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The Obnoxious Competitive Facility Location Model

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Abstract

In this paper we propose a new competitive location model that considers the possible negative impact generated by competing facilities (such as cannabis dispensaries) on surrounding communities. The facilities cannot be located too close to the communities. Therefore, when distances are Euclidean, the facilities must be located at a point outside a set of circles centered at the communities. After formulating the model, a specially designed efficient algorithm that solves the single facility location problem within a given relative accuracy of optimality is constructed. A total of 128 instances are solved in a relatively short time. The largest instance of 10 existing competing facilities and 20,000 demand points was solved in less than 15 min of computer time. This new model opens avenues for future research by designing similar new models. Also, the algorithm designed in this paper can be applied to solving other location problems with outside of a set of circles constraints.

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Data Availability

All data used in the experiments is available in the paper.

References

  • Aurenhammer F, Klein R, Lee D-T (2013) Voronoi Diagrams and Delaunay Triangulations. World Scientific, New Jersey

    Google Scholar 

  • Austin CM (1974) The evaluation of urban public facility location: An alternative to benefit-cost analysis. Geogr Anal 6:135–145

    Google Scholar 

  • Austin CM, Smith TE, Wolpert J (1970) The implementation of controversial facility-complex programs. Geogr Anal 2:315–329

    Google Scholar 

  • Bell D, Ho T, Tang C (1998) Determining where to shop: Fixed and variable costs of shopping. J Mark Res 35(3):352–369

    Google Scholar 

  • Berman O, Krass D (1998) Flow intercepting spatial interaction model: A new approach to optimal location of competitive facilities. Locat Sci 6:41–65

    Google Scholar 

  • Brimberg J, Mladenović N, Todosijević R, Urošević D (2017) Less is more: solving the max-mean diversity problem with variable neighborhood search. Inf Sci 382:179–200

    Google Scholar 

  • Church RL (2019) Understanding the Weber location paradigm. In: Eiselt HA, Marianov V (eds) Contributions to Location Analysis - In Honor of Zvi Drezner’s 75th Birthday. Springer Nature, Switzerland, pp 69–88

    Google Scholar 

  • Church RL, Drezner Z (2022) Review of obnoxious facilities location problems. Computers & Operations Research 138:105468

    Google Scholar 

  • Church RL, Drezner Z, Tamir A (2022) Extensions to the Weber problem. Computers & Operations Research 122:105786

    Google Scholar 

  • Drezner T (1994) Optimal continuous location of a retail facility, facility attractiveness, and market share: An interactive model. J Retail 70:49–64

    Google Scholar 

  • Drezner T (2006) Derived attractiveness of shopping malls. IMA J Manag Math 17:349–358

    Google Scholar 

  • Drezner T (2011) Cannibalization in a competitive environment. Int Reg Sci Rev 34:306–322

    Google Scholar 

  • Drezner T (2022) Competitive location problems. In Salhi S, Boylan, JE, editors, The Palgrave Handbook of Operations Research, pages 209–236. Palgrave, London. ISBN: 978-3-030-96034-9

  • Drezner T, Drezner Z (2004) Finding the optimal solution to the Huff competitive location model. CMS 1:193–208

    Google Scholar 

  • Drezner T, Drezner Z, Kalczynski P (2011) A cover-based competitive location model. Journal of the Operational Research Society 62:100–113

    Google Scholar 

  • Drezner T, Drezner Z, Kalczynski P (2012) Strategic competitive location: Improving existing and establishing new facilities. Journal of the Operational Research Society 63:1720–1730

    Google Scholar 

  • Drezner T, Drezner Z, Kalczynski P (2020) Multiple obnoxious facilities location: A cooperative model. IISE Transactions 52:1403–1412

    Google Scholar 

  • Drezner T, Drezner Z, Schöbel A (2018) The Weber obnoxious facility location model: A Big Arc Small Arc approach. Comput Oper Res 98:240–250

    Google Scholar 

  • Drezner T, Drezner Z, Zerom D (2020) Facility dependent distance decay in competitive location. Netw Spat Econ 20:915–934

    Google Scholar 

  • Drezner Z, Klamroth K, Schöbel A, Wesolowsky GO (2002) The Weber problem. In: Drezner Z, Hamacher HW (eds) Facility Location: Applications and Theory. Springer, Berlin, pp 1–36

    Google Scholar 

  • Drezner Z, Suzuki A (2004) The big triangle small triangle method for the solution of non-convex facility location problems. Oper Res 52:128–135

    Google Scholar 

  • Drezner Z, Wesolowsky GO, Drezner T (1998) On the logit approach to competitive facility location. J Reg Sci 38:313–327

    Google Scholar 

  • Fernández J, Pelegrin B, Plastria F, Toth B (2007) Solving a Huff-like competitive location and design model for profit maximization in the plane. Eur J Oper Res 179:1274–1287

    Google Scholar 

  • Fielding GJ (1970) Transport impact research: Problems of location decisions at the community level. Ann Reg Sci 4:117–126

