Abstract
School location problems are notoriously wicked to tackle due to the multiplicity of actors involved, the emotional value of a child’s education, and the sheer number of conflicting objectives and constraints. School capacity constraints are particularly challenging because they may well invalidate the desirable property that students be assigned to their closest school. In this chapter, we present a new multi-objective problem formulated as a capacitated p-median model that explicitly addresses this point, as well as assignment of students to schools deemed excessively distant. We also propose a two-phase heuristic algorithm where Tabu Search solves the location portion of the problem, while Greedy/Genetic Algorithms solve the student allocation problem, following by a local post-optimization phase. This process is supplemented by a step of spatially local re-optimization. The model is implemented as a tightly-coupled spatial decision support system called the interactive Graphical Location-Allocation School System (iGLASS), which is built on an open-source GIS software platform. We test the location planning system on the Charlotte-Mecklenburg Schools (CMS) system in Charlotte, North Carolina. Overall, our two + one-phase heuristic exhibits a performance close to that of a commercial solver (CPLEX), but requires a much lower computational effort. It is scalable, interactive and offers the opportunity to evaluation a large variety of solutions. The proposed model is beneficial to policy-makers seeking to improve the provision and efficiency of public services. The portability of the interface and the interactive features of the SDSS make it applicable to other location-allocation problems.
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References
Murray AT (2010) Advances in location modeling: GIS linkages and contributions. J Geogr Syst 12(3):335–354
Scott AJ (1970) Location-allocation systems: a review. Geogr Anal 2(2):95–119
Church RL, Murray AT (2009) Business site selection, location analysis, and GIS. Wiley, New York
Weber A (1909) Uber den Standort der Industrien, 1909; (translated as Alfred Weber’s theory of the location of industries in 1929). University of Chicago, Chicago
Brandeau ML, Chiu SS (1989) An overview of representative problems in location research. Manag Sci 35(6):645–674
Hakimi SL (1964) Optimum locations of switching centers and the absolute centers and medians of a graph. Oper Res 12(3):450–459
Francis RL, McGinnis LF, White JA (1983) Locational analysis. Eur J Oper Res 12(3): 220–252
Current J, Min H, Schilling D (1990) Multiobjective analysis of facility location decisions. Eur J Oper Res 49(3):295–307
Mirchandani PB, Francis RL (1990) Discrete location theory. Wiley, New York
Hakimi SL (1965) Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper Res 13(3):462–475
ReVelle CS, Swain RW (1970) Central facilities location. Geogr Anal 2(1):30–42
Kuehn AA, Hamburger MJ (1963) A heuristic program for locating warehouses. Manag Sci 9(4):643–666
Maranzana F (1964) On the location of supply points to minimize transport costs. Oper Res Q 15(3):261–270
Teitz MB, Bart P (1968) Heuristic methods for estimating the generalized vertex median of a weighted graph. Oper Res 16(5):955–961
Salhi S, Gamal M (2003) A genetic algorithm based approach for the uncapacitated continuous location–allocation problem. Ann Oper Res 123(1):203–222
Crainic TG, Gendreau M, Soriano P, Toulouse M (1993) A tabu search procedure for multicommodity location/allocation with balancing requirements. Ann Oper Res 41(4): 359–383
Antunes A, Peeters D (2001) On solving complex multi-period location models using simulated annealing. Eur J Oper Res 130(1):190–201
Li X, He J, Liu X (2009) Intelligent GIS for solving high-dimensional site selection problems using ant colony optimization techniques. Int J Geogr Inf Sci 23(4):399–416
Bischoff M, Dächert K (2009) Allocation search methods for a generalized class of location–allocation problems. Eur J Oper Res 192(3):793–807
Teitz MB (1968) Toward a theory of urban public facility location. Pap Reg Sci Assoc 21(1):35–51
DeVerteuil G (2000) Reconsidering the legacy of urban public facility location theory in human geography. Prog Hum Geogr 24(1):47–69
Church RL, ReVelle C (1974) The maximal covering location problem. Pap Reg Sci Assoc 32(1):101–118
Hillsman E (1984) The p-median structure as a unified linear model for location-allocation analysis. Environ Plan A 16:305–318
Toregas C, Swain R, ReVelle C, Bergman L (1971) The location of emergency service facilities. Oper Res 19(6):1363–1373
Ellwein LB, Gray P (1971) Solving fixed charge location-allocation problems with capacity and configuration constraints. AIIE Trans 3(4):290–298
