The approach described in article is based on the Linear Partial Information (LPI) by E. Kofler. The robust multicriteria ranking is based on the robust dominance relations, which holds under all admissible combinations of criteria weights. In the article the robust dominance relation is defined and the robust ranking method based on the PROMETHEE outranking relations is proposed.
A new methodology for project portfolio scheduling problem has been presented in this paper. This methodology delivers information about project portfolio schedule, which is important for project portfolio managers. The methodology consists of three steps: multiple-criteria mathematical model building, finding non-dominated solutions and choosing one solution from the Pareto set as the final solution. In the first step a multiple-criteria mathematical model for project portfolio scheduling problem is built. Three criteria are considered in the model: the penalty for projects delays minimization, the penalty for resources overusage minimization and NPV maximization. Disadvantage of proposed mathematical model is a big amount of variables, which is J×T×P. In cases when we will have larger projects or larger planning horizon the number of variables will be huge. That is why activities aggregation was proposed. It reduces a number of variables in given model. It also delivers a general information about project portfolio schedule, which is more important for project portfolio managers. In the second step a set of non-dominated solutions is identified by using an elitist evolutionary algorithm. As research shows using an external set with the best solutions in each generation increases an algorithm efficiency. In the third step the LBS procedure is used to identify the final solution. The LBS procedure proposes is a way of learning-oriented interactive search for the best compromise solution for the decision maker. This procedure makes the comparison of non-dominated solution in the decision phase relatively easy. So this step will not burden the decision maker too much. For the future work, the procedure presented in this paper will be applied to the problem described in the section two, and given results will be compared with the current situation in the company.
This paper proposes a new method for ranking a nite set of alternatives evaluated on multiple criteria. The presented method combines the robust ordinal regression (ROR) approach and the ranking score based on the aggregate distance measure function coming from the TOPSIS method. In our method, the preference model is a set of ad- ditive value functions compatible with a non-complete set of pairwise comparisons of some reference alternatives given by the decision maker (DM). Based on this set of compatible value functions, we dene an ag- gregate function representing relative closeness to the reference point (ideal solution) in the value space. The ranking score determined by this distance measure is then used to rank all alternatives. Calculating the distance in the value space permits to avoid normalization used in TOPSIS to transform original evaluations on different criteria scales into a common scale. This normalization is perceived as a weakness of TOPSIS and other methods based on a distance measure, because the ranking of alternatives depends on the normalization technique and the distance measure. Thus, ROR applied to TOPSIS does not only facilitate the preference elicitation but also solves the problem of non-meaningfulness of TOPSIS. Finally, an instructive example is given to illustrate the proposed method.
The paper presents the comparative analysis of dwelling maintenance contractors aimed at determining the degree of their utility for users and bidding price of services by applying the method of multicriteria complex proportional assessment. To compare the performance of various maintenance contractors, the data from 15 dwelling maintenance organizations was used. A questionnaire survey of dwelling owners was conducted. Contractors were evaluated by a set of 44 criteria characterizing them from various perspectives. The analysis was made taking into account the standpoints of building owners (clients). The initial weights of qualitative criteria were calculated by expert methods. Then they were coordinated with the calculated values of quantitative criteria using the method of multicriteria complex proportional assessment. Multicriteria analysis of the performance of maintenance contractors allows us to determine the importance of particular contractor characteristics for achieving the aim to meet the needs of different participants of the maintenance process.
