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Continuous Facility Location Problems

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The Palgrave Handbook of Operations Research

Abstract

In this chapter we review continuous location models. Location models involve locating one or more facilities among a given set of demand points to achieve a certain objective. For example, locating a warehouse that serves a set of stores each requires a given delivery volume. The objective is minimizing the total delivery cost which is the sum of distances, weighted by the volume. In discrete location models, a finite set of potential locations for facilities is given. In continuous location models, facilities can be located anywhere in the plane, or in a limited region with an infinite number of potential locations.

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References

  1. Alumur, S. A. (2019). Hub location and related models. In Contributions to Location Analysis—In Honor of Zvi Drezner’s 75th Birthday, pages 237–252. Springer Nature, Switzerland.

    Google Scholar 

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

    Book  Google Scholar 

  3. Bagherinejad, J., Bashiri, M., and Nikzad, H. (2018). General form of a cooperative gradual maximal covering location problem. Journal of Industrial Engineering International, 14:241–253.

    Article  Google Scholar 

  4. Baron, O., Berman, O., Krass, D., and Wang, Q. (2007). The equitable location problem on the plane. European Journal of Operational Research, 183:578–590.

    Article  Google Scholar 

  5. Berman, O. (1990). Mean-variance location problems. Transportation Science, 24:287–293.

    Article  Google Scholar 

  6. Berman, O. and Drezner, Z. (2007). The multiple server location problem. Journal of the Operational Research Society, 58:91–99.

    Article  Google Scholar 

  7. Berman, O. and Drezner, Z. (2008). A new formulation for the conditional \(p\)-median and \(p\)-center problems. Operations Research Letters, 36:481–483.

    Article  Google Scholar 

  8. Berman, O., Drezner, Z., and Krass, D. (2010). Cooperative cover location problems: The planar case. IIE Transactions, 42:232–246.

    Article  Google Scholar 

  9. Berman, O., Drezner, Z., and Krass, D. (2011). Big segment small segment global optimization algorithm on networks. Networks, 58:1–11.

    Article  Google Scholar 

  10. Berman, O., Drezner, Z., and Krass, D. (2019). The multiple gradual cover location problem. Jornal of the Operational Research Society, 70:931–940.

    Article  Google Scholar 

  11. Berman, O., Drezner, Z., Tamir, A., and Wesolowsky, G. O. (2009). Optimal location with equitable loads. Annals of Operations Research, 167:307–325.

    Article  Google Scholar 

  12. Berman, O., Drezner, Z., and Wesolowsky, G. O. (2003a). The expropriation location problem. Journal of the Operational Research Society, 54:769–776.

    Article  Google Scholar 

  13. Berman, O., Drezner, Z., and Wesolowsky, G. O. (2005). The facility and transfer points location problem. International Transactions in Operational Research, 12:387–402.

    Article  Google Scholar 

  14. Berman, O., Drezner, Z., and Wesolowsky, G. O. (2007). The transfer point location problem. European Journal of Operational Research, 179:978–989.

    Article  Google Scholar 

  15. Berman, O., Drezner, Z., and Wesolowsky, G. O. (2008). The multiple location of transfer points. Journal of the Operational Research Society, 59:805–811.

    Article  Google Scholar 

  16. Berman, O. and Krass, D. (2002). The generalized maximal covering location problem. Computers & Operations Research, 29:563–591.

    Article  Google Scholar 

  17. Berman, O., Krass, D., and Drezner, Z. (2003b). The gradual covering decay location problem on a network. European Journal of Operational Research, 151:474–480.

    Article  Google Scholar 

  18. Berman, O. and Simchi-Levi, D. (1990). The conditional location problem on networks. Transportation Science, 24:77–78.

    Article  Google Scholar 

  19. Bongartz, I., Calamai, P. H., and Conn, A. R. (1994). A projection method for \(\ell _p\) norm location-allocation problems. Mathematical Programming, 66:238–312.

    Google Scholar 

  20. Brimberg, J. and Drezner, Z. (2019). Solving multiple facilities location problems with separated clusters. Operations Research Letters, 47:386–390.

    Article  Google Scholar 

  21. Brimberg, J., Hansen, P., and Mladenović, N. (2006). Decomposition strategies for large-scale continuous location–allocation problems. IMA Journal of Management Mathematics, 17:307–316.

    Article  Google Scholar 

  22. Brimberg, J., Hansen, P., Mladenović, N., and Taillard, E. (2000). Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem. Operations Research, 48:444–460.

    Article  Google Scholar 

  23. Brimberg, J., Hansen, P., Mladonovic, N., and Salhi, S. (2008). A survey of solution methods for the continuous location allocation problem. International Journal of Operations Research, 5:1–12.

