Approximation Algorithms for Problems Combining Facility Location and Network Design

We present approximation algorithms for integrated logistics problems that combine elements of facility location and transport network design. We first study the problem where opening facilities incurs opening costs and transportation from the clients to the facilities incurs buy-at-bulk costs, and provide a combinatorial approximation algorithm. We also show that the integer-programming formulation of this problem has small integrality gap. We extend the model to the version when there is a bound on the number of facilities that may be opened.

[1]  Alex Zelikovsky,et al.  Improved Steiner tree approximation in graphs , 2000, SODA '00.

[2]  Sudipto Guha,et al.  A constant-factor approximation algorithm for the k-median problem (extended abstract) , 1999, STOC '99.

[3]  David P. Williamson,et al.  A general approximation technique for constrained forest problems , 1992, SODA '92.

[4]  J. Current,et al.  THE MULTIPLE DEPOT VEHICLE ROUTING PROBLEM WITH BACKHAULING. , 1992 .

[5]  Éva Tardos,et al.  Approximation algorithms for facility location problems (extended abstract) , 1997, STOC '97.

[6]  R. Ravi,et al.  When trees collide: an approximation algorithm for the generalized Steiner problem on networks , 1991, STOC '91.

[7]  R. Ravi,et al.  Approximation Algorithms for a Capacitated Network Design Problem , 2003, Algorithmica.

[8]  Amin Saberi,et al.  A new greedy approach for facility location problems , 2002, STOC '02.

[9]  Kamesh Munagala,et al.  Local search heuristic for k-median and facility location problems , 2001, STOC '01.

[10]  Tim Roughgarden,et al.  Simpler and better approximation algorithms for network design , 2003, STOC '03.

[11]  Sudipto Guha,et al.  A constant-factor approximation algorithm for the k-median problem (extended abstract) , 1999, STOC '99.

[12]  G D Taylor,et al.  AN INTERACTIVE APPROACH TO LOCATE BREAKBULK TERMINALS FOR LTL TRUCKING OPERATIONS , 1995 .

[13]  Mohammad Mahdian,et al.  Improved Approximation Algorithms for Metric Facility Location Problems , 2002, APPROX.

[14]  R. Ravi,et al.  Approximation algorithms for a capacitated network design problem , 2000, APPROX.

[15]  Rajmohan Rajaraman,et al.  Analysis of a local search heuristic for facility location problems , 2000, SODA '98.

[16]  R. Ravi,et al.  A Primal-Dual Approximation Algorithm for the Steiner Forest Problem , 1993, Inf. Process. Lett..

[17]  Vijay V. Vazirani,et al.  Primal-dual approximation algorithms for metric facility location and k-median problems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[18]  R. Ravi,et al.  Approximating the Single-Sink Link-Installation Problem in Network Design , 2001, SIAM J. Optim..

[19]  R. Ravi,et al.  When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks , 1995, SIAM J. Comput..

[20]  Kamesh Munagala,et al.  Cost-distance: two metric network design , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[21]  David Peleg,et al.  An approximation algorithm for minimum-cost network design , 1994, Robust Communication Networks: Interconnection and Survivability.

[22]  R. Ravi,et al.  Buy-at-bulk network design: approximating the single-sink edge installation problem , 1997, SODA '97.

[23]  A. Meyerson,et al.  Improved Combinatorial Algorithms for Single Sink Edge Installation Problems. , 2000 .

[24]  George L. Nemhauser,et al.  The uncapacitated facility location problem , 1990 .

[25]  Deborah Estrin,et al.  Simultaneous Optimization for Concave Costs: Single Sink Aggregation or Single Source Buy-at-Bulk , 2003, SODA '03.