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1

Optymalizacja wielokryterialna dla wyboru decyzji w procesie negocjacji

Łodziński A.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2016

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z. 88

197--208

PL

W pracy przedstawiono metodę wspomagania wyboru decyzji w procesie negocjacji. Proces negocjacji modeluje się przy pomocy optymalizacji wielokryterialnej. Metoda znajdowania rozwiązania polega na interaktywnym prowadzeniu procesu wyboru kolejnych propozycji rozwiązań. Strony przedstawiają swoje propozycje dotyczące przedmiotów negocjacji, które stanowią parametry zadania optymalizacji wielokryterialnej. Wybór kolejnych rozwiązań dokonuje się przez rozwiązywanie zadania optymalizacji z parametrami, które określają aspiracje każdej ze stron biorących udział w negocjacjach, jak również przez ocenę otrzymywanych rozwiązań przez strony.

EN

The paper presents a method of supporting the decision making in negotiation process. This process is modeled as a multicriteria optimization. It is an interactive choose of subsequent proposals. Parts present their propositions concerning the objects of negotiation that are parameters of multicriteria optimization problem. Choosing subsequent solutions is made by the solution of optimization problem with parameters, that determine the aspiration of each part of negotiation, as well as by valuation of the obtained solutions.

2

Comparison of Selected Fair-optimization Methods for Flow Maximization between Given Pairs of Nodes in Telecommunications Network

Zalewski G., Ogryczak W.

Journal of Telecommunications and Information Technology

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2016

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nr 3

18--24

EN

Dimensioning of telecommunications networks requires the allocation of the ows (bandwidth) to given trac demands for the source-destination pairs of nodes. Unit ow allocated to the given demand is associated with revenue that may vary for dierent demands. Problem the decision-making basic algorithms to maximize the total revenue may lead to the solutions that are unacceptable, due to "starvation" or "locking" of some demand paths less attractive with respect to the total revenue. Therefore, the fair optimization approaches must be applied. In this paper, two fair optimization methods are analyzed: the method of ordered weighted average (OWA) and the reference point method (RPM). The study assumes that ows can be bifurcated thus realized in multiple path schemes. To implement optimization model the AMPL was used with general-purpose linear programming solvers. As an example of the data, the Polish backbone network was used.

3

Zastosowanie metody punktu odniesienia do znajdowania decyzji symetrycznie efektychnych w modelowaniu wielokryterialnym procesu negocjacji dwustronnych

Łodziński Andrzej

Studia i Materiały Informatyki Stosowanej

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2013

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nr 12

19--28

PL

W pracy przedstawiono metodę wyboru decyzji symetrycznie efektywnych w procesie negocjacji dwustronnych. Proces negocjacji modeluje się przy pomocy optymalizacji wielokryterialnej. Metoda znajdowania rozwiązania polega na interaktywnym prowadzeniu procesu wyboru kolejnych propozycji rozwiązań. Strony przedstawiają swoje propozycje dotyczące przedmiotów negocjacji, które stanowią parametry zadania optymalizacji wielokryterialnej. Wybór kolejnych rozwiązań dokonuje się przez rozwiązywanie zadania optymalizacji z parametrami, które określają aspiracje każdej ze stron biorących udział w negocjacjach i przez ocenę przez strony otrzymywanych rozwiązań.

EN

A method of making symmetrically effective decisions in a two-side negotiation is presented. A negotiation process is modeled by multicriteria optimization. The solution finding consists in an interactive choosing among decision proposals. Each part presents its proposition concerning the objects of negotiation that are parameters of multicriteria optimization problem. Choosing subsequent solutions is made by the solution of optimization problem with parameters, that determine the aspiration of each part of negotiation, as well as by estimation of the obtained solution.

4

A reference point method to triple-objective assignment of supporting services in a healthcare institution

Sawik B.

Decision Making in Manufacturing and Services

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2010

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Vol. 4, no. 1-2

37-46

EN

This paper presents an application of mixed integer programming model for optimal allocation of workers among supporting services in a hospital. The services include logistics, inventory management, financial management, operations management, medical analysis, etc. The optimality criterion of the problem is to minimize operational costs of supporting services subject to some specific constraints. The constraints represent specific conditions for resource allocation in a hospital. The overall problem is formulated as a triple-objective assignment model, where the decision variables represent the assignment of people to various jobs. A reference point approach with the Chebyshev metric is applied for the problem solution. The results of computational experiments modeled on a real data from a hospital in Lesser Poland are reported.

5

A reference point approach to bi-objective dynamic portfolio optimization

Sawik B.

Decision Making in Manufacturing and Services

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2009

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Vol. 3, no. 1-2

73-85

EN

The portfolio selection problem presented in this paper is formulated as a bi-objective mixed integer program. The portfolio selection problem considered is based on a dynamic model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to dynamically allocate the wealth on different securities to optimize by reference point method the portfolio expected return and the probability that the return is not less than a required level. In computational experiments the dataset of daily quotations from the Warsaw Stock Exchange were used.

6

Reference Point Method with Importance Weighted Partial Achievements

Ogryczak W.

Journal of Telecommunications and Information Technology

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2008

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nr 4

17-25

EN

The reference point method (RPM) is based on the so-called augmented max-min aggregation where the worst individual achievement maximization process is additionally regularized with the average achievement. In order to avoid inconsistencies caused by the regularization, we replace it with the ordered weighted average (OWA) which combines all the individual achievements allocating the largest weight to the worst achievement, the second largest weight to the second worst achievement, and so on. Further following the concept of the weighted OWA (WOWA) we incorporate the importance weighting of several achievements into the RPM. Such a WOWA RPM approach uses importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements rather than by straightforward rescaling of achievement values. The recent progress in optimization methods for ordered averages allows us to implement the WOWA RPM quite effectively as extension of the original constraints and criteria with simple linear inequalities.

