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


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.


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


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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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