Skip to main content

Advertisement

Springer Nature Link
Log in

Classification of Spatial Properties for Spatial Allocation Modeling

  • Original Article
  • Published:
GeoInformatica Aims and scope Submit manuscript

Abstract

Given a set of spatial units, such as land parcels and grid cells, how to allocate subsets of it to activities of interest while satisfying certain criteria? Such a decision process is here called spatial allocation. Though many problems of spatial allocation share this generic construct, each may have a quite unique set of criteria and interpret even the same criteria in its own way. Such diversity makes it difficult to model spatial allocation problems in unambiguous terms that are amenable to algorithmic solution. This paper proposes a classification scheme for spatial properties that helps to address a variety of spatial properties in establishing spatial allocation criteria. The implication of the paper is that a number of spatial properties and spatial allocation criteria can be decomposed into a few kinds of primitive spatial properties and their relations.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.C.J.H. Aerts and G.B.M. Heuvelink. “Using simulated annealing for resource allocation,” International Journal of Geographical Information Science, Vol. 16:571–587, 2002.

    Article  Google Scholar 

  2. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall: Englewood Cliffs, NJ, 1993.

    Google Scholar 

  3. K.K. Al-Taha and R. Barrera. “Temporal data and GIS: An overview,” in Proc. of GIY’IS ‘, pp. 244–254, 1990.

  4. P.C. Belford and H.D. Ratliff. “A network-flow model for racially balancing schools,” Operations Research, Vol. 20:619–628, 1972.

    Google Scholar 

  5. S. Benabdallah and J.R. Wright. “Shape considerations in spatial optimization,” Civil Engineering Systems, Vol. 8:145–152, 1991.

    Google Scholar 

  6. S. Benabdallah and J.R. Wright. “Multiple subregion allocation models,” ASCE Journal of Urban Planning and Development, Vol. 118:24–40, 1992.

    Google Scholar 

  7. D.J. Blair and T.H. Bliss. “The Measurement of shape in geography: An appraisal of methods and techniques,” Bulletin of Quantitative Data for Geographers, No. 11, 1967.

  8. R.B. Boyce and W.A.V. Clark. “The concept of shape in geography,” Geographical Review, Vol. 54:561–572, 1964.

    Google Scholar 

  9. C.J. Brookes. “A parameterized region-growing programme for region allocation on raster suitability maps,” International Journal of Geographical Information Science, Vol. 11:375–396, 1997.

    Article  Google Scholar 

  10. W. Bunge. Theoretical Geography, Lund Studies in Geography, Series C, General and Mathematical Geography, No. 1. Gleerup: Lund, 1966.

    Google Scholar 

  11. R.L. Church. “Location modelling and GIS,” in P.A. Longley, M.F. Goodchild, D.J. Maguire, and D.W. Rhind (Eds.), Geographical Information Systems, Vol. I, Principles and Technical Issues. 2nd edition. John Wiley & Sons: New York, 293–303, 1999.

    Google Scholar 

  12. T.J. Cova and R.L. Church. “Contiguity constraints for single-region site search problems,” Geographical Analysis, Vol. 32:306–329, 2000.

    Google Scholar 

  13. S.C. Crema. “A comparison between linear programming and a choice heuristic approach to multi-objective decision making using GIS,” in Proc. of GIS/LIS ‘96, pp. 954–963, 1996.

  14. J.R. Eastman, P.A.K. Kyem, and J. Toledano. “A procedure for multi-objective decision making in GIS under conditions of conflicting objectives,” in Proc. of EGIS ‘93, pp. 438–447, 1993.

  15. M. Egenhofer and R. Franzosa. “Point-set topological spatial relations,” International Journal of Geographical Information Systems, Vol. 5:161–174, 1991.

    Google Scholar 

  16. M.J. Egenhofer and J.R. Herring. “Categorizing binary topological relations between regions, lines, and points in geographic databases,” in, Technical Report, Department of Surveying Engineering, University of Maine, Orono, ME, 1990.

