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Location choice and risk attitude of a decision maker

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  • Berman, Oded
  • Sanajian, Nima
  • Wang, Jiamin

Abstract

In this paper we study the effect of a decision maker׳s risk attitude on the median and center problems, two well-known location problems, with uncertain demand in the mean–variance framework. We provide a mathematical programming formulation for both problems in the form of quadratic programming and develop solution procedures. In particular, we consider the vertex and absolute median problems separately, and identify a dominant set for the center problem. Glover׳s linearization method is applied to solve the vertex median problem. We also develop a branch and bound algorithm and a heuristic as the linearization technique takes too long for the vertex median problem on large networks. A computational experiment is conducted to compare the performance of the algorithms. We demonstrate the importance of taking into account the volatility and correlation structure when a location decision is made. The closest assignment property is also discussed for these location problems under the mean–variance objective.

Suggested Citation

  • Berman, Oded & Sanajian, Nima & Wang, Jiamin, 2017. "Location choice and risk attitude of a decision maker," Omega, Elsevier, vol. 66(PA), pages 170-181.
    • Handle: RePEc:eee:jomega:v:66:y:2017:i:pa:p:170-181
    DOI: 10.1016/j.omega.2016.03.002
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    1. James V. Jucker & Robert C. Carlson, 1976. "The Simple Plant-Location Problem under Uncertainty," Operations Research, INFORMS, vol. 24(6), pages 1045-1055, December.
    2. Willard I. Zangwill, 1967. "The Piecewise Concave Function," Management Science, INFORMS, vol. 13(11), pages 900-912, July.
    3. Porter, R Burr & Gaumnitz, Jabk E, 1972. "Stochastic Dominance vs. Mean-Variance Portfolio Analysis: An Empirical Evaluation," American Economic Review, American Economic Association, vol. 62(3), pages 438-446, June.
    4. Hodder, James E. & Jucker, James V., 1985. "A simple plant-location model for quantity-setting firms subject to price uncertainty," European Journal of Operational Research, Elsevier, vol. 21(1), pages 39-41, July.
    5. Partovi, Fariborz Y., 2006. "An analytic model for locating facilities strategically," Omega, Elsevier, vol. 34(1), pages 41-55, January.
    6. R. S. Garfinkel & A. W. Neebe & M. R. Rao, 1977. "The m-Center Problem: Minimax Facility Location," Management Science, INFORMS, vol. 23(10), pages 1133-1142, June.
    7. Peker, Meltem & Kara, Bahar Y., 2015. "The P-Hub maximal covering problem and extensions for gradual decay functions," Omega, Elsevier, vol. 54(C), pages 158-172.
    8. Mavridou, T. & Pardalos, P.M. & Pitsoulis, L.S. & Resende, Mauricio G.C., 1998. "A GRASP for the biquadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 105(3), pages 613-621, March.
    9. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    10. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    11. Oded Berman & Dmitry Krass & Jiamin Wang, 2011. "Stochastic Analysis in Location Research," International Series in Operations Research & Management Science, in: H. A. Eiselt & Vladimir Marianov (ed.), Foundations of Location Analysis, chapter 0, pages 241-271, Springer.
    12. H. Frank, 1966. "Optimum Locations on a Graph with Probabilistic Demands," Operations Research, INFORMS, vol. 14(3), pages 409-421, June.
    13. Haase, Knut & Müller, Sven, 2013. "Management of school locations allowing for free school choice," Omega, Elsevier, vol. 41(5), pages 847-855.
    14. Bieniek, Milena, 2015. "A note on the facility location problem with stochastic demands," Omega, Elsevier, vol. 55(C), pages 53-60.
    15. B. Kalantari & J. B. Rosen, 1987. "An Algorithm for Global Minimization of Linearly Constrained Concave Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 544-561, August.
    16. Choi, Tsan-Ming & Li, Duan & Yan, Houmin & Chiu, Chun-Hung, 2008. "Channel coordination in supply chains with agents having mean-variance objectives," Omega, Elsevier, vol. 36(4), pages 565-576, August.
    17. Grootveld, Henk & Hallerbach, Winfried, 1999. "Variance vs downside risk: Is there really that much difference?," European Journal of Operational Research, Elsevier, vol. 114(2), pages 304-319, April.
    18. George C. Philippatos & Nicolas Gressis, 1975. "Conditions of Equivalence Among E-V, SSD, and E-H Portfolio Selection Criteria: The Case for Uniform, Normal and Lognormal Distributions," Management Science, INFORMS, vol. 21(6), pages 617-625, February.
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    6. Xiao Zhao & Xuhui Xia & Lei Wang & Guodong Yu, 2018. "Risk-Averse Facility Location for Green Closed-Loop Supply Chain Networks Design under Uncertainty," Sustainability, MDPI, vol. 10(11), pages 1-17, November.
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    8. David Kik & Matthias G. Wichmann & Thomas S. Spengler, 2023. "Small- or Medium-Sized Enterprise Uses Operations Research to Select and Develop its Headquarters Location," Interfaces, INFORMS, vol. 53(4), pages 312-331, July.
    9. Zhenzhen Ma & Jianjun Zhu & Shitao Zhang, 2021. "Probabilistic-based expressions in behavioral multi-attribute decision making considering pre-evaluation," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 145-173, March.
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