NCDPI (2012) Highlights of the North Carolina Public School Budget [cited]. Available from http://www.ncpublicschools.org/docs/fbs/resources/data/highlights/2012highlights.pdf
Murray AT, Gerrard RA (1997) Capacitated service and regional constraints in location-allocation modeling. Locat Sci 5(2):103–118
Delmelle EM, Thill J-C, Peeters D, Thomas I (2014) A multi-period capacitated school location problem with modular equipment and closest assignment considerations. J Geogr Syst 16(3):263–286
Araya F, Dell R, Donoso P, Marianov V, Martínez F, Weintraub A (2012) Optimizing location and size of rural schools in Chile. Int Trans Oper Res 19(5):695–710
Teixeira JC, Antunes AP (2008) A hierarchical location model for public facility planning. Eur J Oper Res 185(1):92–104
Gerrard RA, Church RL (1996) Closest assignment constraints and location models: properties and structure. Locat Sci 4(4):251–270
Antunes A, Peeters D (2000) A dynamic optimization model for school network planning. Socio Econ Plan Sci 34(2):101–120
Antunes A, Berman O, Bigotte J, Krass D (2009) A location model for urban hierarchy planning with population dynamics. Environ Plan A 41(4):996–1016
Church RL, Murray AT (1993) Modeling school utilization and consolidation. J Urban Plan Dev 119(1):23–38
Wesolowsky GO (1973) Dynamic facility location. Manag Sci 19(11):1241–1248
Müller S (2008) Dynamic school network planning in urban areas: a multi-period, cost-minimizing location planning approach with respect to flexible substitution patterns of facilities. Lit, Munster
Heckman LB, Taylor HM (1969) School rezoning to achieve racial balance: a linear programming approach. Socio Econ Plan Sci 3(2):127–133
Maxfield D (1972) Spatial planning of school districts. Ann Assoc Am Geogr 62(4):582–590
Clarke S, Surkis J (1968) An operations research approach to racial desegregation of school systems. Socio Econ Plan Sci 1(3):259–272
Church R, Schoepfle OB (1993) The choice alternative to school assignment. Environ Plan B 20(4):447–457
Müller S, Haase K, Kless S (2009) A multiperiod school location planning approach with free school choice. Environ Plan A 41(12):2929–2945
ESRI (2010) ArcGIS 10. online help. ESRI [cited]. Available from http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//004700000050000000
Church RL (2002) Geographical information systems and location science. Comput Oper Res 29(6):541–562
Armstrong M, Densham P (2008) Cartographic support for locational problem-solving by groups. Int J Geogr Inf Sci 22(7):721–749
Densham PJ (1991) Spatial decision support systems. In: Geographical information systems: principles and applications, vol vol 1, pp 403–412
Eldrandaly K (2010) A GEP-based spatial decision support system for multisite land use allocation. Appl Soft Comput 10(3):694–702
Ribeiro A, Antunes AP (2002) A GIS-based decision-support tool for public facility planning. Environ Plan B 29(4):553–570
Tong D, Murray A, Xiao N (2009) Heuristics in spatial analysis: a genetic algorithm for coverage maximization. Ann Assoc Am Geogr 99(4):698–711
Glover F, McMillan C (1986) The general employee scheduling problem. An integration of MS and AI. Comput Oper Res 13(5):563–573
Glover F (1989) Tabu search—part I. ORSA J Comput 1(3):190–206
Black PE (2013) Greedy algorithm. U.S. National Institute of Standards and Technology (NIST), 2005 [cited 2013]
Holland JH (1975) Adaption in natural and artificial systems. University of Michigan Press, Ann Arbor, MI
Hosage C, Goodchild M (1986) Discrete space location-allocation solutions from genetic algorithms. Ann Oper Res 6(2):35–46
Zhang X, Armstrong MP (2008) Genetic algorithms and the corridor location problem: multiple objectives and alternative solutions. Environ Plan B 35(1):148–168
Xiao N, Bennett DA, Armstrong MP (2002) Using evolutionary algorithms to generate alternatives for multiobjective site-search problems. Environ Plan A 34(4):639–656
Li X, Liu Z, Zhang X (2009) Applying genetic algorithm and Hilbert curve to capacitated location allocation of facilities. In: Proceedings of the 2009 international conference on artificial intelligence and computational intelligence, pp 378–383
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The authors are grateful to the Renaissance Computing Institute of North Carolina for funding this research.
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Chen, M., Thill, JC., Delmelle, E. (2018). iGLASS: An Open Source SDSS for Public School Location-Allocation. In: Thill, JC., Dragicevic, S. (eds) GeoComputational Analysis and Modeling of Regional Systems. Advances in Geographic Information Science. Springer, Cham. https://doi.org/10.1007/978-3-319-59511-5_17
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DOI: https://doi.org/10.1007/978-3-319-59511-5_17
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