    Google Scholar 

  24. Brimberg, J. and Hodgson, M. J. (2011). Heuristics for location models. In Eiselt, H. A. and Marianov, V., editors, Foundations of Location Analysis: International Series in Operations Research & Management Science, Vol. 155, pages 335–355. Springer, New York, NY.

    Chapter  Google Scholar 

  25. Brimberg, J. and Love, R. F. (1993). Global convergence of a generalized iterative procedure for the minisum location problem with \(l_p\) distances. Operations Research, 41:1153–1163.

    Article  Google Scholar 

  26. Brimberg, J., Maier, A., and Schöbel, A. (2021). When closest is not always the best: The distributed p-median problem. Journal of the Operational Research Society, 72:200–216.

    Article  Google Scholar 

  27. Brimberg, J. and Salhi, S. (2019). A general framework for local search applied to the continuous p-median problem. In Contributions to Location Analysis—In Honor of Zvi Drezner’s 75th Birthday, pages 89–108. Springer Nature, Switzerland.

    Google Scholar 

  28. Callaghan, B., Salhi, S., and Brimberg, J. (2019). Optimal solutions for the continuous p-centre problem and related-neighbour and conditional problems: A relaxation-based algorithm. Journal of the Operational Research Society, 70:192–211.

    Article  Google Scholar 

  29. Callaghan, B., Salhi, S., and Nagy, G. (2017). Speeding up the optimal method of Drezner for the p-centre problem in the plane. European Journal of Operational Research, 257:722–734.

    Article  Google Scholar 

  30. Campbell, J. F. (1994). Integer programming formulations of discrete hub location problems. European Journal of Operational Research, 72:387–405.

    Article  Google Scholar 

  31. Carrizosa, E. (1998). Minimizing the variance of Euclidean distances. Studies in Locational Analysis, 12:101–118.

    Google Scholar 

  32. Chen, D. and Chen, R. (2009). New relaxation-based algorithms for the optimal solution of the continuous and discrete \(p\)-center problems. Computers & Operations Research, 36:1646–1655.

    Article  Google Scholar 

  33. Chen, P., Hansen, P., Jaumard, B., and Tuy, H. (1992). Weber’s problem with attraction and repulsion. Journal of Regional Science, 32:467–486.

    Article  Google Scholar 

  34. Chen, R. (1983). Solution of minisum and minimax location-allocation problems with Euclidean distances. Naval Research Logistics Quarterly, 30:449–459.

    Article  Google Scholar 

  35. Chen, R. (1988). Conditional minisum and minimax location-allocation problems in Euclidean space. Transportation Science, 22:157–160.

    Article  Google Scholar 

  36. Chen, R. and Handler, G. Y. (1993). The conditional \(p\)-center in the plane. Naval Research Logistics, 40:117–127.

    Article  Google Scholar 

  37. Christaller, W. (1966). Central Places in Southern Germany. Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  38. Chrystal, G. (1885). On the problem to construct the minimum circle enclosing \(n\) given points in the plane. Proceedings of the Edinburgh Mathematical Society, 3:30–33.

    Article  Google Scholar 

  39. Church, R. L. (2019). Understanding the Weber location paradigm. In Eiselt, H. A. and Marianov, V., editors, Contributions to Location Analysis—In Honor of Zvi Drezner’s 75th Birthday, pages 69–88. Springer Nature, Switzerland.

    Chapter  Google Scholar 

  40. Church, R. L. and Cohon, J. L. (1976). Multiobjective location analysis of regional energy facility siting problems. Technical report, Brookhaven National Lab., Upton, NY (USA).

    Google Scholar 

  41. Church, R. L. and Drezner, Z. (2022). Review of obnoxious facilities location problems. Computers and Operations Research, 138, 105468.

    Google Scholar 

  42. Church, R. L. and Garfinkel, R. S. (1978). Locating an obnoxious facility on a network. Transportation Science, 12:107–118.

    Article  Google Scholar 

  43. Church, R. L. and Murray, A. (2018). Location covering models: History, applications, and advancements. Advances in Spatial Science.

    Google Scholar 

  44. Church, R. L. and ReVelle, C. S. (1974). The maximal covering location problem. Papers of the Regional Science Association, 32:101–118.

    Article  Google Scholar 

  45. Church, R. L. and Roberts, K. L. (1984). Generalized coverage models and public facility location. Papers of the Regional Science Association, 53:117–135.

    Article  Google Scholar 

  46. Contreras, I. (2015). Hub location problems. In Laporte, G., Nickel, S., and da Gama, F. S., editors, Location Science, pages 311–344. Springer, Heidelberg.

