The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms

We study a reliable facility location problem wherein some facilities are subject to failure from time to time. If a facility fails, customers originally assigned to it have to be reassigned to other (operational) facilities. We formulate this problem as a two-stage stochastic program and then as a nonlinear integer program. Several heuristics that can produce near-optimal solutions are proposed for this NP-hard problem. For the special case where the probability that a facility fails is a constant (independent of the facility), we provide an approximation algorithm with a worst-case bound of 4. The effectiveness of our heuristics is tested by extensive computational studies, which also lead to some managerial insights.

[1]  Mark S. Daskin,et al.  Planning for Disruptions in Supply Chain Networks , 2006 .

[2]  Lawrence V. Snyder,et al.  Reliability Models for Facility Location: The Expected Failure Cost Case , 2005, Transp. Sci..

[3]  Oded Berman,et al.  Facility Reliability Issues in Network p-Median Problems: Strategic Centralization and Co-Location Effects , 2007, Oper. Res..

[4]  Zuo-Jun Max Shen,et al.  A profit-maximizing supply chain network design model with demand choice flexibility , 2006, Oper. Res. Lett..

[5]  Yanfeng Ouyang,et al.  Reliable Facility Location Design Under the Risk of Disruptions , 2010, Oper. Res..

[6]  David B. Shmoys,et al.  Approximation algorithms for facility location problems , 2000, APPROX.

[7]  Jan-Kees C. W. van Ommeren,et al.  An approximation algorithm for a facility location problem with stochastic demands and inventories , 2006, Oper. Res. Lett..

[8]  Xiangtong Qi,et al.  A logistics scheduling model: scheduling and transshipment for two processing centers , 2006 .

[9]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

[10]  Richard L. Church,et al.  A bilevel mixed-integer program for critical infrastructure protection planning , 2008, Comput. Oper. Res..

[11]  Sudipto Guha,et al.  A constant factor approximation algorithm for the fault-tolerant facility location problem , 2003, J. Algorithms.

[12]  James E. Ward,et al.  The Stochastic Location-Assignment Problem on a Tree , 2005, Ann. Oper. Res..

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

[14]  Evangelos Markakis,et al.  Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP , 2002, JACM.

[15]  Jiawei Zhang,et al.  Approximation algorithms for facility location problems , 2004 .

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

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

[18]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[19]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[20]  Chaitanya Swamy,et al.  Approximation algorithms for 2-stage stochastic optimization problems , 2006, SIGA.

[21]  Jaroslaw Byrka.  An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem , 2007, APPROX-RANDOM.

[22]  Mark S. Daskin,et al.  α-reliable p-minimax regret: a new model for strategic facility location modeling , 1997 .

[23]  ZhangJiawei,et al.  The Reliable Facility Location Problem , 2011 .

[24]  Mark S. Daskin,et al.  Strategic facility location: A review , 1998, Eur. J. Oper. Res..

[25]  Marc Goetschalckx,et al.  A stochastic programming approach for supply chain network design under uncertainty , 2004, Eur. J. Oper. Res..

[26]  P. França,et al.  Solving Stochastic Transportation-Location Problems by Generalized Benders Decomposition , 1982 .

[27]  Alexander Shapiro,et al.  The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study , 2003, Comput. Optim. Appl..

[28]  Chaitanya Swamy,et al.  Fault-tolerant facility location , 2003, SODA '03.