Approximating soft-capacitated facility location problem with uncertainty

In this paper we devise the stochastic and robust approaches to study the soft-capacitated facility location problem with uncertainty. We first present a new stochastic soft-capacitated model called The 2-Stage Soft Capacitated Facility Location Problem and solve it via an approximation algorithm by reducing it to linear-cost version of 2-stage facility location problem and dynamic facility location problem. We then present a novel robust model of soft-capacitated facility location, The Robust Soft Capacitated Facility Location Problem. To solve it, we improve the approximation algorithm proposed by Byrka et al. (LP-rounding algorithms for facility-location problems. CoRR, 2010a) for RFTFL and then treat it similarly as in the stochastic case. The improvement results in an approximation factor of $$\alpha + 4$$ for the robust fault-tolerant facility location problem, which is best so far.

[1]  Chaitanya Swamy,et al.  Sampling-based approximation algorithms for multi-stage stochastic optimization , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[2]  M. Salavatipour,et al.  Approximation algorithms for clustering problems , 2012 .

[3]  David P. Williamson,et al.  Improved approximation algorithms for capacitated facility location problems , 1999, IPCO.

[4]  Aravind Srinivasan,et al.  LP-rounding algorithms for facility-location problems , 2010, ArXiv.

[5]  Yu Li,et al.  Improved Approximation Algorithms for the Facility Location Problems with Linear/submodular Penalty , 2013, COCOON.

[6]  Aravind Srinivasan,et al.  Fault-Tolerant Facility Location: A Randomized Dependent LP-Rounding Algorithm , 2010, IPCO.

[7]  Yinyu Ye,et al.  A Multiexchange Local Search Algorithm for the Capacitated Facility Location Problem , 2005, Math. Oper. Res..

[8]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[9]  Maxim Sviridenko.  An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem , 2002, IPCO.

[10]  Mohammad R. Salavatipour,et al.  New Approximation Algorithms for the Unsplittable Capacitated Facility Location Problem , 2015, Algorithmica.

[11]  Tony J. Van Roy,et al.  A Dual-Based Procedure for Dynamic Facility Location , 1982 .

[12]  Lawrence V. Snyder,et al.  Facility location under uncertainty: a review , 2006 .

[13]  Aravind Srinivasan,et al.  Approximation algorithms for stochastic and risk-averse optimization , 2007, SODA '07.

[14]  Fabián A. Chudak,et al.  Improved Approximation Algorithms for the Uncapacitated Facility Location Problem , 2003, SIAM J. Comput..

[15]  Yu Li,et al.  Improved approximation algorithms for the robust fault-tolerant facility location problem , 2012, Inf. Process. Lett..

[16]  Mohammad Mahdian,et al.  Approximation Algorithms for Metric Facility Location Problems , 2006, SIAM J. Comput..

[17]  Fabián A. Chudak,et al.  Improved approximation algorithms for a capacitated facility location problem , 1999, SODA '99.

[18]  David Peleg,et al.  Robust Fault Tolerant uncapacitated facility location , 2010, STACS.

[19]  Jiawei Zhang,et al.  An Approximation Algorithm for the Dynamic Facility Location Problem , 2006 .

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

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

[22]  Mohammad Mahdian,et al.  A 2-Approximation Algorithm for the Soft-Capacitated Facility Location Problem , 2003, RANDOM-APPROX.