The p-hub center allocation problem

Abstract The p-hub center problem is to locate p hubs and to allocate non-hub nodes to hub nodes such that the maximum travel time (or distance) between any origin–destination pair is minimized. We address the p-hub center allocation problem, a subproblem of the location problem, where hub locations are given. We present complexity results and IP formulations for several versions of the problem. We establish that some special cases are polynomially solvable.

[1]  Morton E. O'Kelly,et al.  The Location of Interacting Hub Facilities , 1986, Transp. Sci..

[2]  Anthony V. Fiacco,et al.  Mathematical programming study 21 , 1985, Mathematical programming.

[3]  Michael J. Todd,et al.  Polynomial Algorithms for Linear Programming , 1988 .

[4]  Andreas T. Ernst,et al.  Solution algorithms for the capacitated single allocation hub location problem , 1999, Ann. Oper. Res..

[5]  Sue Abdinnour-Helm,et al.  A hybrid heuristic for the uncapacitated hub location problem , 1998, Eur. J. Oper. Res..

[6]  Zvi Drezner,et al.  Facility location - applications and theory , 2001 .

[7]  Bahar Yetis Kara,et al.  The Latest Arrival Hub Location Problem , 2001, Manag. Sci..

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  D. Skorin-Kapov,et al.  Tight linear programming relaxations of uncapacitated p-hub median problems , 1996 .

[10]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[11]  Andreas T. Ernst,et al.  The capacitated multiple allocation hub location problem: Formulations and algorithms , 2000, Eur. J. Oper. Res..

[12]  P. Gács,et al.  Khachian's Algorithm for Linear Programming. , 1979 .

[13]  Ananth V. Iyer,et al.  Accumulation Point Location on Tree Networks for Guaranteed Time Distribution , 1990 .

[14]  Andreas T. Ernst,et al.  Efficient algorithms for the uncapac-itated single allocation p-hub median problem , 1996 .

[15]  Bahar Yetis Kara,et al.  On the single-assignment p-hub center problem , 2000, Eur. J. Oper. Res..

[16]  L. Khachiyan.  Polynomial algorithms in linear programming , 1980 .

[17]  J. C. Smith,et al.  Algorithms for solving the conditional covering problem on paths , 2005 .

[18]  Timothy J. Lowe,et al.  The generalized P-forest problem on a tree network , 1992, Networks.

[19]  T. Aykin.  Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem , 1994 .

[20]  J. G. Klincewicz,et al.  A dual algorithm for the uncapacitated hub location problem , 1996 .

[21]  Sungsoo Park,et al.  Efficient solution procedure and reduced size formulations for p-hub location problems , 1998, Eur. J. Oper. Res..

[22]  T. Aykin.  On “a quadratic integer program for the location of interacting hub facilities” , 1990 .

[23]  H. Miller,et al.  Solution strategies for the single facility minimax hub location problem , 1991 .

[24]  James F. Campbell,et al.  Integer programming formulations of discrete hub location problems , 1994 .

[25]  Gerhard J. Woeginger,et al.  Uncapacitated single and multiple allocation p-hub center problems , 2009, Comput. Oper. Res..