IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v66y2017ipap170-181.html
   My bibliography  Save this article

Location choice and risk attitude of a decision maker

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048316000487
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2016.03.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    3. 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.
    4. James V. Jucker & Robert C. Carlson, 1976. "The Simple Plant-Location Problem under Uncertainty," Operations Research, INFORMS, vol. 24(6), pages 1045-1055, December.
    5. 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.
    6. Willard I. Zangwill, 1967. "The Piecewise Concave Function," Management Science, INFORMS, vol. 13(11), pages 900-912, July.
    7. 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.
    8. 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.
    9. Partovi, Fariborz Y., 2006. "An analytic model for locating facilities strategically," Omega, Elsevier, vol. 34(1), pages 41-55, January.
    10. H. Frank, 1966. "Optimum Locations on a Graph with Probabilistic Demands," Operations Research, INFORMS, vol. 14(3), pages 409-421, June.
    11. Haase, Knut & Müller, Sven, 2013. "Management of school locations allowing for free school choice," Omega, Elsevier, vol. 41(5), pages 847-855.
    12. Bieniek, Milena, 2015. "A note on the facility location problem with stochastic demands," Omega, Elsevier, vol. 55(C), pages 53-60.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Serocka Izabela, 2019. "Evaluation of Location Factors of Businesses by Local Authorities of Eastern Poland, with a Particular Emphasis on Spatial Policy," Real Estate Management and Valuation, Sciendo, vol. 27(1), pages 49-58, March.
    2. Liu, Hui-hui & Song, Yao-yao & Yang, Guo-liang, 2019. "Cross-efficiency evaluation in data envelopment analysis based on prospect theory," European Journal of Operational Research, Elsevier, vol. 273(1), pages 364-375.
    3. Wang, Lei & Liu, Qing & Dong, Shiyu & Guedes Soares, C., 2022. "Selection of countermeasure portfolio for shipping safety with consideration of investment risk aversion," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    4. Yu, Guodong & Haskell, William B. & Liu, Yang, 2017. "Resilient facility location against the risk of disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 82-105.
    5. Yu, Guodong & Zhang, Jie, 2018. "Multi-dual decomposition solution for risk-averse facility location problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 70-89.
    6. Guazzelli, Cauê Sauter & Cunha, Claudio B., 2018. "Exploring K-best solutions to enrich network design decision-making," Omega, Elsevier, vol. 78(C), pages 139-164.
    7. 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.
    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.
    10. Yin-Yin Huang & I-Fei Chen & Chien-Liang Chiu & Ruey-Chyn Tsaur, 2021. "Adjustable Security Proportions in the Fuzzy Portfolio Selection under Guaranteed Return Rates," Mathematics, MDPI, vol. 9(23), pages 1-18, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    2. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, vol. 13(1), pages 89-101.
    3. Rosenfield, Donald B., 1996. "Global and variable cost manufacturing systems," European Journal of Operational Research, Elsevier, vol. 95(2), pages 325-343, December.
    4. Unser, Matthias, 2000. "Lower partial moments as measures of perceived risk: An experimental study," Journal of Economic Psychology, Elsevier, vol. 21(3), pages 253-280, June.
    5. Liu, Zugang & Wang, Jia, 2019. "Supply chain network equilibrium with strategic financial hedging using futures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 962-978.
    6. Thomas C. Chiang & Hooi Hooi Lean & Wing-Keung Wong, 2008. "Do REITs Outperform Stocks and Fixed-Income Assets? New Evidence from Mean-Variance and Stochastic Dominance Approaches," JRFM, MDPI, vol. 1(1), pages 1-40, December.
    7. Liu, Zugang & Nagurney, Anna, 2011. "Supply chain outsourcing under exchange rate risk and competition," Omega, Elsevier, vol. 39(5), pages 539-549, October.
    8. Zentner, Robert P. & Greene, Duty D. & Hickenbotham, Terry L. & Eidman, Vernon R., 1981. "Ordinary And Generalized Stochastic Dominance: A Primer," Staff Papers 14184, University of Minnesota, Department of Applied Economics.
    9. Moshe Ben-Horim, 1990. "Stochastic Dominance And Truncated Sample Data," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(2), pages 105-116, June.
    10. Juan F. Gomez & Anna Martínez-Gavara & Javier Panadero & Angel A. Juan & Rafael Martí, 2024. "A Forward–Backward Simheuristic for the Stochastic Capacitated Dispersion Problem," Mathematics, MDPI, vol. 12(6), pages 1-22, March.
    11. Colin Beardsley & John R. O'Brien, 2005. "The Financial Services Reform Act 2001: Impact on Systemic risk in Australia," ICMA Centre Discussion Papers in Finance icma-dp2005-12, Henley Business School, University of Reading.
    12. Pinto, Cristian F. & Acuña, Andres A., 2011. "Consistencia de la evaluación de desempeño de inversiones financieras: Pruebas de dominación estocástica versus índices media-varianza [Consistency in the evaluation of financial investment perform," MPRA Paper 31301, University Library of Munich, Germany.
    13. Schmid Friedrich & Trede Mark, 2000. "Stochastic Dominance in German Asset Returns: Empirical Evidence from the 1990s / Stochastische Dominanz von Renditen deutscher Aktien: Eine empirische Untersuchung für die 90er Jahre," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 220(3), pages 315-326, June.
    14. Kim, Kyoung-Kuk & Park, Kun Soo, 2014. "Transferring and sharing exchange-rate risk in a risk-averse supply chain of a multinational firm," European Journal of Operational Research, Elsevier, vol. 237(2), pages 634-648.
    15. Liu, Weihua & Wang, Yijia, 2015. "Quality control game model in logistics service supply chain based on different combinations of risk attitude," International Journal of Production Economics, Elsevier, vol. 161(C), pages 181-191.
    16. Anderson, Jock R. & Hardaker, J. Brian, 1972. "An Appreciation of Decision Analysis in Management," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 40(04), pages 1-15, December.
    17. Dominic Gasbarro & Wing-Keung Wong & J. Kenton Zumwalt, 2007. "Stochastic Dominance Analysis of iShares," The European Journal of Finance, Taylor & Francis Journals, vol. 13(1), pages 89-101.
    18. Jesica Armas & Angel A. Juan & Joan M. Marquès & João Pedro Pedroso, 2017. "Solving the deterministic and stochastic uncapacitated facility location problem: from a heuristic to a simheuristic," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(10), pages 1161-1176, October.
    19. Kolokolova, Olga & Le Courtois, Olivier & Xu, Xia, 2022. "Is the index efficient? A worldwide tour with stochastic dominance," Journal of Financial Markets, Elsevier, vol. 59(PB).
    20. Bahman Kalantari & Ansuman Bagchi, 1990. "An algorithm for quadratic zero‐one programs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 527-538, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:66:y:2017:i:pa:p:170-181. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.