, Volume 13, Issue 1, pp 1–56 | Cite as

Towards a unified territorial design approach — Applications, algorithms and GIS integration

  • Jörg Kalcsics
  • Stefan Nickel
  • Michael Schröder


Territory design may be viewed as the problem of grouping small geographic areas into larger geographic clusters called territories in such a way that the latter are acceptable according to relevant planning criteria. In this paper we review the existing literature for applications of territory design problems and solution approaches for solving these types of problems. After identifying features common to all applications we introduce a basic territory design model and present in detail two approaches for solving this model: a classical location-allocation approach combined with optimal split resolution techniques and a newly developed computational geometry based method. We present computational results indicating the efficiency and suitability of the latter method for solving large-scale practical problems in an interactive environment. Furthermore, we discuss extensions to the basic model and its integration into Geographic Information Systems.

Key Words

Territory design political districting sales territory alignment optimization algorithms Geographical Information Systems computational geometry 

AMS subject classification

90C59 90B80 68U05 90-02 


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  1. Andria F., Chiancone P. and Piraino S. (1979). Die Anwendung der Dynamischen Optimierung bei der Sozial-Sanitären Bezirkseinteilung.Zeitschrift für Operations Research B 23, 33–43.CrossRefGoogle Scholar
  2. Baker J.R., Clayton E.R. and Moore L.J. (1989). Redesign of Primary Response Areas for County Ambulance Services.European Journal of Operational Research 41, 23–32.CrossRefGoogle Scholar
  3. Bergey P.K., Ragsdale C.T. and Hoskote M. (2003). A Simulated Annealing Genetic Algorithm for the Electrical Power Districting Problem.Annals of Operations Research 121, 33–55.CrossRefGoogle Scholar
  4. Blais M., Lapierre S.D. and Laporte G. (2003). Solving a Home-Care Districting Problem in an Urban Setting.Journal of the Operational Research Society 54, 1141–1147.CrossRefGoogle Scholar
  5. Bodin L.D. (1973). A Districting Experiment with a Clustering Algorithm.Annals of the New York Academy of Sciences 19, 209–214.CrossRefGoogle Scholar
  6. Bourjolly J.-M., Laporte G. and Rousseau J.-M. (1981). Découpage Électoral Automatisé: Application à l’Île de Montréal.INFOR 19, 113–124.Google Scholar
  7. Bozkaya B., Erkut E. and Laporte G. (2003). A Tabu Search Heuristic and Adaptive Memory Procedure for Political Districting.European Journal of Operational Research 144, 12–26.CrossRefGoogle Scholar
  8. Bozkaya B., Erkut E., Laporte G. and Neuman S. (2005).Political Districting: Solving a Multi-Objective Problem Using Tabu Search. Kluwer.Google Scholar
  9. Browdy M.H. (1990). Simulated Annealing: An Improved Computer Model for Political Redistricting.Yale Law and Policy Review 8, 163–179.Google Scholar
  10. Cirincione C., Darling T.A. and O’Rourke T.G. (2000). Assessing South Carolina’s 1990s Congressional Districting.Political Geography 19, 189–211.CrossRefGoogle Scholar
  11. Chance C.W. (1965). Political Studies: Number 2 — Representation and Reappointment. Department of Political Science, Ohio State University, Columbus.Google Scholar
  12. Cloonan J.B. (1975). A Note on the Compactness of Sales Territories.Management Science 19, 469.Google Scholar
  13. Deckro R.F. (1977). Multiple Objective Districting: A General Heuristic Approach Using Multiple Criteria.Operational Research Quarterly 28, 953–961.Google Scholar
  14. Drexl A. and Haase K. (1999). Fast Approximation Methods for Sales Force Deployment.Management Science 45:1307–1323, 1999.Google Scholar