LT
Straipsnyje pateikta daugiabučius namus administruojančių įmonių lyginamoji analizė. Tyrimo tikslas - nustatyti daugiabučius namus administruojančių įmonių paslaugų naudingumą namo naudotojams. Pavyzdžiui išspręsti buvo naudoti penkiolikos daugiabučius namus administruojančių įmonių paslaugų rodikliai. Įmonės pagal 44 juos apibūdinančius kriterijus vertino daugiabučių namų gyventojai. Pradiniai kokybinių rodiklių reikšmingumai nustatyti taikant ekspertinį metodą. Kokybinių ir kiekybinių rodiklių reikšmingumai suderinti, optimalus variantas ir variantų naudingumai nustatyti daugiakriterinio kompleksinio proporcingo vertinimo metodu (angl.method of COmplex PRoportional ASsessment, COPRAS). Pagal taikytą metodą derybų metu galima koreguoti pasiūlymų kainas, atsižvelgiant į nustatytą alternatyvų naudingumą. Daugiakriterinė analizė leidžia nustatyti konkretaus rangovo rodiklių reikšmingumus, įvertinus skirtingus daugiabučių namų priežiūros proceso dalyvių poreikius.
In this paper we discuss the possibility of applying the various game-theoretic mechanisms to support the postnegotiation analysis of the multi-issue two-party negotiation. We analyze the negotiation problem stucturized and evaluated by parties by means of the simple additive weighting model, which is typical approach implemented in very many negotiation support systems. In particular, we focus on such negotiation processed that result in an inefficient negotiation outcome. We show how to identify the set of efficient solutions for each negotiation problem and then, how to find the efficient improvements of the agreement that the parties have agreed on. We propose a novel mechanism of finding such improvements, that stems from Nash bargaining solution and some previous concepts of Raiffa's potentials of the negotiators. We show an example of how this mechanism works when applied to find an improvement in bilateral negotiation supported by Inspire negotiation support system.
The article presents practical applications of chosen multiple criteria decision making method - AHP (Analytic Hierarchy Process). The main purpose is to build portfolios on the basis of this method. It is important to make the best decision when there are many alternatives (objects) that are evaluating under differing criteria. AHP is one of multiple criteria decision making methods; it enables to compare considered objects for each criterion and creates a ranking of all the objects. Building a portfolio is a problem of selecting these objects (quoted companies) that have, for example, high return rate and low variance, but also other features, like low β coefficient or high skewness coefficient. To built a portfolio according to the classical approach of using AHP method, all mentioned measures can be considered as criteria. In the other approach - fundamental one, some diagnostic features that characterize financial and economic condition of companies can be used as criteria. Created multiple criteria rankings can help to choose the best listed companies to the portfolio. In the paper, portfolios built on the basis of AHP rankings were estimated. To compare the profit rate of created this way portfolios, a classical portfolio based on Markowitz approach also was appointed. The profit rate of each portfolio designed on the basis of AHP method was over 19,5% and was higher than the profit rate of classical Markowitz one. Besides, the portfolios profit rates estimated for next three months were also better than Markowitz portfolio profit rate what confirms that using proposed approach may bring in interesting results.
An important part of the innovation management is to select the best new product project from the preliminary large set of potential alternatives. This problem is broadly discussed in the extant literature. Although the qualitative approaches dominate in literature, there are few examples of more formal decision procedures based on multiple criteria analysis. This article brings an example of interactive procedure that can help decision making in the new product development. As to the authors knowledge, such approach has not been proposed so far to the problem of selecting new product. The interactive procedure gives to the DM an opportunity to actively participate in the whole process and observe its development. During the procedure, the DM can disclose his preferences and values of trade-offs. This kind of assessment of differences in importance of criteria is assumed as more reliable then the direct assessment of weights.
Drzewo decyzyjne jest efektywnym narzędziem opisu dynamicznych procesów decyzyjnych w warunkach ryzyka. Korzystając z niego dąży się zwykle do wyznaczenia rozwiązania optymalizującego wartość oczekiwaną rozważanego kryterium decyzyjnego. Stosunkowo rzadko narzędzie to jest wykorzystywane do rozwiązywania problemu wielokryterialnego, w którym decydent jest zainteresowany realizacją kilku wzajemnie konfliktowych celów. W pracy przedstawiono metodę pozwalającą na rozwiązanie problemu opisanego wielokryterialnym drzewem decyzyjnym za pomocą podejścia quasi-hierarchicznego. Zakładamy, że decydent jest w stanie określić hierarchię kryteriów oraz określić, w jakim stopniu można pogorszyć optymalną wartość kryterium o wyższym priorytecie w celu poprawy wartości kryterium o niższej wadze. Sposób działania metody zilustrowano przykładem opartym na danych umownych.