    Google Scholar 

  47. Cooper, L. (1963). Location-allocation problems. Operations Research, 11:331–343.

    Article  Google Scholar 

  48. Cooper, L. (1964). Heuristic methods for location-allocation problems. SIAM Review, 6:37–53.

    Article  Google Scholar 

  49. Dasarathy, B. and White, L. (1980). A maximin location problem. Operations Research, 28(6):1385–1401.

    Article  Google Scholar 

  50. Daskin, M. S. (1995). Network and Discrete Location: Models, Algorithms, and Applications. John Wiley & Sons, New York.

    Book  Google Scholar 

  51. Daskin, M. S. and Maass, K. L. (2015). The p-median problem. In Laporte, G., Nickel, S., and da Gama, F. S., editors, Location Science, pages 21–45. Springer, Heidelberg.

    Google Scholar 

  52. Drezner, T. (2021). Competitive location problems. In Salhi S. and Boylan J.E., editors, The Palgrave Handbook of Operations Research. Palgrave, London.

    Google Scholar 

  53. Drezner, T. and Drezner, Z. (2001). A note on applying the gravity rule to the airline hub problem. Journal of Regional Science, 41:67–73.

    Article  Google Scholar 

  54. Drezner, T. and Drezner, Z. (2006). Multiple facilities location in the plane using the gravity model. Geographical Analysis, 38:391–406.

    Article  Google Scholar 

  55. Drezner, T. and Drezner, Z. (2007a). Equity models in planar location. Computational Management Science, 4:1–16.

    Article  Google Scholar 

  56. Drezner, T. and Drezner, Z. (2007b). The gravity p-median model. European Journal of Operational Research, 179:1239–1251.

    Article  Google Scholar 

  57. Drezner, T. and Drezner, Z. (2008). Lost demand in a competitive environment. Journal of the Operational Research Society, 59:362–371.

    Article  Google Scholar 

  58. Drezner, T. and Drezner, Z. (2011a). The gravity multiple server location problem. Computers & Operations Research, 38:694–701.

    Article  Google Scholar 

  59. Drezner, T. and Drezner, Z. (2011b). A note on equity across groups in facility location. Naval Research Logistics, 58:705–711.

    Google Scholar 

  60. Drezner, T. and Drezner, Z. (2014). The maximin gradual cover location problem. OR Spectrum, 36:903–921.

    Article  Google Scholar 

  61. Drezner, T. and Drezner, Z. (2021). Asymmetric distance location model. INFOR: Information Systems and Operational Research, 59:102–110.

    Google Scholar 

  62. Drezner, T., Drezner, Z., and Goldstein, Z. (2010). A stochastic gradual cover location problem. Naval Research Logistics, 57:367–372.

    Article  Google Scholar 

  63. Drezner, T., Drezner, Z., and Guyse, J. (2009a). Equitable service by a facility: Minimizing the Gini coefficient. Computers & Operations Research, 36:3240–3246.

    Article  Google Scholar 

  64. Drezner, T., Drezner, Z., and Hulliger, B. (2014). The quintile share ratio in location analysis. European Journal of Operational Research, 236:166–174.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  67. Drezner, T., Drezner, Z., and Kalczynski, P. (2016a). The multiple markets competitive location problem. Kybernetes, 45:854–865.

    Article  Google Scholar 

  68. Drezner, T., Drezner, Z., and Kalczynski, P. (2019a). A directional approach to gradual cover. TOP, 27:70–93.

    Article  Google Scholar 

  69. Drezner, T., Drezner, Z., and Kalczynski, P. (2020a). Directional approach to gradual cover: A maximin objective. Computational Management Science, 17:121–139.

    Article  Google Scholar 

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

    Article  Google Scholar 

  71. Drezner, T., Drezner, Z., and Kalczynski, P. (2021). Directional approach to gradual cover: The continuous case. Computational Management Science, 18:25–47.

    Article  Google Scholar 

  72. Drezner, T., Drezner, Z., and Schöbel, A. (2018). The Weber obnoxious facility location model: A Big Arc Small Arc approach. Computers and Operations Research, 98:240–250.

    Article  Google Scholar 

  73. Drezner, T., Drezner, Z., and Scott, C. H. (2009b). Location of a facility minimizing nuisance to or from a planar network. Computers & Operations Research, 36:135–148.

    Article  Google Scholar 

  74. Drezner, Z. (1979). Bounds on the optimal location to the Weber problem under conditions of uncertainty. Journal of the Operational Research Society, 30:923–931.

    Article  Google Scholar 

  75. Drezner, Z. (1981). On a modified one-center model. Management Science, 27:848–851.

    Article  Google Scholar 

  76. Drezner, Z. (1983). Constrained location problems in the plane and on a sphere. IIE Transactions, 15:300–304.

    Article  Google Scholar 

  77. Drezner, Z. (1984a). The p-center problem—Heuristic and optimal algorithms. Journal of the Operational Research Society, 35:741–748.