  15. D’Amico S.J., Wang S.-J., Batta R. and Rump C.M. (2002). A Simulated Annealing Approach to Police District Design.Computers and Operations Research 29, 667–684.CrossRefGoogle Scholar
  16. Easingwood C. (1973). A Heuristic Approach to Selecting Sales Regions and Territories.Operational Research Quarterly 24, 527–534.Google Scholar
  17. Ferland J.A. and Guénette G. (1990). Decision Support System for a School Districting Problem.Operations Research 38, 15–21.Google Scholar
  18. Fleischmann B. and Paraschis J.N. (1988). Solving a Large Scale Districting Problem: A Case Report.Computers and Operations Research 15, 521–533.CrossRefGoogle Scholar
  19. Forman S.L. and Yue Y. (2003). Congressional Districting Using a TSP-Based Genetic Algorithm. In: Cantu-Paz E., Foster J.A., Deb K., David L., Rajkumar R. (eds.),Genetic and Evolutionary Computation-GECCO 2003. Proceedings, Lecture Notes in Computer Science 2723. Springer Verlag, 2072–2083.Google Scholar
  20. Forrest E. (1964). Apportionment by Computer.American Behavioral Scientist 23, 23–35.CrossRefGoogle Scholar
  21. Garfinkel R.S. (1968).Optimal Political Districting. PhD thesis, The Johns Hopkins University, 1968. Also as working paper # 6812, College of Business Administration. University of Rochester.Google Scholar
  22. Garfinkel R.S. and Nemhauser G.L. (1970). Optimal Political Districting by Implicit Enumeration Techniques.Management Science 16, 495–508.Google Scholar
  23. George J.A., Lamar B.W. and Wallace C.A. (1997). Political District Determination Using Large-Scale Network Optimization.Socio-Economic Planning Sciences 31, 11–28.CrossRefGoogle Scholar
  24. Glaze T.A. and Weinberg C.B. (1979). A Sales Territory Alignment Program and Account Planning System. In: Bagozzi R. (ed.),Sales Management: New Developments from Behavioral and Decision Model Research. Marketing Science Institute, Cambridge, 325–343.Google Scholar
  25. Grilli di Cortona P., Manzi C., Pennisi A., Ricca F. and Simeone B. (1999).Evaluation and Optimization of Electoral Systems. SIAM Monographs on Discrete Mathematics and Applications.Google Scholar
  26. Hanafi S., Freville A. and Vaca P. (1999). Municipal Solid Waste Collection: An Effective Data Structure for Solving the Sectorization Problem with Local Search Methods.INFOR 37, 236–254.Google Scholar
  27. Helbig R.E., Orr P.K. and Roediger R.R. (1972). Political Redistricting by Computer.Communications of the ACM 15, 735–741.CrossRefGoogle Scholar
  28. Hess S.W. and Samuels S.A. (1971). Experiences with a Sales Districting Model: Criteria and Implementation.Management Science 18, 41–54.Google Scholar
  29. Hess S.W., Weaver J.B., Siegfeldt H.J., Whelan J.N. and Zitlau P.A. (1965). Nonpartisan Political Redistricting by Computer.Operations Research 13, 998–1008.Google Scholar
  30. Hojati M. (1996). Optimal Political Districting.Computers and Operations Research 23, 1147–1161.CrossRefGoogle Scholar
  31. Horn D.L., Hampton C.R. and Vandenberg A.J. (1993). Practical Application of District Compactness.Political Geography 12, 103–120.CrossRefGoogle Scholar
  32. Howick R.S. and Pidd M. (1990). Sales Force Deployment Models.European Journal of Operational Research 48, 295–310.CrossRefGoogle Scholar
  33. Kalcsics J., Melo T., Nickel S. and Gündra H. (2001). Planning Sales Territories - a Facility Location Approach. Operations Research Proceedings 2001. Springer Verlag, 141–148.Google Scholar
  34. Lewyn M.E. (1993). How to Limit Gerrymandering.Florida Law Review 45, 403–486.Google Scholar
  35. Lodish L.M. (1975). Sales Territory Alignment to Maximize Profit.Journal of Marketing Research 12, 30–36.CrossRefGoogle Scholar
  36. Macmillan W. and Pierce T. (1992). Optimization Modelling in a GIS Framework: The Problem of Political Districting. Specialist meeting, April 16–18, 1992. National Center for Geographic Information and Analysis.Google Scholar
