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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 deals with a model of the allocation and reliability problem. This static problem, presented as a multistage decision process, can be solved using multiobjective dynamic programming. The goal of this paper is to formulate the allocation and reliability problem as a multistage decision process, to find the set of all its efficient solutions, to use the weighted sum method for multistage and single-stage criteria, as well as to perform sensitivity analysis. [ABSTRACT FROM AUTHOR]

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We consider multiobjective, multistage discrete dynamic decision processes. In this paper we propose an interactive procedure which allows to solve the problem of optimal control of such a process in the case when the decision maker has determined a group hierarchy of stage criteria. This hierarchy is changeable and depends on the stage of the process. The proposed algorithm is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

One of the methods of scalarization of a multi-criteria problem is the application of a quasi-hierarchy, determined by the decision maker. In discrete problems, to apply this method it is necessary to have an algorithm which generates the optimal solution and the consecutive solutions, contained within the tolerance interval determined by the decision maker. This paper presents algorithms generating the consecutive realizations for a multi-stage deterministic decision-making process as well as an algorithm generating the consecutive strategies for a multi-stage stochastic decision- making process. Algorithms using these solutions in a multi-criteria quasi-hierarchical process are also proposed. [ABSTRACT FROM AUTHOR]

In this paper a stochastic multiobjective allocation problem is considered. We assume that a particular resource should be allocated to T projects. Depending on the amount of allocated resource it is possible (with known probabilities) to obtain a specified level of each goal. The considered criteria are divided into two groups. The first group consists of financial criteria, the second one, of qualitative criteria, representing the degree to which the projects contribute to reaching strategic goals. We propose a two-phase procedure for identifying the strategy that should be implemented by a decision maker. Our technique combines multiobjective dynamic programming and interactive approach. First, efficient strategies are identified using Bellman's principle of optimality adapted to the multiobjective problem. Next, a dialog procedure is applied to identify the solution that satisfies the decision maker. A numerical example is presented to show the applicability of the procedure. [ABSTRACT FROM AUTHOR]

The article offers information on the interactive approach for project portfolio management. It informs that improper selection of projects and their improper formulation limits the growth potential of the organization and undermines its competitive advantage. It discusses topics including consideration of multiple goals during portfolio selection, the methodology for choosing right project, and analytical hierarchy process for prioritizing projects.

The aim of the paper is to perform ex-post analysis for of a portable organ restoration applying a hybrid method, which combines DEMATEL, ANP and VICOR multicriteria approaches. The analysis of results and comparison with the earlier research based in the scheme of ELECTRE I method is included. [ABSTRACT FROM AUTHOR]

An Enterprise Resource Planning (ERP) system has a major impact on a company's performance; therefore it is a critical investment. This paper presents a framework for selecting a suitable ERP system using the Analytic Network Process (ANP) methodology. The proposed framework establishes a set of criteria with respect to the support of business goals and enterprise strategies. The method is explained on a numerical example based on the choice of an ERP for a small manufacturing enterprise. [ABSTRACT FROM AUTHOR]

A preface to the book "International Workshop on Multiple Criteria Decision Making" edited by Tadeusz Trzaskalik and Tomasz Wachowicz is presented.

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]

In the paper the problem of choosing logistics methods for control the level of stock is considered. The aim of the paper is to show how the AHP method can be applied for each sort of raw material stock management. For numerical illustration we use nu-merical data from a ceramic factory. [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.

A preface to the book "International Workshop on Multiple Criteria Decision Making" is presented.

A preface to the book "Multiple Criteria Decision Making '09," edited by Tadeusz Trzaskalik and Tomasz Wachowicz is presented.