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Interactive procedure for a multiobjective stochastic discrete dynamic problem

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  • Maciej Nowak
  • Tadeusz Trzaskalik

Abstract

Multiple objectives and dynamics characterize many sequential decision problems. In the paper we consider returns in partially ordered criteria space as a way of generalization of single criterion dynamic programming models to multiobjective case. In our problem evaluations of alternatives with respect to criteria are represented by distribution functions. Thus, the overall comparison of two alternatives is equivalent to the comparison of two vectors of probability distributions. We assume that the decision maker tries to find a solution preferred to all other solutions (the most preferred solution). In the paper a new interactive procedure for stochastic, dynamic multiple criteria decision making problem is proposed. The procedure consists of two steps. First, the Bellman principle is used to identify the set of efficient solutions. Next interactive approach is employed to find the most preferred solution. A numerical example and a real-world application are presented to illustrate the applicability of the proposed technique. Copyright The Author(s) 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:2:p:315-330
    DOI: 10.1007/s10898-012-0019-9
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    References listed on IDEAS

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    1. Nijkamp, P. & Spronk, J., 1978. "Interactive multiple goal programming," Serie Research Memoranda 0003, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    3. Maciej Nowak, 2010. "Trade-Off Analysis in Discrete Decision Making Problems Under Risk," Lecture Notes in Economics and Mathematical Systems, in: Dylan Jones & Mehrdad Tamiz & Jana Ries (ed.), New Developments in Multiple Objective and Goal Programming, pages 103-115, Springer.
    4. 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.
    5. Mordechai I. Henig, 1985. "The Principle of Optimality in Dynamic Programming with Returns in Partially Ordered Sets," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 462-470, August.
    6. Nowak, Maciej, 2004. "Preference and veto thresholds in multicriteria analysis based on stochastic dominance," European Journal of Operational Research, Elsevier, vol. 158(2), pages 339-350, October.
    7. Edward P. C. Kao, 1978. "A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem," Operations Research, INFORMS, vol. 26(6), pages 1033-1045, December.
    8. Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
    9. Zaras, Kazimierz, 2004. "Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems," European Journal of Operational Research, Elsevier, vol. 159(1), pages 196-206, November.
    10. Fan, Zhi-Ping & Liu, Yang & Feng, Bo, 2010. "A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations," European Journal of Operational Research, Elsevier, vol. 207(2), pages 906-915, December.
    11. Lahdelma, Risto & Miettinen, Kaisa & Salminen, Pekka, 2003. "Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA)," European Journal of Operational Research, Elsevier, vol. 147(1), pages 117-127, May.
    12. A. M. Geoffrion & J. S. Dyer & A. Feinberg, 1972. "An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department," Management Science, INFORMS, vol. 19(4-Part-1), pages 357-368, December.
    13. Matthew J. Sobel, 1975. "Ordinal Dynamic Programming," Management Science, INFORMS, vol. 21(9), pages 967-975, May.
    14. L. G. Mitten, 1974. "Preference Order Dynamic Programming," Management Science, INFORMS, vol. 21(1), pages 43-46, September.
    15. Stanley Zionts & Jyrki Wallenius, 1976. "An Interactive Programming Method for Solving the Multiple Criteria Problem," Management Science, INFORMS, vol. 22(6), pages 652-663, February.
    16. Urli, Bruno & Nadeau, Raymond, 2004. "PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty," European Journal of Operational Research, Elsevier, vol. 155(2), pages 361-372, June.
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    1. Krzysztof S. Targiel & Maciej Nowak & Tadeusz Trzaskalik, 2018. "Scheduling non-critical activities using multicriteria approach," 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. 26(3), pages 585-598, September.
    2. Maciej Nowak & Tadeusz Trzaskalik, 2022. "A trade-off multiobjective dynamic programming procedure and its application to project portfolio selection," Annals of Operations Research, Springer, vol. 311(2), pages 1155-1181, April.

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