  17. A. Frank, J. Raper, and J.P. Cheylan. Life and Motion of Socio-Economic Units. Taylor & Francis: London, 2001.

    Google Scholar 

  18. B. Fleischmann and J.N. Paraschis. “Solving a large scale districting problem: A case report,” Computers and Operations Research, Vol. 15:521–533, 1988.

    Article  Google Scholar 

  19. A.D. Franklin and E. Koenigsberg. “Computed school assignments in a large district,” Operations Research, Vol. 21:413–426, 1973.

    Google Scholar 

  20. Y. Frolov. “Measuring the shape of geographical phenomena: A history of the issue,” Soviet Geography: Review and Translation, Vol. 16:676–687, 1974.

    Google Scholar 

  21. R.S. Garfinkel and G.L. Nemhauser. “Optimal political districting by implicit enumeration techniques,” Management Science, Vol. 16:B495–B508, 1970.

    Google Scholar 

  22. K.C. Gilbert, D.D. Holmes, and R.E. Rosenthal. “A multiobjective discrete optimization model for land allocation,” Management Science, Vol. 31:1509–1522, 1985.

    Google Scholar 

  23. M.F. Goodchild, “Towards an enumeration and classification of GIS functions,” in Proc. of International Geographic Information Systems (IGIS) Symposium: The Research Agenda, NASA, Washington, Vol. 2:67–77, 1988.

  24. M.F. Goodchild. “Geographical data modeling,” Computers & Geosciences, Vol. 18:401–408, 1992.

    Google Scholar 

  25. T. Hagerstrand. “What about people in regional science?” Papers of the regional Science Association, Vol. 24:7–21, 1970.

    Google Scholar 

  26. S.W. Hess. “Compactness-what shape and size? Conflicts among possible criteria for rational districting,” National Municipal League, 15–23, 1969.

  27. S.W. Hess and S.A. Samuels. “Experiences with a sales districting model: Criteria and implementation,” Management Science, Vol. 18(No. 4, Part II):41–54, 1971.

    Google Scholar 

  28. S.W. Hess, J.B. Weaver, H.J. Siegfeldt, J.N. Whelan, and P.A. Zitlau, “Nonpartisan political redistricting by computer,” Operations Research, Vol. 13:998–1006, 1965.

    Google Scholar 

  29. M. Hojati. “Optimal political districting,” Computers & Operations Research, Vol. 23:1147–1161, 1996.

    Google Scholar 

  30. M. Kavouras. “Understanding and modeling spatial change,” in A. Frank, J. Raper, and J.P. Cheylan (Eds.), Life and Motion of Socio-Economic Units. Taylor & Francis: London, 2001.

    Google Scholar 

  31. G. Langran. Time in Geographic Information Systems. Taylor & Francis: London, 1992.

    Google Scholar 

  32. D.R. Lee and G.T. Sallee. “A method of measuring shape,” Geographical Review, Vol. 60:555–563, 1970.

    Google Scholar 

  33. A.M. MacEachren. “Compactness of geographic shape: Comparison and evaluation of measures,” Geografiska Annaler, Vol. 67B:53–67, 1985.

    Google Scholar 

  34. P.G. Marlin. “Application of the transportation model to a large-scale “districting” problem,” Computers and Operations Research, Vol. 8:83–96, 1981.

    Article  Google Scholar 

  35. B.H. Massam and M.F. Goodchild. “Temporal trends in the spatial organization of a service agency,” Canadian Geographer, Vol. 15:193–206, 197l.

    Google Scholar 

  36. A. Mehrotra, E.L. Johnson, and G.L. Nemhauser. “An optimization based heuristic for political districting,” Management Science, Vol. 44:1100–1114, 1998.