    Google Scholar 

  78. Drezner, Z. (1984b). The planar two-center and two-median problems. Transportation Science, 18:351–361.

    Article  Google Scholar 

  79. Drezner, Z. (1985). Sensitivity analysis of the optimal location of a facility. Naval Research Logistics Quarterly, 32:209–224.

    Article  Google Scholar 

  80. Drezner, Z. (1989a). On the conditional \(p\)-center problem. Transportation Science, 23:51–53.

    Article  Google Scholar 

  81. Drezner, Z. (1989b). Stochastic analysis of the Weber problem on the sphere. Journal of the Operational Research Society, 40:1137–1144.

    Article  Google Scholar 

  82. Drezner, Z. (1992). A note on the Weber location problem. Annals of Operations Research, 40:153–161.

    Article  Google Scholar 

  83. Drezner, Z. (1995). On the conditional \(p\)-median problem. Computers & Operations Research, 22:525–530.

    Article  Google Scholar 

  84. Drezner, Z. (1996). A note on accelerating the Weiszfeld procedure. Location Science, 3:275–279.

    Article  Google Scholar 

  85. Drezner, Z. (2007). A general global optimization approach for solving location problems in the plane. Journal of Global Optimization, 37:305–319.

    Article  Google Scholar 

  86. Drezner, Z. (2011). Continuous center problems. In Eiselt, H. A. and Marianov, V., editors, Foundations of Location Analysis, pages 63–78. Springer, New York.

    Chapter  Google Scholar 

  87. Drezner, Z. (2015). The fortified Weiszfeld algorithm for solving the Weber problem. IMA Journal of Management Mathematics, 26:1–9.

    Article  Google Scholar 

  88. Drezner, Z., Brimberg, J., Salhi, S., and Mladenović, N. (2015). New heuristic algorithms for solving the planar \(p\)-median problem. Computers & Operations Research, 62:296–304.

    Article  Google Scholar 

  89. Drezner, Z., Brimberg, J., Salhi, S., and Mladenović, N. (2016b). New local searches for solving the multi-source Weber problem. Annals of Operations Research, 246:181–203.

    Article  Google Scholar 

  90. Drezner, Z., Drezner, T., and Wesolowsky, G. O. (2009c). Location with acceleration-deceleration distance. European Journal of Operational Research, 198:157–164.

    Article  Google Scholar 

  91. Drezner, Z. and Drezner, T. D. (2020). Biologically inspired parent selection in genetic algorithms. Annals of Operations Research, 287:161–183.

    Article  Google Scholar 

  92. Drezner, Z. and Erkut, E. (1995). Solving the continuous \(p\)-dispersion problem using non-linear programming. Journal of the Operational Research Society, 46:516–520.

    Article  Google Scholar 

  93. Drezner, Z., Gelfand, R. J., and Drezner, T. D. (2019b). Sensitivity of large scale facility location solutions. Journal of Supply Chain and Operations Management, 17:157–168.

    Google Scholar 

  94. Drezner, Z. and Goldman, A. (1991). On the set of optimal points to the Weber problem. Transportation Science, 25:3–8.

    Article  Google Scholar 

  95. Drezner, Z. and Kalczynski, P. (2020). Solving non-convex non-linear programs with reverse convex constraints by sequential linear programming. International Transactions in Operational Research, 27:1320–1342.

    Article  Google Scholar 

  96. Drezner, Z., Kalczynski, P., and Salhi, S. (2019c). The multiple obnoxious facilities location problem on the plane: A Voronoi based heuristic. OMEGA: The International Journal of Management Science, 87:105–116.

    Google Scholar 

  97. Drezner, Z., Klamroth, K., Schöbel, A., and Wesolowsky, G. O. (2002). The Weber problem. In Drezner, Z. and Hamacher, H. W., editors, Facility Location: Applications and Theory, pages 1–36. Springer, Berlin.

    Chapter  Google Scholar 

  98. Drezner, Z. and Nickel, S. (2009). Constructing a DC decomposition for ordered median problems. Journal of Global Optimization, 45:187–201.

    Article  Google Scholar 

  99. Drezner, Z. and Salhi, S. (2017). Incorporating neighborhood reduction for the solution of the planar \(p\)-median problem. Annals of Operations Research, 258:639–654.

    Article  Google Scholar 

  100. Drezner, Z. and Scott, C. H. (2010). Optimizing the location of a production firm. Networks and Spatial Economics, 10:411–425.

    Article  Google Scholar 

  101. Drezner, Z., Scott, C. H., and Turner, J. (2016c). Mixed planar and network single-facility location problems. Networks, 68:271–282.

    Article  Google Scholar 

  102. Drezner, Z. and Shelah, S. (1987). On the complexity of the Elzinga-Hearn algorithm for the one-center problem. Mathematics of Operations Research, 12:255–261.

