Short-Term Land use Planning and Optimal Subsidies

  • L. M. Briceño-Arias
  • F. MartínezEmail author


Urban planning is a complex problem which includes choosing a social objective for a city, finding the associated optimal allocation of agents and identifying instruments like subsidies to decentralize this allocation as a market equilibrium. We split the problem in two independent steps. First, we find the short-term optimal allocation for a social objective and, second, we derive subsidies that reproduce this optimal allocation as a market equilibrium. This splitting is supported by a fundamental result asserting that the optimal allocation of any social objective can be decentralized by applying feasible subsidies, which can be computed even in the case with location externalities and transportation costs. In the first step, we compute the optimal allocation using an algorithm to solve a convex urban planning problem, which is applicable to a wide class of objective functions. In the second step, we compute optimal subsidies in several political situations for the planner, like budget constraints and limited impact on specific agents, zones, rents and/or utilities. As an example, we simulate a prototype city which aims at improving social inclusion.


Convex optimization Land use planning problem Location subsidies Urban segregation 



This work is supported by the Complex Engineering Systems Institute, ISCI (ICM-FIC: P05-004-F, CONICYT: FB0816), by project FONDECYT 11140360, and by “Programa de financiamiento basal” from the Center for Mathematical Modeling, Universidad de Chile. The authors thanks C. Vigouroux for his help with simulations.


  1. Águila LF (2006) Modelo Operativo de planificación Óptima de Subsidios en Sistemas Urbanos MSc. Thesis, Universidad de ChileGoogle Scholar
  2. Anas A (1982) Residential location markets and urban transportation. Academic Press, LondonGoogle Scholar
  3. Bauschke HH, Combettes PL (2011) Convex analysis and monotone operator theory in hilbert spaces. Springer, New YorkCrossRefGoogle Scholar
  4. Bravo M, Briceño-Arias LM, Cominetti R, Cortés CE, Martínez FJ (2010) An integrated behavioral model of the land-use and transport systems with network congestion and location externalities. Transp Res B Methodol 44(4):584–596CrossRefGoogle Scholar
  5. Briceño-Arias LM, Cominetti R, Cortés CE, Martínez FJ (2008) An integrated behavioral model of land use and transport system: a hyper-network equilibrium approach. Netw Spatial Econ 8:201–224CrossRefGoogle Scholar
  6. Briceño-Arias LM, Combettes PL (2011) A monotone+skew splitting model for composite monotone inclusions in duality. SIAM J Optim 21:1230–1250CrossRefGoogle Scholar
  7. Combettes PL, Wajs VR (2005) Signal recovery by proximal forward-backward splitting. SIAM J Multiscale Model Simul 4:1168–1200CrossRefGoogle Scholar
  8. Ellickson B (1981) An alternative test of the hedonic theory of housing markets. J Urban Econ 9(1):56–79CrossRefGoogle Scholar
  9. Hiriart-Urruty J-B, Lemaréchal C (1993) Convex analysis and minimization algorithms I. Springer, BerlinCrossRefGoogle Scholar
  10. Hunt JD, Kriger DS, Miller EJ (2005) Current operational urban land-use-transport modelling frameworks: a review. Transp Rev 25(3):329–376CrossRefGoogle Scholar
  11. Ma X, Lo HK (2012) Modeling transport management and land use over time. Transp Res B Methodol 46(6):687–709CrossRefGoogle Scholar
  12. Macgill SM (1977) Theoretical properties of biproportional matrix adjustments. Environ Plann A 9(6):687—701CrossRefGoogle Scholar
  13. Martínez F (1992) The Bid-Choice land use model: an integrated economic framework. Environ Plann A 24(6):871–885CrossRefGoogle Scholar
  14. Martínez F, Henríquez R (2007) A random bidding and supply land use model. Transp Res Part B: Methodol 41(6):632–651CrossRefGoogle Scholar
  15. Preston J, Simmonds D, Pagliara F (2010) Residential location choice: Models and applications. Springer, BerlinGoogle Scholar
  16. Rockafellar RT (1970) Convex analysis. Princeton Mathematical Series, vol 28. Princeton University Press, PrincetonGoogle Scholar
  17. Rossi-Hansberg E (2004) Optimal urban land use and zoning. Rev Econ Dyn 7:69–106CrossRefGoogle Scholar
  18. Timmermans HJP, Zhang J (2009) Modeling household activity travel behavior: Example of the state of the art modeling approaches and research agenda. Transp Res B Methodol 43:187–190CrossRefGoogle Scholar
  19. Wegener M (1994) Operational urban models: State of the art. J Am Plan Assoc 60(1):17–29CrossRefGoogle Scholar
  20. Wegener M, Kim TJ (1998) Models of urban land use, transport and environment. In: Lundqvist, L, Mattsson, L-G (eds) Network Infrastructure and the Urban Environment. Advances in Spatial science. Springer, BerlinGoogle Scholar
  21. Ying JQ (2015) Optimization for multiclass residential location models with congestible transportation networks. Transp Sci 49(3):452–471CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaSantiagoChile
  2. 2.Departamento de Ingeniería CivilUniversidad de Chile e Instituto Sistemas Complejos de IngenieríaSantiagoChile

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