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A Multiobjective Discrete Optimization Model for Land Allocation

Author

Listed:
  • Kenneth C. Gilbert

    (Department of Management, The University of Tennessee, Knoxville, Tennessee 37996)

  • David D. Holmes

    (Intergraph Corporation, Madison Industrial Park, Huntsville, Alabama 35807)

  • Richard E. Rosenthal

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

Abstract

A multiobjective integer programming model is presented for allocating an area of land for development. The objectives considered in the allocation are cost, proximity to desirable and undesirable land features and the shape of the area. An interactive multiobjective optimization algorithm is presented and applied to the model. The algorithm generates a subset of efficient solutions with some guidance from the decision maker at each iteration as to what constitutes a "preferred" efficient point. The algorithm calls for the frequent solution of subproblems which constrain all but one of the objectives while optimizing the remaining one. In the land allocation model, the subproblems are integer programs solved efficiently by specialized enumeration techniques. For some of the subproblems (namely, those using proximity as the single objective), the first feasible solution we enumerate is guaranteed optimal. For the other subproblems, we show that an algorithm with this fortunate property would require the solution of an NP-hard problem at each step of the enumeration. The model and algorithm were tested in locating potential sites for a 13-acre residential development within a 2250-acre study area near Norris, Tennessee.

Suggested Citation

  • Kenneth C. Gilbert & David D. Holmes & Richard E. Rosenthal, 1985. "A Multiobjective Discrete Optimization Model for Land Allocation," Management Science, INFORMS, vol. 31(12), pages 1509-1522, December.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:12:p:1509-1522
    DOI: 10.1287/mnsc.31.12.1509
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    Citations

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    Cited by:

    1. Gabriel, Steven A. & Faria, Jose A. & Moglen, Glenn E., 2006. "A multiobjective optimization approach to smart growth in land development," Socio-Economic Planning Sciences, Elsevier, vol. 40(3), pages 212-248, September.
    2. H. Murat Çelik & Ersin Türk, 2010. "Determination of Optimum Environmental Conservation: Using Multi-Criteria Decision-Making Techniques," European Planning Studies, Taylor & Francis Journals, vol. 19(3), pages 479-499, March.
    3. Brian Lunday & Hanif Sherali & Kevin Lunday, 2012. "The coastal seaspace patrol sector design and allocation problem," Computational Management Science, Springer, vol. 9(4), pages 483-514, November.
    4. George, John A. & Lamar, Bruce W. & Wallace, Chris A., 1997. "Political district determination using large-scale network optimization," Socio-Economic Planning Sciences, Elsevier, vol. 31(1), pages 11-28, March.
    5. Michael Johnson & David Turcotte & Felicia Sullivan, 2010. "What Foreclosed Homes Should a Municipality Purchase to Stabilize Vulnerable Neighborhoods?," Networks and Spatial Economics, Springer, vol. 10(3), pages 363-388, September.
    6. Justus Bonz, 2021. "Application of a multi-objective multi traveling salesperson problem with time windows," Public Transport, Springer, vol. 13(1), pages 35-57, March.
    7. Ersin Türk & Hüseyin Murat Çelik, 2013. "Impacts of Planners' Different Viewpoints on Optimum Land-Use Allocation," European Planning Studies, Taylor & Francis Journals, vol. 21(12), pages 1937-1957, December.
    8. Liu, Fuh-Hwa Franklin & Huang, Chueng-Chiu & Yen, Yu-Lee, 2000. "Using DEA to obtain efficient solutions for multi-objective 0-1 linear programs," European Journal of Operational Research, Elsevier, vol. 126(1), pages 51-68, October.
    9. Shukui Tan & Lu Zhang & Min Zhou & Yanan Li & Siliang Wang & Bing Kuang & Xiang Luo, 2017. "A hybrid mathematical model for urban land-use planning in association with environmental–ecological consideration under uncertainty," Environment and Planning B, , vol. 44(1), pages 54-79, January.
    10. Ningchuan Xiao & David A Bennett & Marc P Armstrong, 2002. "Using Evolutionary Algorithms to Generate Alternatives for Multiobjective Site-Search Problems," Environment and Planning A, , vol. 34(4), pages 639-656, April.
    11. Xiaoya Ma & Xiang Zhao, 2015. "Land Use Allocation Based on a Multi-Objective Artificial Immune Optimization Model: An Application in Anlu County, China," Sustainability, MDPI, vol. 7(11), pages 1-20, November.
    12. Leibowicz, Benjamin D., 2020. "Urban land use and transportation planning for climate change mitigation: A theoretical framework," European Journal of Operational Research, Elsevier, vol. 284(2), pages 604-616.
    13. Miguel Ángel Gutiérrez-Andrade & Eric Alfredo Rincón-García & Sergio Gerardo de-los-Cobos-Silva & Pedro Lara-Velázquez & Roman Anselmo Mora-Gutiérrez & Antonin Ponsich, 2019. "Simulated Annealing and Artificial Bee Colony for the Redistricting Process in Mexico," Interfaces, INFORMS, vol. 49(3), pages 189-200, May.

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