EN
Decision tree is an effective tool for describing dynamic decision making processes under risk. It is usually used to identify the solution optimizing the expected value of the analyzed criterion. However, it is relatively rarely used when multiple conflicting criteria are considered. In the paper a quasi-hierarchical approach is used to solve a problem represented by a multiple criteria decision tree. It is assumed that the decision maker is able to define a hierarchy of the criteria and specify how much the optimal value of a more important criterion can be decreased in order to improve the value of a less important criterion. A numerical example is presented to show the applicability of the procedure.
In this paper we discuss the mechanism for building the negotiation offers' scoring system by means of the automatically generated indifference surfaces. We introduce the classic approach based on trade-off analysis first , that derives from multiple attribute value theory and present its application for the simplest case of two- and three-criteria decision problem. Then we analyze its generalization for the cases with more than three decision criteria, which involves also the interaction with decision maker. Finally we present the models software implementation that is applied in the negotiation support system called NegoManage.
This paper presents the order-picking problem as a multicriteria task. Using simulation tool 360 variants of solution were generated. The different combinations of the picking zone's shape, the number of forklift trucks and the picker-routing methods were considered. The variants were evaluated by seven criteria and the dominated solutions were removed. Then, using the Electre I method, the number of solutions was even more limited. The paper discusses and presents conclusions how to optimize the order-picking process.
In a negotiation process, building a negotiation offer scoring system consistent with the preferences of the decision-maker is a very intricate task. A variety of methods can be used to develop such a negotiation support tool, e.g. SAW and TOPSIS, but they have several disadvantages. In this paper the issue of evaluating the negotiation template using a novel tool called SIPRES is discussed. The algorithm proposed employs the key notions of the revised Simos' procedure and ZAPROS method to elicit the negotiator's preferences over some reference solutions. On the one hand, it allows decision-makers to define their preferences in a simple and effortless way and provides a straightforward yet effective method for analyzing the trade-offs between the alternatives using selected reference alternatives only (the ZAPROS-like approach). On the other hand, the revised Simos' procedure applied in the method allows determining the cardinal scores for the alternatives. The scoring system obtained this way makes it possible to conduct a sophisticated symmetric and asymmetric negotiation analysis. An illustrative example presented in the paper concerns the European Union's multiannual financial framework negotiations.
With respect to the complex nature of negotiation situation, in analysis of the negotiation, mathematical tools of multi-criteria decision making can be used. The aim of the paper is presentation of some applications of the classical TOPSIS method in analysis of the process of negotiation. The TOPSIS method let us to order offers, according to the value of the result of synthesis of multi-criteria evaluation, with respect to their similarities to the most preferable one, assignment of the alternative offers, estimating the value of concessions, or the estimation of the negotiation agreement. The similarity is determined on basis of minimization of distance negotiation offer, to the most preferable, and maximization of distance to the least preferable one.
Celem pracy było przedstawienie możliwości wykorzystania rozmytej wielokryterialnej metody podejmowania decyzji do konstrukcji cechy syntetycznej. Zaproponowana metoda polega na utworzeniu struktury hierarchicznej badanego problemu decyzyjnego oraz wykorzystaniu zmiennych lingwistycznych i trapezoidalnych liczb rozmytych do ratingu kryteriów i cech prostych (atrybutów) w każdym ocenianym obiekcie. W pracy podjęto próbę zastosowania tej metody do oceny poziomu społeczno-gospodarczego obszarów wiejskich w układzie powiatów woj. wielkopolskiego. Uzyskane uszeregowanie powiatów pokazuje, że najlepiej rozwinięte były powiaty: poznański i szamotulski, a najgorzej - powiaty położone peryferyjnie (we wschodniej części województwa).
