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A robust decision-making approach for p-hub median location problems based on two-stage stochastic programming and mean-variance theory: a real case study

  • Taher Ahmadi
  • Hadi Karimi
  • Hamid Davoudpour
  • Seyed Abbas Hosseinijou
ORIGINAL ARTICLE

Abstract

The stochastic location-allocation p-hub median problems are related to long-term decisions made in risky situations. Due to the importance of this type of problems in real-world applications, the authors were motivated to propose an approach to obtain more reliable policies in stochastic environments considering the decision makers’ preferences. Therefore, a systematic approach to make robust decisions for the single location-allocation p-hub median problem based on mean-variance theory and two-stage stochastic programming was developed. The approach involves three main phases, namely location modeling, risk modeling, and decision making, each including several steps. In the first phase, the pertinent location-allocation model of the problem is developed in the form of a two-stage stochastic model based on its deterministic version. A risk measure, based on total cost function and mean-variance theory, is derived in the second phase. Furthermore, two heterogeneous terms of the risk measure have been normalized and an innovative procedure has been proposed to significantly improve the calculation efficiency. In the third phase, the Pareto solution is obtained, the frontier curve is depicted to determine the decision maker’s risk aversion coefficient, and a robust policy is obtained through optimization based on decision makers’ preferences. Finally, a case study of an automobile part distribution system with stochastic demand is described to further illustrate our risk management and analysis approach.

Keywords

p-Hub location-allocation median problem Two-stage stochastic programming Risk analysis and management Robust decision making Risk aversion coefficient 

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References

  1. 1.
    Markowitz H (1959) Portfolio selection: efficient diversification of investments. Cowles Foundation, New Haven, p 94Google Scholar
  2. 2.
    O’Kelly ME (1986) Activity levels at hub facilities in interacting networks. Geogr Anal 18(4):343–356CrossRefGoogle Scholar
  3. 3.
    O’Kelly ME (1987) A quadratic integer program for the location of interacting hub facilities. Eur J Oper Res 32(3):393–404CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Campbell JF, Ernst AT, Krishnamoorthy M (2002) Hub location problems. Facil Locat Appl Theory 1:373–407CrossRefMathSciNetGoogle Scholar
  5. 5.
    Alumur S, Kara BY (2008) Network hub location problems: the state of the art. Eur J Oper Res 190(1):1–21CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Farahani RZ, Hekmatfar M, Arabani AB, Nikbakhsh E (2013) Hub location problems: a review of models, classification, solution techniques, and applications. Comput Ind Eng 64(4):1096–1109CrossRefGoogle Scholar
  7. 7.
    Louveaux F (1986) Discrete stochastic location models. Ann Oper Res 6(2):21–34CrossRefGoogle Scholar
  8. 8.
    Louveaux FV, Peeters D (1992) A dual-based procedure for stochastic facility location. Oper Res 40(3):564–573CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Laporte G, Louveaux FV, van Hamme L (1994) Exact solution to a location problem with stochastic demands. Transp Sci 28(2):95–103CrossRefzbMATHGoogle Scholar
  10. 10.
    Snyder LV (2006) Facility location under uncertainty: a review. IIE Trans 38(7):547–564CrossRefGoogle Scholar
  11. 11.
    Marianov V, Serra D (2003) Location models for airline hubs behaving as M/D/c queues. Comput Oper Res 30(7):983–1003CrossRefzbMATHGoogle Scholar
  12. 12.
    Mohammadi M, Jolai F, Rostami H (2011) An M/M/c queue model for hub covering location problem. Math Comput Model 54(11):2623–2638CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Sim T, Lowe TJ, Thomas BW (2009) The stochastic p-hub center problem with service-level constraints. Comput Oper Res 36(12):3166–3177CrossRefzbMATHGoogle Scholar
  14. 14.
    Yang TH (2009) Stochastic air freight hub location and flight routes planning. Appl Math Model 33(12):4424–4430CrossRefzbMATHGoogle Scholar
  15. 15.
    Contreras I, Cordeau JF, Laporte G (2011) Stochastic uncapacitated hub location. Eur J Oper Res 212(3):518–528CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Hult E, Jiang H, Ralph D (2011) Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem. Comput Optim Appl 1–16Google Scholar
  17. 17.
    Alumur SA, Nickel S, Saldanha-da-Gama F (2012) Hub location under uncertainty. Transp Res B Methodol 46(4):529–543CrossRefGoogle Scholar
  18. 18.
    Bradley JV (1975) Probability, decision, statistics. Prentice-Hall, Englewood CliffsGoogle Scholar
  19. 19.
    Wagner MR, Bhadury J, Peng S (2009) Risk management in uncapacitated facility location models with random demands. Comput Oper Res 36(4):1002–1011CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Wang S, Watada J (2012) A hybrid modified PSO approach to VaR-based facility location problems with variable capacity in fuzzy random uncertainty. Inf Sci 192:3–18CrossRefzbMATHGoogle Scholar
  21. 21.
    Azad N, Davoudpour H (2010) A two echelon location-routing model with considering value-at-risk measure. Int J Manag Sci Eng Manag 5(3):235–240Google Scholar
  22. 22.
    Zhai H, Liu Y, Chen W (2012) Applying minimum-risk criterion to stochastic hub location problems. Procedia Eng 29:2313–2321CrossRefGoogle Scholar
  23. 23.
    Mohammadi M, Jolai F, Tavakkoli-Moghaddam R (2013) Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm. Appl Math Model 37(24):10053–10073CrossRefMathSciNetGoogle Scholar
  24. 24.
    Kara BY, Tansel BC (2000) On the single-assignment p-hub center problem. Eur J Oper Res 125(3):648–655CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Taher Ahmadi
    • 1
    • 2
  • Hadi Karimi
    • 1
  • Hamid Davoudpour
    • 1
  • Seyed Abbas Hosseinijou
    • 1
  1. 1.Department of Industrial EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Pars Khodro Automobile Manufacturer CompanyTehranIran

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