The paper addresses the optimal bus stops allocation in the Laško municipality. The goal is to achieve a cost reduction by proper re-designing of a mandatory pupils’ transportation to their schools. The proposed heuristic optimization algorithm relies on data clustering and Monte Carlo simulation. The number of bus stops should be minimal possible that still assure a maximal service area, while keeping the minimal walking distances children have to go from their homes to the nearest bus stop. The working mechanism of the proposed algorithm is explained. The latter is driven by three-dimensional GIS data to take into account as much realistic dynamic properties of terrain as possible. The results show that the proposed algorithm achieves an optimal solution with only 37 optimal bus stops covering 94.6 % of all treated pupils despite the diversity and wideness of municipality, as well as the problematic characteristics of terrains’ elevation. The calculated bus stops will represent important guidelines to their actual physical implementation.
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 J. Park and B.-i. Kim “The school bus routing problem : A review” European Journal of Operational Research vol. 202 no. 2 pp. 311-319 2010.
 J. Desrosiers J. Ferland J. Rousseau and G. Lapalme “TRANSCOL: a multi-period school bus routing and scheduling system” TIMS Studies in the Management Sciences vol. 22 1986.
 K. Worwa “Minimization of Number of Buses in the School Bus Routing Problem” Research in logistics and producton vol. 7 no. 2 pp. 127-141 2017.
 R. Farahani and M. Hekmatfar Facility Location: Concepts Models Algorithms and Case Studies. Springer 2009.
 R. L. Francis F. M. Jr and J. A. White Facility Layout and Location: An Analytical Approach 2 edition ed. Englewood Cliffs N.J: Pearson 1991 p. 592.
 R. Church and C. R. ReVelle “The Maximal Covering Location Problem” Papers in Regional Science vol. 32 no. 1 pp. 101-1181974.
 D. Dragan T. Kramberger and M. Lipičnik “Monte Carlo Simulation-based Approach to Optimal Bus Stops Allocation in the Municipality of Laško” PROMET - Traffic&Transportation vol. 23 no. 4 pp. 265-278 2012.
 D. Dragan T. Kramberger A. Lisec M. Intihar and K. Prah “Using GIS for the Optimization of Pupils Transportation: The Case of Laško Municipality” Logistics & sustainable transport vol. 2 pp. 35-51 2011.
 T. Kramberger D. Dragan and K. Prah “A heuristic approach to reduce carbon dioxide emissions” Proceedings of the Institution of Civil Engineers - Transport vol. 167 no. 5 pp. 296-305 2014.
 D. Dragan T. Kramberger and K. Prah “Transport Optimization and Estimation of Reduced CO2 Emissions” in Sustainable Logistics and Strategic Transportation Planning T. Kramberger Ed.Tomaž Kramberger Vesna Ipavec: IGI Glogal 2016 pp. 412-443.
 J. E. Harmon and S. J. Anderson The Design and Implementation of Geographic Information Systems 1 edition ed. Hoboken N.J: Wiley 2003 p. 272.
 V. Marianov and D. Serra Location Problems in the Public Sector. Facility Location: Applications and Theory. Berlin 2002.
 M. S. Daskin Network and Discrete Location: Models Algorithms and Applications 2 edition ed. Hoboken New Jersey: Wiley 2013 p. 536.
 X. Li and A. G.-O. Yeh “Integration of genetic algorithms and GIS for optimal location search” International Journal of Geographical Information Science vol. 19 no. 5 pp. 581-601 2005.
 J. H. Jaramillo J. Bhadury and R. Batta “On the Use of Genetic Algorithms to Solve Location Problems” Computers & Operations Research vol. 29 pp. 761-779 2002.
 A. T. Murray and R. L. Church “Applying simulated annealing to location-planning models” (in en) Journal of Heuristics vol. 2 no. 1 pp. 31-53 1996.
 J. Aerts and G. Heuvelink “Using Simulated Annealing for Resource Allocation” International Journal of Geographical Information Science vol. 16 pp. 571-587 2002.
 D. M. Jaeggi G. T. Parks T. Kipouros and P. J. Clarkson “The development of a multi-objective Tabu Search algorithm for continuous optimisation problems” European Journal of Operational Research vol. 185 no. 3 pp. 1192-1212 2008.
 M. Sun “Solving the uncapacitated facility location problem using tabu search” Computers & Operations Research vol. 33 no. 9 pp. 2563-2589 2006.
 R. D. Galvao and C. Revelle “A Lagrangean heuristic for the maximal covering location problem” European Journal of Operational Research vol. 88 no 1 pp. 114-123 1996.
 V. Marianov and D. Serra “New Trends in Public Facility Location Modeling” in UPF Economics and Business Working Paper 755 2004.
 J. M. Gleason “A set covering approach to bus stop location” Omega vol. 3 no. 5 pp. 605-608 1975.
 E. Carrizosa J. Harbering and A. Schöbel “The Stop Location Problem with Realistic Traveling Time” in ATMOS - 13th Workshop on Algorithmic Approaches for Transportation Modelling Optimization and Systems - 2013 Schloss Dagstuhl―Leibniz-Zentrum fuer Informatik vol. 33 pp. 80-93 2013.
 A. Schöbel Optimization in Public Transportation: Stop Location Delay Management and Tariff Zone Design in a Public Transportation Network. Springer 2007 p. 267.
 R. L. Church “Geographical information systems and location science” Computers & Operations Research vol. 29 pp. 541-562 2002.
 L. Y. O. Li and Z. Fu “The school bus routing problem: a case study” Journal of the Operational Research Society vol. 53 no. 5 pp. 552-558 2002.
 Statistični Urad. (2017 March 24). Občina Laško. Available: http://www.stat.si/obcine/sl/2014/Municip/Index/78
 P. Horvat Geografija občine Laško. Filozofska fakulteta Univerze v Ljubljani 2006.
 P. Kovač “The Geography of the Municipality of Laško” University of Ljubljana 2006.
 D. Perko and A. M. Orožen Slovenija: pokrajine in ljudje. Ljubljana 2001.
 P. Očkerl Priročnik za izvajanje in spremljanje poti v šolo Ljubljana 2017
 M. Ogrin T. R. Planinc M. Ilc and A. Plevnik Trajnostna mobilnost: priročnik za učitelje v osnovnih šolah Ljubljana: Ministrstvo za infrastrukturo in prostor 2013.
 GURS: Geodetska uprava Republike Slovenije: Digitalni ortofoto 050 2017.
 R. S. King Cluster Analysis and Data Mining: An Introduction Har/Cdr edition ed. Dulles Virginia; Boston Massachusetts; New Delhi: Mercury Learning & Information 2014 p. 300.
 C. C. Aggarwal and C. K. Reddy Data Clustering: Algorithms and Applications 1 edition. Boca Raton: Chapman and Hall/CRC 2013 p. 652.
 B. Everitt Cluster analysis. Chichester West Sussex: Wiley 2011.