7

Reference distribution based decision support platform

Breja K., Ogryczak W.

Journal of Telecommunications and Information Technology

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2008

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nr 3

5-14

EN

There many decision problems where numerous partial achievement functions are considered impartially which makes the distribution of achievements more important than the assignment of several achievements to the specific criteria. Such models are generally related to the evaluation and optimization of various systems which serve many users where quality of service for every individual user defines the criteria. This applies to various technical systems, like to telecommunication ones among others, as well as to social systems. An example arises in location theory, where the clients of a system are entitled to equal treatment according to some community regulations. This paper presents an implementation of decision support framework for such problems. This platform is designed for multiple criteria problems analyzed with the reference distribution approach. Reference distribution approach is an extension of the reference point method.

8

Wspomaganie procesu ustalania cen detalicznych na konkurencyjnym rynku usług telekomunikacyjnych z asymetrią informacyjną

Laskowski S.

Telekomunikacja i Techniki Informacyjne

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2006

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nr 1-2

25-50

PL

Na podstawie elementów teorii gier i wspomagania decyzji zaprezentowano analityczne narzędzia, wspierające graczy rynkowych w procesie ustalania cen detalicznych za świadczone usługi, w przypadku braku informacji o macierzy wypłat graczy konkurencyjnych.

EN

Basing on elements of game theory and theory of decision support, analytical tools of supporting market players in setting detail prices for telecommunication services in the situation of unknown payoff matrix of competitive player have been proposed.

9

Fair and efficient network dimensioning with the reference point methodology

Goryczak W., Wierzbicki A., Milewski M.

Journal of Telecommunications and Information Technology

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2006

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nr 4

21-30

EN

The dimensioning of telecommunication networks that carry elastic traffic requires the fulfillment of two conflicting goals: maximizing the total network throughput and providing fairness to all flows. Fairness in telecommunication network design is usually provided using the so-called max-min fairness (MMF) approach. However, this approach maximizes the performance of the worst (most expensive) flows which may cause a large worsening of the overall throughput of the network. In this paper we show how the concepts of multiple criteria equitable optimization can be effectively used to generate various fair and efficient allocation schemes. We introduce a multiple criteria model equivalent to equitable optimization and we develop a corresponding reference point procedure for fair and efficient network dimensioning for elastic flows. The procedure is tested on a sample network dimensioning problem for elastic traffic and its abilities to model various preferences are demonstrated.

10

The MOORA method and its application to privatization in a transition economy

Brauers W. K., Zavadskas E. K.

Control and Cybernetics

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2006

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Vol. 35, no 2

445-469

EN

A new method is proposed for multi-objective optimization with discrete alternatives: MOORA (Multi-Objective Optimization on the basis of Ratio Analysis). This method refers to a matrix of responses of alternatives to objectives, to which ratios are applied. A well established other method for multi-objective optimization is used for comparison, namely the reference point method. Later on, it is demonstrated that this is the best choice among the different competing methods. In MOORA the set of ratios has the square roots of the sum of squared responses as denominators. These ratios, as dimensionless. seem to be the best choice among different ratios. These dimensionless ratios, situated between zero and one, are added in the case of maximization or subtracted in case of minimization. Finally, all alternatives are ranked, according to the obtained ratios. Eventually, to give more importance to an objective, an objective can be replaced by different sub-objectives or a coefficient of importance can be specified. An example on privatization in a transition economy illustrates the application of the method. If application is situated originally in a "welfare" economy, centered on production, MOORA becomes even more significant in a 'wellbeing economy", where consumer sovereignty is assumed.

11

On multi-criteria approaches to bandwidth allocation

Ogryczak W., Wierzbicki A.

Control and Cybernetics

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2004

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Vol. 33, no 3

427-448

EN

Modern telecommunication networks face an increasing demand for services. Among these, an increasing number are services that can adapt to available bandwidth, and are therefore referred to as elastic traffic. Nominal network design for elastic traffic becomes increasingly significant. Typical resource allocation methods are concerned with the allocation of limited resources among competing activities so as to achieve the best overall performance of the system. In the network dimensioning problem for elastic traffic, one needs to allocate bandwidth to maximize service flows and simultaneously to reach a fair treatment of all the elastic services. Thus, both the overall efficiency (throughput) and the fairness (equity) among various services are important. In such applications, the so-called Max-Min Fairness (MMF) solution concept is widely used to formulate the resource allocation scheme. This approach guarantees fairness but may lead to significant losses in the overall throughput of the network. In this paper we show how the concepts of multiple criteria equitable optimization can be effectively used to generate various fair resource allocation schemes. We introduce a multiple criteria model ecluivalent to equitable optimization and we develop a corresponding reference point procedure to generate fair efficient bandwidth allocations. The procedure is tested on a sample network dimensioning problem and its abilities to model various preferences are demonstrated.

12

The reachable sets concept applied to a class of min-max optimization problems

Terlikowski T.

Archives of Control Sciences

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2003

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Vol. 13, no. 1

47-58

EN

A multi-criteria control problem over the infinite time horizon for periodical system is considered. our aim is solve problems of type using the known idea of reachable sets. The worst case approach applied concerns e.g. a system of water resources distribution. The min-max opimisation problem obtained occurs to fit naturally the scheme of reachable sets concept. applicability of this concept to that particular case is discussed and the algorithm is presented.