EN
The aim of this paper was to investigate the applicability of the fuzzy multi-criteria decision-making method to the construction of synthetic characteristics. The method proceeds from the erection of a hierarchic structure for the examined decision problem and utilizes linguistic variables and trapezoidal fuzzy numbers to rate basic characteristics and criteria for each decision element. The proposed procedure was employed to assess the socio-economic development of rural Wielkopolska seen as a collection of counties. Obtained results show that the best developed are the Poznaä and Szamotuy counties, which surround the urban metropolis of Poznaä. The most backward are the remote counties of eastern part of the province. (original abstract)
The aim of this research work was to develop an optimization model for the problem of time-cost trade-off, taking into account the impact of the planned tasks or activities of contractors on the project. As a methodological basis for the proposed model the concept of critical chain E. Goldratt, which introduces the behavioral aspect of estimating the time steps in the project, but does not indicate the specific methods of quantification estimations. The presented model assumes the possibility of quantifying the workload of the project components in a set of fuzzy numbers and the ability to extract from these estimates reasonable and acceptable level of risk of non-compliance and security allowances, administered only to increase the safety assessment. The mechanism operates on optimization of decision variables representing the amount of work assigned to each resource in order to minimize the criterion function summarizing the direct costs of the activities in the project the costs of acceleration (or delays).
In the paper we propose a practical application of the path goal programming approach, by which we understand a goal programming approach with goals being not numbers, but paths in networks. This method, with goal paths corresponding to desired schedules of environmental investment implementation, is used for the environmental decision-making in a selected company. The company has to introduce some investments aimed at natural resources reduction. However, not all the required investments can be realized in one budgeting period, because of budget constraints. The desired compromise schedule of investment realization has to be worked out. This schedule becomes the goal. The path goal programming method helps to reduce the undesired deviations from the goal schedule.
W artykule podjęto zagadnienie oceny poziomu życia w Polsce w ujęciu regionalnym z zastosowaniem dwóch ujęć: wielowymiarowego oraz wielokryterialnego. W rozważaniach porównuje się wyniki analiz przeprowadzonych za pomocą miary syntetycznej z alternatywnym sposobem wykorzystującym wybraną wielokryterialną metodę (metodę AHP), która umożliwia ocenę i porównanie obiektów (województw) przez pryzmat wielu kryteriów. W przeprowadzanych analizach uwzględnia się m.in. takie charakterystyki, jak: dochody na 1 mieszkańca, stopa bezrobocia, nakłady na środki trwałe na 1 mieszkańca służące ochronie środowiska, ale również zmienne typu: absolwenci szkół wyższych na 10 tys. ludności, drogi o twardej nawierzchni na 100 km2 itp., które zostały wyłonione w procedurze doboru zmiennych do badania. Powyższe charakterystyki w ujęciu wielowymiarowym są traktowane jako zmienne diagnostyczne, natomiast w podejściu wielokryterialnym - jako kryteria wyboru.
EN
Many researchers are interested in analyzing the phenomenon of standard of living. It is complex issue and it is characterized with variables that come from different fields of life. The researches are mainly concentrated on building a synthetic indicator which enables to describe the phenomenon and to compare analyzed objects. The purpose of the paper is to compare Polish voivodeships in terms of living standard using two research approaches: the common multivariate one (with building a synthetic measure) and multi-criteria one (using the AHP method). In the multi-criteria approach the variables that characterize the phenomenon are treated as criteria.
The use of the dominance-based rough set approach (DRSA) to help identify and prioritize strategic political, economic, sociological and technological (PEST) objectives for European Union (EU) countries is presented. The countries are first grouped into three categories: [A] those that are doing well according to the selected indicators; [B] those that need support to acquire category A status; [C] those ranked the lowest and needing special support with regard to the criteria considered. The categories correspond to tertiles within the average ranking of all EU countries. DRSA then provides decision rules based on PEST needs in order to improve the development and classification of the country. We conclude that by using this methodology, the EU could identify the strategic objectives to be given priority in order to stimulate its economic development or to improve the economic and sociological status of any country in the union. The case of Poland, a category C country from an economic perspective, is of particular interest.
