Skip to main content
SpringerLink
Log in

Multiple obnoxious facility location: the case of protected areas

  • Original Paper
  • Published:
Computational Management Science Aims and scope Submit manuscript

Abstract

Most of the existing obnoxious facility location models use points to represent locations of demand centers and facilities. These points are typically centroids of geographical regions, such as cities or protected wildlife areas. Representing areas as points is convenient for the development and analysis of location models, but it may hinder the models’ practical applications. In continuous models, facilities may be located far from the centroid but close to (or even inside) the boundaries of the protected area. Also, some centroids may be located outside of the areas which they represent. We propose a heuristic that leverages the existing point-based models to locate multiple obnoxious facilities around protected areas and, at the same time, minimize the negative impact on those areas. The effectiveness of our approach is illustrated with both generated and real-world instances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data availability statement

The data generated during and/or analysed during the current study are available in the Open Science Framework repository, https://osf.io/t65dr.

References

  • Aneja YP, Parlar M (1994) Algorithms for Weber facility location in the presence of forbidden regions and/or barriers to travel. Transp Sci 28(1):70–76

    Article  Google Scholar 

  • Batta R, Ghose A, Palekar US (1989) Locating facilities on the Manhattan metric with arbitrarily shaped barriers and convex forbidden regions. Transp Sci 23(1):26–36

    Article  MathSciNet  Google Scholar 

  • Bennell J, Scheithauer G, Stoyan Y, Romanova T (2010) Tools of mathematical modeling of arbitrary object packing problems. Ann Oper Res 179(1):343–368

    Article  MathSciNet  Google Scholar 

  • Berman O, Drezner Z, Wesolowsky GO (2003) The expropriation location problem. J Oper Res Soc 54(7):769–776

    Article  Google Scholar 

  • Bischoff M, Klamroth K (2007) An efficient solution method for Weber problems with barriers based on genetic algorithms. Eur J Oper Res 177(1):22–41

    Article  MathSciNet  Google Scholar 

  • Brimberg J, Juel H (1998) A minisum model with forbidden regions for locating a semi-desirable facility in the plane. Locat Sci 6(1–4):109–120

    Article  Google Scholar 

  • Butt SE, Cavalier TM (1996) An efficient algorithm for facility location in the presence of forbidden regions. Eur J Oper Res 90(1):56–70

    Article  Google Scholar 

  • Byrne T, Kalcsics J (2022) Conditional facility location problems with continuous demand and a polygonal barrier. Eur J Oper Res 296(1):22–43

    Article  MathSciNet  Google Scholar 

  • Canbolat MS, Wesolowsky GO (2010) The rectilinear distance Weber problem in the presence of a probabilistic line barrier. Eur J Oper Res 202(1):114–121

    Article  MathSciNet  Google Scholar 

  • Canbolat MS, Wesolowsky GO (2012) On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers. Eur J Oper Res 217(2):241–247

    Article  MathSciNet  Google Scholar 

  • Carrizosa E, Plastria F (1998) Locating an undesirable facility by generalized cutting planes. Math Oper Res 23(3):680–694

    Article  MathSciNet  Google Scholar 

  • Carrizosa E, Plastria F (1999) Location of semi-obnoxious facilities. Stud Locat Anal 12(1999):1–27

    MathSciNet  Google Scholar 

  • Church RL, Drezner Z (2022) Review of obnoxious facilities location problems. Comput Oper Res 138:105468

    Article  MathSciNet  Google Scholar 

  • Church RL, Garfinkel RS (1978) Locating an obnoxious facility on a network. Transp Sci 12(2):107–118

    Article  MathSciNet  Google Scholar 

  • Coletti K, Kalczynski P, Drezner Z (2023) On the combined inverse-square effect of multiple point sources in multidimensional space. arXiv:2305.02912

  • Dearing PM, Klamroth K, Segars R (2005) Planar location problems with block distance and barriers. Ann Oper Res 136(1):117–143

    Article  MathSciNet  Google Scholar 

  • Drezner Z, Wesolowsky GO (1995) Obnoxious facility location in the interior of a planar network. J Reg Sci 35(4):675–688

    Article  Google Scholar 

  • Drezner Z, Kalczynski P, Salhi S (2019) The planar multiple obnoxious facilities location problem: a Voronoi based heuristic. Omega 87:105–116

    Article  Google Scholar 

  • Drezner T, Drezner Z, Kalczynski P (2020) Multiple obnoxious facilities location: a cooperative model. IISE Trans 52(12):1403–1412

    Article  Google Scholar 

  • Erkut E, Neuman S (1989) Analytical models for locating undesirable facilities. Eur J Oper Res 40(3):275–291

    Article  MathSciNet  Google Scholar 

  • Erkut E, Neuman S (1992) A multiobjective model for locating undesirable facilities. Ann Oper Res 40(1):209–227

    Article  Google Scholar 

  • Fernández J, Fernández P, Pelegrın B (2000) A continuous location model for siting a non-noxious undesirable facility within a geographical region. Eur J Oper Res 121(2):259–274

    Article  Google Scholar 

  • Gill PE, Murray W, Saunders MA (2005) Snopt: an SQP algorithm for large-scale constrained optimization. SIAM Rev 47(1):99–131

    Article  ADS  MathSciNet  Google Scholar 

  • Hamacher HW, Klamroth K (2000) Planar Weber location problems with barriers and block norms. Ann Oper Res 96(1):191–208