    Article  Google Scholar 

  103. Drezner, Z. and Simchi-Levi, D. (1992). Asymptotic behavior of the Weber location problem on the plane. Annals of Operations Research, 40:163–172.

    Article  Google Scholar 

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

    Article  Google Scholar 

  105. Drezner, Z., Thisse, J.-F., and Wesolowsky, G. O. (1986). The minimax-min location problem. Journal of Regional Science, 26:87–101.

    Article  Google Scholar 

  106. Drezner, Z. and Wesolowsky, G. O. (1978). Facility location on a sphere. Journal of the Operational Research Society, 29:997–1004.

    Article  Google Scholar 

  107. Drezner, Z. and Wesolowsky, G. O. (1980a). A maximin location problem with maximum distance constraints. AIIE Transactions, 12(3):249–252.

    Article  Google Scholar 

  108. Drezner, Z. and Wesolowsky, G. O. (1980b). Single facility lp distance minimax location. SIAM Journal of Algebraic and Discrete Methods, 1:315–321.

    Article  Google Scholar 

  109. Drezner, Z. and Wesolowsky, G. O. (1983). Minimax and maximin facility location problems on a sphere. Naval Research Logistics Quarterly, 30:305–312.

    Article  Google Scholar 

  110. Drezner, Z. and Wesolowsky, G. O. (1989). The asymmetric distance location problem. Transportation Science, 23:201–207.

    Article  Google Scholar 

  111. Drezner, Z. and Wesolowsky, G. O. (1991). The Weber problem on the plane with some negative weights. Information Systems and Operational Research, 29:87–99.

    Article  Google Scholar 

  112. Drezner, Z. and Wesolowsky, G. O. (1996). Obnoxious facility location in the interior of a planar network. Journal of Regional Science, 35:675–688.

    Article  Google Scholar 

  113. Drezner, Z. and Wesolowsky, G. O. (1997). On the best location of signal detectors. IIE Transactions, 29:1007–1015.

    Article  Google Scholar 

  114. Drezner, Z., Wesolowsky, G. O., and Drezner, T. (2004). The gradual covering problem. Naval Research Logistics, 51:841–855.

    Article  Google Scholar 

  115. Eiselt, H. A. and Laporte, G. (1995). Objectives in location problems. In Drezner, Z., editor, Facility Location: A Survey of Applications and Methods, pages 151–180. Springer, New York, NY.

    Chapter  Google Scholar 

  116. Eiselt, H. A. and Marianov, V. (2009). Gradual location set covering with service quality. Socio-Economic Planning Sciences, 43:121–130.

    Article  Google Scholar 

  117. Eiselt, H. A. and Marianov, V. (2014). A bi-objective model for the location of landfills for municipal solid waste. European Journal of Operational Research, 235:187–194.

    Article  Google Scholar 

  118. Elzinga, J. and Hearn, D. (1972). Geometrical solutions for some minimax location problems. Transportation Science, 6:379–394.

    Article  Google Scholar 

  119. Eurostat (2012). Income quintile share ratio (s80/s20) (source: Silc). Eurostat Structural Indicators.

    Google Scholar 

  120. Farahani, R., Drezner, Z., and Asgari, N. (2009). Single facility location and relocation problem with time dependent weights and discrete planning horizon. Annals of Operations Research, 167:353–368.

    Article  Google Scholar 

  121. Fetter, F. A. (1924). The economic law of market areas. The Quarterly Journal of Economics, 38:520–529.

    Article  Google Scholar 

  122. Francis, R. L., McGinnis Jr., L. F., and White, J. A. (1992). Facility Layout and Location: An Analytical Approach. Prentice Hall, Englewood Cliffs, NJ, Second edition.

    Google Scholar 

  123. García, S., Labbé, M., and Marín, A. (2011). Solving large p-median problems with a radius formulation. INFORMS Journal on Computing, 23:546–556.

    Article  Google Scholar 

  124. García, S. and Marín, A. (2015). Covering location problems. In Laporte, G., Nickel, S., and da Gama, F. S., editors, Location Science, pages 93–114. Springer, Heidelberg.

    Google Scholar 

  125. Gill, P. E., Murray, W., and Saunders, M. A. (2005). SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM review, 47:99–131.

    Article  Google Scholar 

  126. Gini, C. (1921). Measurement of inequality and incomes. The Economic Journal, 31:124–126.

    Article  Google Scholar 

  127. Glover, F. and Laguna, M. (1997). Tabu Search. Kluwer Academic Publishers, Boston.

    Book  Google Scholar 

  128. Goldberg, D. E. (2006). Genetic Algorithms. Pearson Education, Delhi, India.

    Google Scholar 

  129. Hanselman, D. and Littlefield, B. C. (1997). Mastering MATLAB 5: A Comprehensive Tutorial and Reference. Prentice Hall PTR.