    Google Scholar 

  37. D.J. Peuquet. “Time in GIS and geographical databases,” in P.A. Longley, M.F. Goodchild, D.J. Maguire, and D.W. Rhind (Eds.), Geographical Information Systems, Vol. I, Principles and Technical Issues, 2nd edition. John Wiley & Sons: New York, pp. 91–103, 1999.

    Google Scholar 

  38. M. Segal and D.B. Weinberger. “Turting,” Operations Research, Vol. 25:367–386, 1977.

    Google Scholar 

  39. R.J. Shanker, R.E. Turner, and A.A. Zoltners. “Sales territory design: An integrated approach,” Management Science, Vol. 22:309–320, 1975.

    Google Scholar 

  40. T. Shirabe. A model of contiguity for spatial unit allocation, in revision.

  41. T. Shirabe and C.D. Tomlin. “Decomposing integer programming models for spatial allocation,” in M.J. Egenhofer and D.M. Mark (Eds.), Geographic Information Science, Proc. of GIScience 2002, Lecture Notes in Computer Science, Vol. 2478:300–312, 2002.

  42. B. Smith. “On drawing lines on a map,” in A.U. Frank and W. Kuhn (Eds.), Spatial Information Theory, Proc. of COSIT ‘95, Lecture Notes in Computer Science, Vol. 988:475–484, 1995.

  43. P.J. Taylor. “Distances within shapes: An introduction to a family of finite frequency distributions,” Discussion Paper, No. 16, University of Iowa, 1–20, 1970.

  44. P.J. Taylor. “Distances within shapes: An introduction to a family of finite frequency distributions,” Geografiska Annaler, Vol. 53B(1):1971.

  45. C.D. Tomlin. Geographic Information Systems and Cartographic Modeling. Prentice Hall: Englewood Cliffs, NJ, 1990.

    Google Scholar 

  46. C.D. Tomlin and K.M. Johnston. “An experiment in land-use allocation with a geographic information system,” in D.J. Peuquet and D.F. Marble (Eds.), Introductory Readings in Geographic Information Systems. Taylor & Francis: London, 159–169, 1990.

    Google Scholar 

  47. M.L. Vidale. “A graphical solution of the transportation problem,” Operations Research, Vol. 4:193–203, 1956.

    Google Scholar 

  48. E.A. Wentz. “A shape definition for geographic applications based on edge, elongation, and perforation,” Geographical Analysis, Vol. 32:95–112, 2000.

    Google Scholar 

  49. C.L. White and G.T. Renner. College Geography: Natural Environment and Human Society. New York, pp. 590–599, 1957.

  50. J.C. Williams. “Political districting: A review. Papers in Regional Science,” Papers in Regional Science: The Journal of the Regional Science Association International, Vol. 74:13–40, 1995.

    Google Scholar 

  51. J.C. Williams, “A zero–one programming model for contiguous land acquisition,” Geographical Analysis, Vol. 34:330–349, 2002.

    Google Scholar 

  52. J. Wright, C. ReVelle, and J. Cohon. “A multiple objective integer programming model for the land acquisition problem,” Regional Science and Urban Economics, Vol. 13:31–53, 1983.

    Article  Google Scholar 

  53. M. Yeates. “Hinterland Delimitation: A distance minimizing approach,” The Professional Geographer, Vol. 15(No. 6):7–10, 1963.

    Article  Google Scholar 

  54. A.A. Zoltners and P. Sinha, “Sales territory alignment: A review and Model,” Management Science, Vol. 29:1237–1256, 1983.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Geoinformation, Technical University of Vienna, Gusshausstr 27–29, 1040, Vienna, Austria

    Takeshi Shirabe

Authors
  1. Takeshi Shirabe
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Takeshi Shirabe.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shirabe, T. Classification of Spatial Properties for Spatial Allocation Modeling. Geoinformatica 9, 269–287 (2005). https://doi.org/10.1007/s10707-005-1285-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10707-005-1285-1

Key Words