    Article  MathSciNet  Google Scholar 

  • Hamacher HW, Nickel S (1995) Restricted planar location problems and applications. Nav Res Logist (NRL) 42(6):967–992

    Article  MathSciNet  Google Scholar 

  • Hamacher HW, Schöbel A (1997) A note on center problems with forbidden polyhedra. Oper Res Lett 20(4):165–169

    Article  MathSciNet  Google Scholar 

  • Hansen P, Cohon J (1981) On the location of an obnoxious facility. Sistemi urbani Napoli 3(3):299–317

    Google Scholar 

  • Kalczynski P, Drezner Z (2019) Locating multiple facilities using the max-sum objective. Comput Ind Eng 129:136–143

    Article  Google Scholar 

  • Kalczynski P, Suzuki A, Drezner Z (2022) Multiple obnoxious facilities with weighted demand points. J Oper Res Soc 73(3):598–607

    Article  Google Scholar 

  • Klamroth K (2001) A reduction result for location problems with polyhedral barriers. Eur J Oper Res 130(3):486–497

    Article  MathSciNet  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):1–15

    Article  Google Scholar 

  • McGarvey RG, Cavalier TM (2005) Constrained location of competitive facilities in the plane. Comput Oper Res 32(2):359–378

    Article  MathSciNet  Google Scholar 

  • Melachrinoudis E, Cullinane TP (1986) Locating an undesirable facility with a minimax criterion. Eur J Oper Res 24(2):239–246

    Article  MathSciNet  Google Scholar 

  • Melachrinoudis E, Xanthopulos Z (2003) Semi-obnoxious single facility location in Euclidean space. Comput Oper Res 30(14):2191–2209

    Article  MathSciNet  Google Scholar 

  • Munoz-Perez J, Saameno-Rodriguez JJ (1999) Location of an undesirable facility in a polygonal region with forbidden zones. Eur J Oper Res 114(2):372–379

    Article  Google Scholar 

  • Oğuz M, Bektaş T, Bennell JA, Fliege J (2016) A modelling framework for solving restricted planar location problems using phi-objects. J Oper Res Soc 67(8):1080–1096

    Article  Google Scholar 

  • Oğuz M, Bektaş T, Bennell JA (2018) Multicommodity flows and benders decomposition for restricted continuous location problems. Eur J Oper Res 266(3):851–863

    Article  MathSciNet  Google Scholar 

  • Ohsawa Y, Tamura K (2003) Efficient location for a semi-obnoxious facility. Ann Oper Res 123(1):173–188

    Article  MathSciNet  Google Scholar 

  • Plastria F, Carrizosa E (1999) Undesirable facility location with minimal covering objectives. Eur J Oper Res 119(1):158–180

    Article  Google Scholar 

  • Plastria F, Gordillo J, Carrizosa E (2013) Locating a semi-obnoxious covering facility with repelling polygonal regions. Discrete Appl Math 161(16–17):2604–2623

    Article  MathSciNet  Google Scholar 

  • Savaş S, Batta R, Nagi R (2002) Finite-size facility placement in the presence of barriers to rectilinear travel. Oper Res 50(6):1018–1031

    Article  MathSciNet  Google Scholar 

  • Shamos MI, Hoey D (1975) Closest-point problems. In: 16th annual symposium on foundations of computer science (sfcs 1975). IEEE, pp 151–162

  • Shimrat M (1962) Algorithm 112: position of point relative to polygon. Commun ACM 5(8):434

    Article  Google Scholar 

  • UNEP-WCMC, IUCN (2021) Protected planet: the world database on protected areas (WDPA) and world database on other effective area-based conservation measures (WD-OECM). Protected Planet. www.protectedplanet.net. Accessed 22

  • van den Bossche J, Jordahl K, Fleischmann M (2021) Geopandas: Python tools for geographic data

  • Wolfram Research, Inc. (2022) Mathematica, Version 13.1. Champaign, IL, 2020

Download references

Author information

Authors and Affiliations

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

    Malgorzata Miklas-Kalczynska & Pawel Kalczynski

Authors
  1. Malgorzata Miklas-Kalczynska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pawel Kalczynski
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.M-K and P.K.: made substantial contributions to the conception or design of the work; drafted the work or revised it critically for important intellectual content; approved the version to be published; and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Corresponding author

Correspondence to Pawel Kalczynski.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Generating multiple instances, each with a set of random non-overlapping simple polygons (convex and non-convex) was necessary for our simulation. We used the following approach, which yields patterns similar to real-world protected areas.

First, we randomly generate 100 points in a 100 by 100 square and superimpose a Voronoi mesh on this square. Next, we randomly choose between 1 and 50 of the Voronoi mesh polygons and unionize them. If all the resulting polygonal areas are simple polygons, we consider an instance valid, otherwise the instance is rejected. The vertices of these polygonal protected areas are used to determine their centroids.

In our experiment, this process resulted in discarding 33 instances in order to generate 100 valid simulated instances. Figure 6 shows five examples of valid instances with protected areas (shown in black) covering between 1.3 and 48% of the total area of the square.

Fig. 6
figure 6

Sample simulated instances

Full size image

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Miklas-Kalczynska, M., Kalczynski, P. Multiple obnoxious facility location: the case of protected areas. Comput Manag Sci 21, 23 (2024). https://doi.org/10.1007/s10287-024-00503-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10287-024-00503-4

Keywords

Search

Navigation