    Google Scholar 

  130. Hansen, P., Jaumard, B., and Krau, S. (1995). An algorithm for Weber’s problem on the sphere. Location Science, 3:217–237.

    Article  Google Scholar 

  131. Hansen, P. and Mladenović, N. (1997). Variable neighborhood search for the \(p\)-median. Location Science, 5:207–226.

    Article  Google Scholar 

  132. Hansen, P., Mladenović, N., and Taillard, É. (1998). Heuristic solution of the multisource Weber problem as a \(p\)-median problem. Operations Research Letters, 22:55–62.

    Article  Google Scholar 

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

    Google Scholar 

  134. Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI.

    Google Scholar 

  135. Horne, J. and Smith, J. (2005). A dynamic programming algorithm for the conditional covering problem on tree graphs. Networks, 46:186–197.

    Article  Google Scholar 

  136. Huff, D. L. (1964). Defining and estimating a trade area. Journal of Marketing, 28:34–38.

    Article  Google Scholar 

  137. Huff, D. L. (1966). A programmed solution for approximating an optimum retail location. Land Economics, 42:293–303.

    Article  Google Scholar 

  138. Kalczynski, P. and Drezner, Z. (2019). Locating multiple facilities using the max-sum objective. Computers and Industrial Engineering, 129:136–143.

    Article  Google Scholar 

  139. Kalczynski, P. and Drezner, Z. (2021a). Extremely non-convex optimization problems: The case of the multiple obnoxious facilities location. Optimization Letters. https://doi.org/10.1007/s11590-021-01731-2.

    Article  Google Scholar 

  140. Kalczynski, P. and Drezner, Z. (2021b). The obnoxious facilities planar \(p\)-median problem. OR Spectrum, 43:577–593.

    Article  Google Scholar 

  141. Kalczynski, P., Suzuki, A., and Drezner, Z. (2021). Multiple obnoxious facilities with weighted demand points. Journal of the Operational Research Society. https://doi.org/10.1080/01605682.2020.1851149.

    Article  Google Scholar 

  142. Kalczynski, P., Suzuki, A., and Drezner, Z. (2021). Obnoxious facility location in multiple dimensional space. In review.

    Google Scholar 

  143. Karasakal, O. and Karasakal, E. (2004). A maximal covering location model in the presence of partial coverage. Computers & Operations Research, 31:15–26.

    Article  Google Scholar 

  144. Karatas, M. (2017). A multi-objective facility location problem in the presence of variable gradual coverage performance and cooperative cover. European Journal of Operational Research, 262:1040–1051.

    Article  Google Scholar 

  145. Kariv, O. and Hakimi, S. L. (1979). An algorithmic approach to network location problems. I: The \(p\)-centers. SIAM Journal on Applied Mathematics, 37:513–538.

    Article  Google Scholar 

  146. Katz, I. N. and Cooper, L. (1980). Optimal location on a sphere. Computers & Mathematics with Applications, 6:175–196.

    Article  Google Scholar 

  147. Krarup, J. and Vajda, S. (1997). On Torricelli’s geometrical solution to a problem of fermat. IMA Journal of Management Mathematics, 8:215–224.

    Article  Google Scholar 

  148. Krau, S. (1997). Extensions du problème de Weber. PhD thesis, École Polytechnique de Montréal.

    Google Scholar 

  149. Kuby, M. (1987). Programming models for facility dispersion: The \(p\)-dispersion and maxisum dispersion problems. Geographical Analysis, 19(4):315–329.

    Article  Google Scholar 

  150. Kuenne, R. E. and Soland, R. M. (1972). Exact and approximate solutions to the multisource Weber problem. Mathematical Programming, 3:193–209.

    Article  Google Scholar 

  151. Launhardt, W. (1885). Mathematische Begründung der Volkswirthschaftslehre. W. Engelmann.

    Google Scholar 

  152. Law, A. M. and Kelton, W. D. (1991). Simulation Modeling and Analysis. McGraw-Hill, New York, Second edition.

    Google Scholar 

  153. Lee, D. T. and Schachter, B. J. (1980). Two algorithms for constructing a Delaunay triangulation. International Journal of Parallel Programming, 9:219–242.

    Google Scholar 

  154. Locatelli, M. and Raber, U. (2002). Packing equal circles in a square: A deterministic global optimization approach. Discrete Applied Mathematics, 122:139–166.

    Article  Google Scholar 

  155. Lopez, C. and Beasley, J. E. (2011). A heuristic for the circle packing problem with a variety of containers. European Journal of Operational Research, 214:512–525.

    Article  Google Scholar 

  156. Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9:209–219.

