Skip to main content
Log in

Pareto optimal allocations and dynamic programming

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The aim of the paper is to show the relations between dynamic programming (DP) and the Pareto optimal allocations (PAO) problem. Moreover, the paper shows how to use DP methods in order to find the Pareto optimal allocations at a particular point in time.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson, E. W. (2005). The dynamics of risk-sensitive allocations. Journal of Economic Theory, 125, 93–150.

    Article  Google Scholar 

  • Arrow, K., & Intrilligator, M. (Ed.). (1981). Handbook of mathematical economics. Amsterdam: North Holland.

    Google Scholar 

  • Brown, T. A., & Strauch, R. E. (1965). Dynamic programming in multiplicative lattices. Journal of Mathematical Analysis and Applications, 12(2), 364–370.

    Article  Google Scholar 

  • Dorta-Gonzalez, P., Santos-Penate, D. R., & Suarez-Vega, R. (2002). Pareto optimal allocation and price equilibrium for a duopoly with negative externality. Annals of Operations Research, 116, 129–152.

    Article  Google Scholar 

  • Ekeland, I. (1979). Elements d’economic mathematic. Paris: Hermann.

    Google Scholar 

  • Eschenauer, H. A., Koski, J., & Osyczka, A. (1986). Multicriteria design optimization: procedures and applications. New York: Springer.

    Google Scholar 

  • Gale, D., Kuhn, H. W., & Tucker, A. W. (1951). Linear programming and theory of games. In T. C. Koopman (Ed.), Activity analysis of production and allocation. New York: Willey.

    Google Scholar 

  • Henig, M. I. (1983). Vector-valued dynamic programming. SIAM Journal on Control and Optimization, 21, 3.

    Article  Google Scholar 

  • Jouini, E., & Napp, C. (2003). Comonotonic processes. Insurance: Mathematics and Economics, 32, 255–265.

    Article  Google Scholar 

  • Klamroth, K., & Wiecek, M. M. (2000). Dynamic programming approaches to multiple criteria knapsack problem. Naval Research Logistics, 47, 57–76.

    Article  Google Scholar 

  • Mitten, L. G. (1974). Preference order dynamic programming. Management Science, 21(1), 43–46.

    Article  Google Scholar 

  • Mordukhovich, B. S. (2005). Nonlinear prices in nonconvex economies with classical Pareto and strong Pareto optimal allocations. Positivity, 9, 541–568.

    Article  Google Scholar 

  • Pallaschke, D., & Rolewicz, S. (1997). Mathematical applications: Vol. 388. Foundations of mathematical optimization. Dordrecht: Kluwer.

    Google Scholar 

  • Pareto, V. (1896). Cours d’economic politique. Lausanne: Rouge.

    Google Scholar 

  • Sitarz, S. (2003), Discrete dynamic programming in ordered structures and its applications. PhD thesis, University of Lodz, Poland (in Polish).

  • Sitarz, S. (2006). Hybrid methods in multi-criteria dynamic programming. Applied Mathematics and Computation, 180(1), 38–45.

    Article  Google Scholar 

  • Trzaskalik, T., & Sitarz, S. (2007). Discrete dynamic programming with outcomes in random variable structures. European Journal of Operational Research, 177(3), 1535–1548.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sebastian Sitarz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sitarz, S. Pareto optimal allocations and dynamic programming. Ann Oper Res 172, 203–219 (2009). https://doi.org/10.1007/s10479-009-0558-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-009-0558-8

Keywords

Navigation