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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.10.019 Byline: Tadeusz Trzaskalik (a), Sebastian Sitarz (b) Keywords: Dynamic programming; Discrete optimization; Multiobjective decision making; Stochastic orders Abstract: Multiobjective approach is the common way of generalization single-criterion dynamic programming models. Another way is to consider partially ordered criteria structures. That approach is rather rare. The aim of the paper is to present such a model. Generalization of Bellman's principle of optimality is employed to create a forward procedure to find the set of all maximal elements. As this set is usual large, the second problem under consideration is to find its subsets. To reduce the number of solutions presented to decision maker we propose to apply a family of narrowing relations. That approach is similar to scalarization in multiobjective programming. Ordered structures of random variables based on mean-variance, stochastic dominance and inverse stochastic dominance are considered. Numerical illustration is given at the end of the paper. Author Affiliation: (a) Department of Operations Research, The Karol Adamiecki University of Economics, ul. Bogucicka 14, 40-226 Katowice, Poland (b) Institute of Mathematics, The University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland

The paper introduces a new software package, MOLPTOL, for sensitivity analysis in multi-objective linear programming. In this application, which is available for free of charge on the web page (https:// sites.google.com/view/molptol), the tolerance approach as a measure of sensitivity is used. The motivation for creating MOLPTOL is the lack of such tools to date. MOLPTOL is novel for multi-criteria decision-making methods based on sensitivity analysis. The paper presents some new computational methods for obtaining the supremal tolerances as well. [ABSTRACT FROM AUTHOR]

The paper presents a multiobjective dynamic programming problem with the values of the criteria function in ordered structures. The first problem is a model with deterministic values; the second, one with triangular fuzzy numbers; and the third, one with discrete random variables with the k-th absolute moment finite. The fourth model is a product of the three models listed above. The aim of the paper is to present an interactive procedure which uses trade-offs and which allows to determine the final solution in the mixed ordered structure. The ordered structures and the proposed procedure are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

The aim of the work is to present a method of ranking a finite set of discrete random variables. The proposed method is based on two approaches: the stochastic dominance model and the compromise hypersphere. Moreover, a numerical illustration of the method presented is given. [ABSTRACT FROM AUTHOR]

Stochastic dynamic programming (DP) is a strong mathematical tool allowing modeling and solving many multiperiod decision processes. Multiple objective and dynamics characterize many sequential decision problems. In the paper we consider returns in partially ordered criteria set as a way of generalization of single criterion DP models to multiobjective case. In the present paper, on the basis of theoretical findings, described in our previous papers we consider exemplary stochastic DP profit maximization processes. Because of the lack of space we omit the general, formal description of such a process and concentrate on explanation, how the theory of DP models in partially ordered criteria space works. Both in level-volume and velocity-volume process we will consider formulated problems step by step, first as single criterion problems and next as bi- -criteria ones. Conclusions are presented in the last section. [ABSTRACT FROM AUTHOR]

Compromise programming is one of the most often applied methods of multi-criteria optimization, both discrete and continuous. This paper deals with decision making in multicriteria linear programming problems. The approach presented here is based on finding a hypersphere (in the criteria space), which minimalizes the distance from the set of all nondominated extreme points. Next, we look for the nondominated extreme point closest to the hypersphere found previously. This point, called the best compromise nondominated solution, depends on the chosen metric. We consider the method of compromise hypersphere with different metrics and analyze their influence on the best compromise nondominated solution. [ABSTRACT FROM AUTHOR]

In this paper the element-wise analysis approach to sensitivity analysis in linear vector optimization is presented. Two cases are considered: sensitivity analysis of efficient solutions and sensitivity analysis of dominating solutions. The results obtained allow to create methods based on the analysis of a simplex tableau. The presented approach allowed to obtain the intervals of the parameter for which a given solution is efficient or dominating. [ABSTRACT FROM AUTHOR]

The article discusses the application of triangular norms in discrete dynamic programming. It explores the concept of using triangular norms to make ordered structures and provides 15 examples of ordered structures that are based on triangular norms. It also presents a numerical analysis for the structures.

In this paper we propose a new approach for solving dynamic multiobjective decision making problems. The decision variants are generated in a discrete multistage model by forward/backward procedure of finding the set of all maximal elements based on Bellman's principle of optimality. As the set of all maximal elements consists of a number of elements - decision variants, our problem is to find among them a compromise element based on decision maker's preferences with respect to several decision criteria. The evaluation of the weights of the criteria is based on data given by pairwise comparison matrices using triangular fuzzy numbers. Extended arithmetic operations with fuzzy numbers for application of the generalized logarithmic least squares method are defined and six methods for ranking fuzzy numbers to compare fuzzy outcomes are proposed. A numerical example is presented to clarify the methodo-logy [ABSTRACT FROM AUTHOR]