    Article  Google Scholar 

  157. Lösch, A. (1954). The Economics of Location. Yale University Press, New Haven, CT.

    Google Scholar 

  158. Love, R. F., Morris, J. G., and Wesolowsky, G. O. (1988). Facilities Location: Models & Methods. North Holland, New York, NY.

    Google Scholar 

  159. Maimon, O. (1986). The variance equity measure in locational decision theory. Annals of Operations Research, 6:147–160.

    Article  Google Scholar 

  160. Maranas, C. D. and Floudas, C. A. (1993). A global optimization method for Weber’s problem with attraction and repulsion. In Hager, W. W., Hearn, D. W., and Pardalos, P. M., editors, Large Scale Optimization: State of the Art, pages 259–293. Kluwer, Dordrecht.

    Google Scholar 

  161. Maranas, C. D., Floudas, C. A., and Pardalos, P. M. (1995). New results in the packing of equal circles in a square. Discrete Mathematics, 142:287–293.

    Article  Google Scholar 

  162. Medhi, J. (2002). Stochastic Models in Queueing Theory. Elsevier, San Diego, CA.

    Google Scholar 

  163. Megiddo, N. and Supowit, K. J. (1984). On the complexity of some common geometric location problems. SIAM Journal on Computing, 13:182–196.

    Article  Google Scholar 

  164. Melachrinoudis, E. (2011). The location of undesirable facilities. In Foundations of Location Analysis, pages 207–239. Springer, New York.

    Chapter  Google Scholar 

  165. Melachrinoudis, E. and Cullinane, P. (1985). Locating an undesirable facility within a geographical region using the maximin criterion. Journal of Regional Science, 25:115–127.

    Article  Google Scholar 

  166. Melachrinoudis, E., Min, H., and Cullinane, P. (1996). A multiobjective model for the dynamic location of landfills. Location Science, 3:143–166.

    Article  Google Scholar 

  167. Melachrinoudis, E. and Xanthopulos, Z. (2003). Semi-obnoxious single facility location in euclidean space. Computers & Operations Research, 30:2191–2209.

    Article  Google Scholar 

  168. Minieka, E. (1980). Conditional centers and medians on a graph. Networks, 10:265–272.

    Article  Google Scholar 

  169. Mladenović, N. and Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24:1097–1100.

    Article  Google Scholar 

  170. Morohosi, H. and Furuta, T. (2017). Two approaches to cooperative covering location problem and their application to ambulance deployment. In Operations Research Proceedings 2015, pages 361–366. Springer, Cham, Switzerland.

    Chapter  Google Scholar 

  171. Murtagh, B. A. and Niwattisyawong, S. R. (1982). An efficient method for the multi-depot location-allocation problem. Journal of the Operational Research Society, 33:629–634.

    Google Scholar 

  172. Nickel, S. and Puerto, J. (2005). Facility Location—A Unified Approach. Springer Verlag, Berlin.

    Google Scholar 

  173. Nurmela, K. J. and Oestergard, P. (1999). More optimal packings of equal circles in a square. Discrete & Computational Geometry, 22:439–457.

    Article  Google Scholar 

  174. Ogryczak, W. and Zawadzki, M. (2002). Conditional median: A parametric solution concept for location problems. Annals of Operations Research, 110:167–181.

    Article  Google Scholar 

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

    Book  Google Scholar 

  176. O’kelly, M. E. (1987). A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research, 32:393–404.

    Google Scholar 

  177. Ostresh Jr., L. M. (1978). On the convergence of a class of iterative methods for solving the Weber location problem. Operations Research, 26:597–609.

    Article  Google Scholar 

  178. Plastria, F. (1991). The effects of majority in Fermat-Weber problems with attraction and repulsion. Yugoslav Journal of Operations Research, 1:141–146.

    Google Scholar 

  179. Plastria, F. (2002). Continuous covering location problems. In Drezner, Z. and Hamacher, H. W., editors, Facility Location: Applications and Theory, pages 39–83. Springer, Berlin.

    Google Scholar 

  180. Prömel, H. J. and Steger, A. (2012). The Steiner Tree Problem: A Tour Through Graphs, Algorithms, and Complexity. Springer Science & Business Media.

    Google Scholar 

  181. Reilly, W. J. (1931). The Law of Retail Gravitation. Knickerbocker Press, New York, NY.

    Google Scholar 

  182. ReVelle, C. (1986). The maximum capture or sphere of influence problem: Hotelling revisited on a network. Journal of Regional Science, 26:343–357.

    Article  Google Scholar 

  183. ReVelle, C., Toregas, C., and Falkson, L. (1976). Applications of the location set covering problem. Geographical Analysis, 8:65–76.

    Article  Google Scholar 

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

    Article  Google Scholar 

  185. Shamos, M. and Hoey, D. (1975). Closest-point problems. Proceedings 16th Annual Symposium on the Foundations of Computer Science, pages 151–162, Berkeley, CA.

