The capacitated-facilities location problem (CFLP) deals with opening facilities with a finite capacity to serve a set of customers. This paper addresses the discrete CFLP when the opened facilities are unreliable, i.e. they are unavailable to provide service to customers. Such problems have gained prominence in the recent past owing to their application in the area of supply-chain disruptions. A stochastic programming formulation for the CFLP with unreliable facilities is presented and the benefit of investing in redundant facility locations is demonstrated. A sampling-based algorithm called the sample average approximation algorithm is used to approximately solve this model and present computational results.
CurrentJ.DaskinM. SSchillingDDreznerZHamacherH. W‘Discrete network location’Facility location: applications and theory (Berlin: Springer2004): pp. 82–84
2.
SheffiY.The resilient enterprise: Overcoming vulnerability for competetive advantage (Cambridge, Massachusetts: MIT Press2005): pp. 61–69
3.
AkincU.KhumawalaB. M‘An efficient branch and bound algorithm for the capacitated warehouse location problem’Mgmt Sci.23 (6) (1977): 585–594
DavisP.RayT. A‘A branch-and-bound algorithm for the capacitated facilities location problem’Naval Res. Log. Quart.16 (3) (1969): 331–344
6.
GuignardM.SpielbergK‘A direct dual method for the mixed plant location problem with some side constraints’Math. Prog.17 (1) (1979): 198–228
7.
SnyderL. VScaparraM. PDaskinM. SChurchR. CGreenbergH‘Planning for disruptions in supply chain networks’Tutorials in operations research (Baltimore, Maryland: INFORMS2006): pp. 234–257
8.
SnyderL. VDaskinM. S‘Reliability models for facility location: the expected failure cost case’Transport Sci.39 (3) (2005): 400–416
9.
CoulbournC. JThe combinatorics of network reliability (New York: Oxford University Press1987)
10.
EiseltH.GendreauMLaporteG‘Optimal location of facilities on a network with an unreliable node or link’Inform. Process. Lett.58 (2) (1996): 71–74
11.
ChurchR.WeaverJ‘A median location model with non-closest facility service’Transport Sci.19 (1) (1985): 58–74
DaskinM. S‘Application of an expected covering model to emergency medical service system design’Decis. Sci.13 (3) (1982): 416–439
14.
VidalC. JGoetschalckxM‘Modeling the effect of uncertainties in global supply logisitcs systems’J. Bus. Logist.21 (1) (2000): 95–121
15.
GaonkarR.VishwanadhamN‘A conceptual and analytical framework for the management of risk in supply chains’Proc. IEEE Conf. Robotics & Automation (2004): pp. 2669–2704
16.
BallM. OLinF. L‘A reliability model applied to emergency vehicle location’Oper. Res.41 (1) (1993): 18–36
BirgeJ. RLouveauxFIntroduction to stochastic programming (New York: Springer1997)
23.
CornuejolsG.NemhauserGWolseyLMirhcandaniP. BFrancisR. L‘The uncapacitated facility location problem’Discrete location theory (New York: Wiley1990): pp. 119–171
24.
KleywegtA.ShapiroA‘The sample average approximation method for stochasitc programming with recourse’SIAM J. Optim.24 (2) (2002): 479–502
25.
ShapiroA.‘A simulation-based approach to two-stage stochastic programming with recourse’Math. Prog.81 (3) (1998): 301–325
26.
SantosoT.AhmedSGoetschalckxMShapiroA‘A stochastic programming approach for supply chain network design under uncertainty’Eur. J. Oper. Res.167 (1) (2005): 96–115
27.
VerweijB.AhmedSKleywegtA. JNemhauserGShapiroA‘The sample average approximation method applied to stochastic routing problems: a computational study’Comput. Option. Applic.24 (2) (2003): 289–333
28.
MakW. KMortonDWoodK. R‘Monte Carlo bounding techniques for determining solution quality in stochastic programs’Oper. Res. Lett.24 (1) (1999): 47–56
29.
ILOG, ILOG CPLEX 10.0. users manual (2006)
30.
GadeD.Capacitated facilities location problems with unreliable facilities (2007) Master's Thesis.
31.
KeltonW. DLawA. MSimulation modeling and analysis (New York: McGraw Hill2006)
32.
LaporteG.LouveauxF. V‘The integer L-shaped method for stochastic integer programs with complete recourse’Oper. Res. Lett.23 (3) (1993): 133–142