Production structure problem, also known as product mix problem (PMP) has been in the area of interest of many researchers. Among many different ways to solve this problem, theory of constraints (TOC) is one of the more frequently chosen ones. However this solution is not universal and in some cases does not generate an optimal solution. In this paper a multi-criteria integer model has been introduced to enhance the concept. Thanks to a thorough analysis of the problem, model can be used both in the companies that have identified the one and only constraint as well as companies that characterize with multi-constraint environment.
Happy Planet Index (HPI) is an aggregated index that measures the extent to which each nation produces long and happy lives per unit of environmental input. The HPI uses global data on life expectancy, experienced well-being, and ecological footprint to rank countries. The last HPI report was published in 2012 and it contains data for 151 countries from all continents. The aim of the paper is to re-calculate the HPI using DEA models and other multiple criteria decision making techniques and compare the results obtained results. MCDM methods evaluate alternatives (countries) according to the set of criteria with respect to given preferences. Most of them allow ranking of alternatives according to aggregated indices defined by various methods. DEA models compare the countries with the best performers in the data set and measure the efficiency of transformation of multiple inputs into multiple outputs. Even though they are based on different principles than MCDM methods they allow ranking of evaluated units according to their efficiency or super-efficiency scores. The paper analyzes both methodological approaches and compares their results.
Celem artykułu jest przedstawienie dwóch propozycji metodycznych konstruowania cechy syntetycznej oraz ich zastosowania do oceny poziomu rozwoju społeczno-gospodarczego powiatów woj. wielkopolskiego. W pierwszej części pracy opisane są podstawy teoretyczne i etapy postępowania w tworzeniu cechy syntetycznej. Proponowane podejście opiera się na metodzie analitycznego procesu hierarchicznego (Analytic Hierarchy Process - AHP) oraz zmodyfikowanych przez Autorów metodach rozmytych Chenga-Lina i TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). Zaproponowane podejście może być przydatne w tworzeniu cechy syntetycznej, zwłaszcza, gdy w rozważanym problemie oceny obiektów występują kryteria podrzędne (bezpośrednio mierzalne), a w zbiorze cech prostych zarówno cechy o charakterze ilościowym, jak i jakościowym - porządkowym. Dodatkową zaletą proponowanego podejścia jest możliwość przyporządkowania kryteriom i cechom prostym zróżnicowanych współczynników wagowych dzięki zastosowaniu metody analitycznego procesu hierarchicznego. W części empirycznej pracy proponowaną procedurę budowy cechy syntetycznej zastosowano do oceny poziomu rozwoju społeczno-gospodarczego powiatów woj. wielkopolskiego.
EN
The aim of this paper was to investigate the applicability of the two fuzzy multi-criteria linear ordering methods to the construction of synthetic characteristic. The proposed procedure was employed to assess the socio-economic development of rural Wielkopolska seen as a collection of counties. The first part of this paper presents theoretical rudiments and stage of procedure of construction of synthetic characteristics. The proposed approach is based on two group methods: Analytical Hierarchy Process (AHP) (to calculate weight of criteria) and fuzzy methods modified by author: Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) or Chang-Lin method (to ranking of objects). Proposed approach can be useful to construction synthetic characteristic. Particularly when in consideration problem appear secondary criterions (directly measurable) and qualitative and quantitative characteristic in the set of basic characteristics. Additional advantage of proposed approach is possibility criterions and basic characteristics appropriate differential weighed coefficients owing to application of analytic hierarchy process. In the empirical part, the proposed procedure was employed to assess the socio-economic development of rural Wielkopolska seen as a collection of counties.
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