    Google Scholar 

  186. Shier, D. R. (1977). A min-max theorem for p-center problems on a tree. Transportation Science, 11:243–252.

    Article  Google Scholar 

  187. Skorin-Kapov, D., Skorin-Kapov, J., and O’Kelly, M. (1996). Tight linear programming relaxations of uncapacitated \(p\)-hub median problems. European Journal of Operational Research, 94:582–593.

    Article  Google Scholar 

  188. Snyder, L. V. (2011). Covering problems. In Eiselt, H. A. and Marianov, V., editors, Foundations of Location Analysis, pages 109–135. Springer, New York.

    Chapter  Google Scholar 

  189. Sugihara, K. (2002). Laguerre voronoi diagram on the sphere. Journal for Geometry and Graphics, 6:69–81.

    Google Scholar 

  190. Sugihara, K. and Iri, M. (1992). Construction of the voronoi diagram for “one million" generators in single-precision arithmetic. Proceedings of the IEEE, 80:1471–1484.

    Article  Google Scholar 

  191. Sugihara, K. and Iri, M. (1994). A robust topology-oriented incremental algorithm for Voronoi diagram. International Journal of Computational Geometry and Applications, 4:179–228.

    Article  Google Scholar 

  192. Suzuki, A. (2019). Big triangle small triangle method for the Weber problem on the sphere. In Eiselt, H. A. and Marianov, V., editors, Contributions to Location Analysis—In Honor of Zvi Drezner’s 75th Birthday, pages 109–123. Springer Nature, Switzerland.

    Chapter  Google Scholar 

  193. Suzuki, A. and Drezner, Z. (2009). The minimum equitable radius location problem with continuous demand. European Journal of Operational Research, 195:17–30.

    Article  Google Scholar 

  194. Suzuki, A. and Okabe, A. (1995). Using Voronoi diagrams. In Drezner, Z., editor, Facility Location: A Survey of Applications and Methods, pages 103–118. Springer, New York.

    Chapter  Google Scholar 

  195. Sylvester, J. (1857). A question in the geometry of situation. Quarterly Journal of Mathematics, 1:79.

    Google Scholar 

  196. Sylvester, J. (1860). On Poncelet’s approximate linear valuation of Surd forms. Philosophical Magazine, 20 (Fourth series):203–222.

    Google Scholar 

  197. Szabo, P. G., Markot, M., Csendes, T., and Specht, E. (2007). New Approaches to Circle Packing in a Square: With Program Codes. Springer, New York.

    Google Scholar 

  198. Taillard, É. (2003). Heuristic methods for large centroid clustering problems. Journal of Heuristics, 9:51–73.

    Article  Google Scholar 

  199. Teran-Somohano, A. and Smith, A. E. (2019). Locating multiple capacitated semi-obnoxious facilities using evolutionary strategies. Computers & Industrial Engineering, 133:303–316.

    Article  Google Scholar 

  200. Voronoï, G. (1908). Nouvelles applications des paramètres continus à la théorie des formes quadratiques. deuxième mémoire. recherches sur les parallélloèdres primitifs. Journal für die reine und angewandte Mathematik, 134:198–287.

    Article  Google Scholar 

  201. Wang, S.-C. and Chen, T.-C. (2017). Multi-objective competitive location problem with distance-based attractiveness and its best non-dominated solution. Applied Mathematical Modelling, 47:785–795.

    Article  Google Scholar 

  202. 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.

    Google Scholar 

  203. Weiszfeld, E. (1937). Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Mathematical Journal, First Series, 43:355–386.

    Google Scholar 

  204. Weiszfeld, E. and Plastria, F. (2009). On the point for which the sum of the distances to n given points is minimum. Annals of Operations Research, 167:7–41 (English Translation of Weiszfeld [203]).

    Google Scholar 

  205. Welch, S. B., Salhi, S., and Drezner, Z. (2006). The multifacility maximin planar location problem with facility interaction. IMA Journal of Management Mathematics, 17:397–412.

    Article  Google Scholar 

  206. Wendell, R. E. and Hurter, A. P. (1973). Location theory, dominance and convexity. Operations Research, 21:314–320.

    Article  Google Scholar 

  207. Wesolowsky, G. O. (1993). The Weber problem: History and perspectives. Location Science, 1:5–23.

    Google Scholar 

  208. Wolfram, S. (2020). Mathematica, Version 12.2. Champaign, IL. https://www.wolfram.com/mathematica.

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    Zvi Drezner

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Drezner, Z. (2022). Continuous Facility Location Problems. In: Salhi, S., Boylan, J. (eds) The Palgrave Handbook of Operations Research . Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-96935-6_9

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