    Google Scholar 

  • Francis RL, McGinnis Jr. LF, White JA (1992) Facility Layout and Location: An Analytical Approach. Prentice Hall, Englewood Cliffs, NJ, second edition

  • Hansen P, Peeters D, Thisse J-F (1981) On the location of an obnoxious facility. Sistemi Urbani 3:299–317

    Google Scholar 

  • Hodgson MJ (1981) The location of public facilities intermediate to the journey to work. Eur J Oper Res 6:199–204

    Google Scholar 

  • Hotelling H (1929) Stability in competition. Economic Journal 39:41–57

    Google Scholar 

  • Huff DL (1964) Defining and estimating a trade area. J Mark 28:34–38

    Google Scholar 

  • Huff DL (1966) A programmed solution for approximating an optimum retail location. Land Econ 42:293–303

    Google Scholar 

  • Law AM, Kelton WD (1991) Simulation modeling and analysis. McGraw-Hill, New York, second edition

  • Leonardi G, Tadei R (1984) Random utility demand models and service location. Reg Sci Urban Econ 14:399–431

    Google Scholar 

  • Love RF, Morris JG, Wesolowsky GO (1988) Facilities Location: Models & Methods. North Holland, New York, NY

    Google Scholar 

  • Mason CH, Milne GR (1994) An approach for identifying cannibalization within product line extensions and multi-brand strategies. J Bus Res 31:163–170

    Google Scholar 

  • McGarvey RG, Cavalier TM (2003) A global optimal approach to facility location in the presence of forbidden regions. Comput Ind Eng 45:1–15

    Google Scholar 

  • Mladenović N, Alkandari A, Pei J, Todosijević R, Pardalos PM (2020) Less is more approach: basic variable neighborhood search for the obnoxious p-median problem. Int Trans Oper Res 27:480–493

    Google Scholar 

  • Mladenović N, Drezner Z, Brimberg J, Urošević D (2022) Less is more approach in heuristic optimization. In Salhi, S. and Boylan, J. E., editors, The Palgrave Handbook of Operations Research, pages 469–499. Palgrave, London. ISBN: 978-3-030-96034-9

  • Mladenović N, Todosijević R, Urošević D (2016) Less is more: basic variable neighborhood search for minimum differential dispersion problem. Inf Sci 326:160–171

    Google Scholar 

  • Moorthy KS, Png IP (1992) Market segmentation, cannibalization, and the timing of product introductions. Manage Sci 38:345–359

    Google Scholar 

  • Mumphrey AJ, Seley JE, Wolpert J (1971) A decision model for locating controversial facilities. J Am Inst Plann 37:397–402

    Google Scholar 

  • Mumphrey AJ, Wolpert J (1973) Equity considerations and concessions in the siting of public facilities. Econ Geogr 49:109–121

    Google Scholar 

  • Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley Series in Probability and Statistics, John Wiley, Hoboken, NJ

    Google Scholar 

  • Orloff CS (1977) A theoretical model of net accessibility in public facility location. Geogr Anal 9:244–256

    Google Scholar 

  • Plastria F (2005) Avoiding cannibalisation and/or competitor reaction in planar single facility location. Journal of the Operational Research Society of Japan 48:148–157

    Google Scholar 

  • Reilly WJ (1931) The Law of Retail Gravitation. Knickerbocker Press, New York, NY

    Google Scholar 

  • Schöbel A, Scholz D (2010) The big cube small cube solution method for multidimensional facility location problems. Computers & Operations Research 37:115–122

    Google Scholar 

  • Weber A (1909) Über den Standort der Industrien, 1. Teil: Reine Theorie des Standortes. English Translation: on the Location of Industries. University of Chicago Press, Chicago, IL. Translation published in 1929

  • Wendell RE, Hurter AP (1973) Location theory, dominance and convexity. Oper Res 21:314–320

    Google Scholar 

  • Wesolowsky GO (1993) The Weber problem: History and perspectives. Locat Sci 1:5–23

    Google Scholar 

  • Wilson AG (1976) Retailers’ profits and consumers’ welfare in a spatial interaction shopping mode. In: Masser I (ed) Theory and Practice in Regional Science. Pion, London, pp 42–59

    Google Scholar 

  • Wolpert J (1976) Regressive siting of public facilities. Nat Resour J 16:103–115

    Google Scholar 

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Authors and Affiliations

  1. College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Tammy Drezner, Zvi Drezner & Dawit Zerom

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  1. Tammy Drezner
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  2. Zvi Drezner
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  3. Dawit Zerom
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Contributions

Tammy Drezner came up with the idea, literature review and most of the writing. Zvi Drezner and Dawit Zerom did the analysis and the computational experiments.

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Correspondence to Zvi Drezner.

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Drezner, T., Drezner, Z. & Zerom, D. The Obnoxious Competitive Facility Location Model. Netw Spat Econ 23, 885–903 (2023). https://doi.org/10.1007/s11067-023-09603-1

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