  37. Marlin P.G. (1981). Application of the Transportation Model to a Large-Scale “Districting” Problem.Computers and Operations Research 8, 83–96.CrossRefGoogle Scholar
  38. Mehrotra A., Johnson E.L. and Nemhauser G.L. (1998). An Optimization Based Heuristic for Political Districting.Management Science 44, 1100–1114.CrossRefGoogle Scholar
  39. Minciardi R., Puliafito P.P. and Zoppoli R. (1981). A Districting Procedure for Social Organizations.European Journal of Operational Research 8, 47–57.CrossRefGoogle Scholar
  40. Muyldermans L., Cattrysse D., van Oudheusden D. and Lotan T. (2002). Districting for Salt Spreading Operations.European Journal of Operational Research 139, 521–532.CrossRefGoogle Scholar
  41. Niemi R.G., Grofman B., Carlucci C. and Hofeller T. (1990). Measuring Compactness and the Role of a Compactness Standard in a Test for Partisan and Racial Gerrymandering.Journal of Politics 52, 1155–1181.CrossRefGoogle Scholar
  42. Nygreen B. (1988). European Assembly Constituencies for Wales: Comparing of Methods for Solving a Political Districting Problem.Mathematical Programing 42, 159–169.CrossRefGoogle Scholar
  43. Parker F.R. (1990).Black Votes Count. Chapel Hill: The University of North Carolina Press.Google Scholar
  44. Palermo P.C., De Giorgi C. and Tagliabue G. (1977). An Interactive Approach to the Facility Location Districting Problem.Adv. Operations Research, 341–346.Google Scholar
  45. Ricca F. (1996). Algorthmi di Ricerca Locale per la Distrettizzazione Elettorale.Atti Giorante AIRO 634–637.Google Scholar
  46. Ricca F. and Simeone B. (1997). Political Districting: Traps, Criteria, Algorithms and Tradeoffs.Ricerca Operativa AIRO 27, 81–119.Google Scholar
  47. Ronan R. (1983). Sales Territory Alginment for Sparse Accounts.OMEGA The International Journal of Management Science 11, 501–505.CrossRefGoogle Scholar
  48. Schröder M. (2001).Gebiete Optimal Aufteilen. Ph.D. Thesis, University of Karlsruhe, 2001. Google Scholar
  49. Segal M. and Weinberger D.B. (1977). Turfing.Operations Research 25, 367–386.Google Scholar
  50. Simchi-Levi D., Kaminsky P. and Simchi-Levi E. (2003).Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies. McGraw-Hill/Irwin.Google Scholar
  51. Shanker R.J., Turner R.E. and Zoltners A.A. (1975). Sales Territory Design: An Integrated Approach.Management Science 22, 309–320.Google Scholar
  52. Skiera B. (1997). Wieviel Deckungsbeitrag Verschenkt Man Durch Eine Gleichartige Einteilung der Verkaufsgebiete?Zeitschrift für Betriebswirtschaftliche Forschung 49, 723–746.Google Scholar
  53. Skiera B. and Albers S. (1994). Costa: Ein Entscheidungs-Unterstützungs-System zur deckungsbeitragsmaximalen Einteilung von Verkaufsgebieten.Zeitschrift für Betriebswirtschaft 64, 1261–1283.Google Scholar
  54. Teitz M.B. and Bart P. (1968). Heuristic Methods for Estimating Generalized Vertex Median of a Weighted Graph.Operations Research 16, 955–961.Google Scholar
  55. Williams J.C. Jr. (1995). Political Redistricting: A Review.Papers in Regional Science 74, 13–40.CrossRefGoogle Scholar
  56. Zoltners A.A. (1979). A Unified Approach to Sales Territory Alignment. In: Bagozzi R. (ed.),Sales Management: New Developments from Behavioral and Decision Model Research. Marketing Science Institute, 360–376.Google Scholar
  57. Zoltners A.A. and Sinha P. (1983). Sales Territory Alignment: A Review and Model.Management Science 29, 1237–1256.Google Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2005

Authors and Affiliations

  • Jörg Kalcsics
    • 1
  • Stefan Nickel
    • 2
  • Michael Schröder
    • 3
  1. 1.Universität des SaarlandesGermany
  2. 2.Universität des Saarlandes and Fraunhofer Institut für Techno- und WirtschaftsmathematikGermany
  3. 3.Fraunhofer Institut für Techno- und WirtschaftsmathematikGermany

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