Abstract.Multi-objective analysis is a popular tool to solve many economic, managerial and construction problems. The objective of this research is to develop and implement a methodology for multi-objective optimization of multi-alternative decisions in road construction. After a rough overview of the articles dealing with the multi-objective decision and assessment of road design alternatives described by discrete values, Multi-Objective Optimization on the basis of the Ratio Analysis (MOORA) method was selected. This method focuses on a matrix of alternative responses on the objectives. A case study demonstrates the concept of multi-objective optimization of road design alternatives and the best road design alternative is determined.
Abstract. The game theory allows mathematical solutions of conflict situations. Besides the fairly established application to economical problems, approaches to problems in construction operation have been worked out. An overview of applications is given. Solution strategies for such engineering problems are collected. Furthermore, concrete application examples are presented and an overview of further potential applications is given. Solutions of two-person zero-sum games are discussed as well as approaches to fuzzy games.
This paper considers the main positions of one-sided and two-sided problems. For onesided problems only the method of solution "the distance to the ideal point" is discussed in the actual version. For two-sided problems a distinction is made between games with rational behaviour and games against nature. The main strategic principles are as follows: simple min-max principle, extended min-max principle, Wald's rule, Savage criterion, Hurwicz's rule, Laplace's rule, Bayes's rule, Hodges-Lehmann rule. Questions of transforming the decision-making matrix are considered. The article gives the description of a software as well as an example of an investment variant estimation.
For many decades we have been dealing with problems of multi‐criteria decisions. Numerous methods have been developed in this field and new methods are continuously being created. In the light of a great number of methods currently proposed, it is difficult to gain a profound overview. Comparisons on the performance of various methods are done to a small extent only. When applying the methods, in some cases many mathematical operations are performed, which renders it impossible to sufficiently assess their effect with such a complexity. It is therefore aimed at analysing the peculiarities of several methods in a critical review and to give hints for possible consequences. The analysis is primarily concentrated on the normalisation of indices in the mapping to the interval [1; 0] or [1; ∼ 0]. This includes linear functions (the relative difference and the calculation with interval boundaries) and non‐linear functions (the hyperbolic function, the quadratic and cubic function, the square root and the logarithmic function). With the critical review, the possibility is offered to the decision maker to better assess the quality of his solution. Santrauka Jau daugelį dešimtmečių susiduriame su daugiakriterinių sprendimų problemomis. Daug metodų iki šiol jau yra sukurta, bet tebekuriami nauji. Dėl metodų įvairovės sudėtinga atlikti išsamią jų apžvalgą. Įvairių metodų palyginimų nėra daug. Kai kuriais atvejais, taikant daugiakriterinius metodus, atliekama daug matematinių operacijų, todėl sunku įvertinti skaičiavimo rezultatus. Dėl šios priežasties galimiems sprendiniams prognozuoti nagrinėjami metodų ypatumai. Atliekama metodų analizė normalizuojant rodiklius intervale [1; 0] arba [1; ~ 0]. Tai linijinė funkcija ir netiesinės (hiperbolinė, kvadratinė ir kubinė, kvadratinės šaknies, logaritminė) funkcijos. Straipsnyje pasiūlyta, kaip sprendimo priėmėjui įvertinti jo sprendimo kokybę.
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