Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns
AbstractIn this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of information, and problem objective affect the optimal location patterns. In particular, we want to find analytical confirmations for location patterns observed in numerical experiments with network location models. To derive closed-form analytical results the analysis is restricted to a simple (yet classic) setting: a 2-facility problem on a unit segment, with customer demand distributed uniformly over the segment (results can be extended to other demand distributions as well). We derive explicit expressions for facility trajectories as functions of model parameters, obtaining a number of managerial insights. In addition we provide the decomposition of the optimal cost into the closed form components corresponding to the cost of travel, the cost of facility unreliability and the cost of incomplete information. Most of the theoretical insights are confirmed via numerical experiments for models with larger (3–5) number of facilities.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Omega.
Volume (Year): 41 (2013)
Issue (Month): 4 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- N. Rao Chaganty & Harry Joe, 2006. "Range of correlation matrices for dependent Bernoulli random variables," Biometrika, Biometrika Trust, Biometrika Trust, vol. 93(1), pages 197-206, March.
- Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, Elsevier, vol. 189(1), pages 76-92, August.
- Li, Xiaopeng & Ouyang, Yanfeng, 2010. "A continuum approximation approach to reliable facility location design under correlated probabilistic disruptions," Transportation Research Part B: Methodological, Elsevier, Elsevier, vol. 44(4), pages 535-548, May.
- Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, Biometrika Trust, vol. 90(2), pages 455-463, June.
- Cui, Tingting & Ouyang, Yanfeng & Shen, Zuo-Jun Max J, 2010. "Reliable Facility Location Design under the Risk of Disruptions," University of California Transportation Center, Working Papers qt5sh2c7pw, University of California Transportation Center.
- James A. Fitzsimmons, 1973. "A Methodology for Emergency Ambulance Deployment," Management Science, INFORMS, INFORMS, vol. 19(6), pages 627-636, February.
- GÃ¼den, HÃ¼seyin & SÃ¼ral, Haldun, 2014. "Locating mobile facilities in railway construction management," Omega, Elsevier, Elsevier, vol. 45(C), pages 71-79.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.