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Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns

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  • Berman, Oded
  • Krass, Dmitry
  • Menezes, Mozart B.C.

Abstract

In 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.

Suggested Citation

  • Berman, Oded & Krass, Dmitry & Menezes, Mozart B.C., 2013. "Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns," Omega, Elsevier, vol. 41(4), pages 766-779.
  • Handle: RePEc:eee:jomega:v:41:y:2013:i:4:p:766-779
    DOI: 10.1016/j.omega.2012.09.002
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    References listed on IDEAS

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    1. N. Rao Chaganty & Harry Joe, 2006. "Range of correlation matrices for dependent Bernoulli random variables," Biometrika, Biometrika Trust, vol. 93(1), pages 197-206, March.
    2. Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
    3. 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.
    4. Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 189(1), pages 76-92, August.
    5. Li, Xiaopeng & Ouyang, Yanfeng, 2010. "A continuum approximation approach to reliable facility location design under correlated probabilistic disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 535-548, May.
    6. James A. Fitzsimmons, 1973. "A Methodology for Emergency Ambulance Deployment," Management Science, INFORMS, vol. 19(6), pages 627-636, February.
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    Cited by:

    1. Akgün, İbrahim & Gümüşbuğa, Ferhat & Tansel, Barbaros, 2015. "Risk based facility location by using fault tree analysis in disaster management," Omega, Elsevier, vol. 52(C), pages 168-179.
    2. repec:eee:jomega:v:72:y:2017:i:c:p:38-49 is not listed on IDEAS
    3. repec:eee:ejores:v:267:y:2018:i:2:p:496-512 is not listed on IDEAS
    4. Albareda-Sambola, Maria & Landete, Mercedes & Monge, Juan F. & Sainz-Pardo, José L., 2017. "Introducing capacities in the location of unreliable facilities," European Journal of Operational Research, Elsevier, vol. 259(1), pages 175-188.
    5. Güden, Hüseyin & Süral, Haldun, 2014. "Locating mobile facilities in railway construction management," Omega, Elsevier, vol. 45(C), pages 71-79.
    6. Albareda-Sambola, Maria & Hinojosa, Yolanda & Puerto, Justo, 2015. "The reliable p-median problem with at-facility service," European Journal of Operational Research, Elsevier, vol. 245(3), pages 656-666.
    7. Davood Shishebori & Lawrence Snyder & Mohammad Jabalameli, 2014. "A Reliable Budget-Constrained FL/ND Problem with Unreliable Facilities," Networks and Spatial Economics, Springer, vol. 14(3), pages 549-580, December.

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