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Preference Order Dynamic Programming

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  • L. G. Mitten

    (University of British Columbia)

Abstract

The dynamic programming recursive procedure has provided an efficient method for solving a variety of multi-stage decision problems in which the objective is measured by a real valued utility function. In this paper we propose that the real valued objective function be replaced by preference relations. Sufficient conditions are given on the structure of the preference relations to insure that the recursive dynamic programming procedure yields an optimal sequence of decisions. The solution method is well adapted to an interactive mode of implementation in which there is a dialogue between the decision maker and a source of information and analysis (e.g., a computer). The "computer" collects, analyzes, and presents information on a set of alternatives to the decision maker who then communicates to the "computer" his choice of the best alternatives in the set. The process is repeated, stage by stage, thus generating an optimal sequence of decisions. The approach should be particularly useful in dealing with multi-stage decision problems involving design and/or operation of facilities and multi-period public projects where a variety of desiderata must be considered (i.e., a simple cost or benefit function is inadequate).

Suggested Citation

  • L. G. Mitten, 1974. "Preference Order Dynamic Programming," Management Science, INFORMS, vol. 21(1), pages 43-46, September.
    • Handle: RePEc:inm:ormnsc:v:21:y:1974:i:1:p:43-46
    DOI: 10.1287/mnsc.21.1.43
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    Cited by:

    1. Trzaskalik, Tadeusz & Sitarz, Sebastian, 2007. "Discrete dynamic programming with outcomes in random variable structures," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1535-1548, March.
    2. Imani, Saba & Vahed, Majid & Vahed, Mohammad, 2021. "T-Ridership: a web tool for reprogramming public transportation fleet to minimize COVID-19 transmission," SocArXiv casb7, Center for Open Science.
    3. Sebastian Sitarz, 2009. "Pareto optimal allocations and dynamic programming," Annals of Operations Research, Springer, vol. 172(1), pages 203-219, November.
    4. Frini, Anissa & Guitouni, Adel & Martel, Jean-Marc, 2012. "A general decomposition approach for multi-criteria decision trees," European Journal of Operational Research, Elsevier, vol. 220(2), pages 452-460.
    5. Maciej Nowak & Tadeusz Trzaskalik, 2013. "Interactive procedure for a multiobjective stochastic discrete dynamic problem," Journal of Global Optimization, Springer, vol. 57(2), pages 315-330, October.
    6. Daniel Leitold & Agnes Vathy-Fogarassy & Janos Abonyi, 2019. "Empirical working time distribution-based line balancing with integrated simulated annealing and dynamic programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 455-473, June.

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