two mixed integer programming formulations for the SRS problem by implementing Miller-Tucker-Zemlin (MTZ) and Sarin-Sherali-Bhootra (SSB) subtour elimination constraints, and then apply the reformulation-linearization technique (RLT) to enhance the lower bound obtained by the LP relaxation. By exploiting the ring-star structure of underlying network, we devise some valid inequalities that tighten the LP relaxation. Computational results demonstrate the effectiveness of the proposed solution procedure.
Keywords
Steiner Ring Star Problem; Mixed Integer Programming; Reformulation-Linearization Technique;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Lee, Y., S.Y. Chiu, and J. Ryan, "A Branch and Cut Algorithm for a Steiner Tree-Star Problem," INFORMS Journal on Computing, Vol.8(1996), pp.194-201.   DOI   ScienceOn
2 Lee, Y., S.Y. Chiu, and J. Sanchez, "A Branch and Cut Algorithm for the Steiner Ring Star Problem," International Journal of Management Science, Vol.4(1998), pp.21-34.
3 Myung, Y., "A Comparison of Group Steiner Tree Formulations," Journal of the Korean Institute of Industrial Engineers, Vol.37 (2011), pp.191-197.   과학기술학회마을   DOI   ScienceOn
4 Sarin, S.C., H.D. Sherali, and A. Bhootra, "New Tighter Polynomial Length Formulations for the Asymmetric Traveling Salesman Problem with and without Precedence Constraints," Operations Research Letters, Vol.33, No.1(2005), pp.62-70.   DOI   ScienceOn
5 Sherali, H.D., W.P. Adams, and P.J. Driscroll, "Exploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problem," Operations Research, Vol.46(1998), pp.396-405.   DOI   ScienceOn
6 Sherali, H.D. and P.J. Driscroll, "On Tightening the Relaxations of Miller-Tucker-Zemlin Formulations for Asymmetric Traveling Salesman Problems," Operations Research, Vol.50, No.4(2002), pp.656-669.   DOI   ScienceOn
7 Simonetti, L., Y. Frota, and C.C. de Souza, "The Ring-Star Problem : A New Integer Programming Formulation and a Branchand-Cut Algorithm," Discrete Applied Mathematics, Vol.159, No.16(2011), pp.1901-1914.   DOI   ScienceOn
8 Labbe, M., G. Laporte, I.R. Martin, and J.J.S. Gonzalez, "The Ring Star Problem : Polyhedral Analysis and Exact Algorithm," Networks, Vol.43(2004), pp.177-189.   DOI   ScienceOn
9 Sherali, H.D., S.C. Sarin, and P.-F. Tsai, "A Class of Lifted Path and Flow-Based Formulations for the Asymmetric Traveling Salesman Problem with and without Precedence Constraints," Discrete Optimization, Vol.6(2006), pp.20-32.