Fuzzy Data Envelopment Analysis And Its Applications For Aggregating Preference Ranking

Over the past two decades, Data Envelopment Analysis (DEA) has appeared as an important tool in the field of efficiency measurement. DEA is used to compare Decision Making Units (DMUs) such as bank branches, hospitals, sales outlets, which consume one or more non-homogenous inputs to produce one or more nonhomogenous outputs. The DMUs consume the same inputs and produce the same outputs but generally at varying levels. One of the main characteristics of DEA is its sensitivity to data. That is, inaccurate data may divert effectively the results of efficiency analysis from its actual value. But accurate measurement in many real world problems, due to either non-availability of sophisticated measurement tools or qualitative nature of the phenomena may not be possible. This kind of information can be represented as fuzzy numbers or linguistic terms

Pronóstico del intervalo de confianza en la eficiencia de las unidades de toma de decisiones en el análisis envolvente de datos

Data Envelopment Analysis (DEA) is a well-known method for calculating the efficiency of Decision-Making Units (DMUs) based on their inputs and outputs. When the data is known and in the form of an interval in a given time period, this method can calculate the efficiency interval. Unfortunately, DEA is not capable of forecasting and estimating the efficiency confidence interval of the units in the future. This article, proposes a efficiency forecasting algorithm along with 95% confidence interval to generate interval data set for the next time period. What’s more, the manager’s opinion inserts and plays its role in the proposed forecasting model. Equipped with forecasted data set and with respect to data set from previous periods, the efficiency for the future period can be forecasted. This is done by proposing a proposed model and solving it by the confidence interval method. The proposed method is then implemented on the data of an automotive industry and, it is compared with the Monte Carlo simulation methods and the interval model. Using the results, it is shown that the proposed method works better to forecast the efficiency confidence interval. Finally, the efficiency and confidence interval of 95% is calculated for the upcoming period using the proposed model.El análisis envolvente de datos (DEA) es un método bien conocido para calcular la eficiencia de las unidades de toma de decisiones (DMU) en función de sus entradas y salidas. Cuando los datos son conocidos y en forma de intervalo en un período de tiempo dado, este método puede calcular el intervalo de eficiencia. Desafortunadamente, la DEA no es capaz de pronosticar y estimar el intervalo de confianza de eficiencia de las unidades en el futuro. Este artículo propone un algoritmo de pronóstico de eficiencia junto con un intervalo de confianza del 95% para generar un conjunto de datos de intervalo para el próximo período de tiempo. Además, la opinión del gerente se inserta y desempeña su papel en el modelo de pronóstico propuesto. Equipado con un conjunto de datos pronosticado y con respecto al conjunto de datos de períodos anteriores, se puede pronosticar la eficiencia para el período futuro. Esto se hace proponiendo un modelo propuesto y resolviéndolo mediante el método del intervalo de confianza. A continuación, el método propuesto se implementa sobre los datos de una industria automotriz y se compara con los métodos de simulación de Monte Carlo y el modelo de intervalo. Usando los resultados, se muestra que el método propuesto funciona mejor para pronosticar el intervalo de confianza de eficiencia. Finalmente, se calcula la eficiencia y el intervalo de confianza del 95% para el próximo período utilizando el modelo propuesto

Integration of preference elicitation and the development of alternative forest plans : focusing on the requirements of the decision maker

Modern forest management frequently revolves around the concepts of developing strategic, tactical and operational level plans. These plans are developed through the use of simulation and optimization software, based on scientific models and mathematical programming. The optimal management schedule depends upon the decision maker(s) (DM) preferences. When developing forest plans for the DM(s) the method of acquiring preference information should be as value free as possible. To facilitate a DM-orientated approach, a selection of alternatives based on the acquired preferences should be made available to the DM so that a true choice can be made. The development of the forest plans should represent the desires and wishes of the forest owner at the time the plan is created. In order to balance the costs with the quality of the service provided, tools are required which develop client specific forest plans. The first objective of this thesis is to analyse different preference elicitation methods and study the impacts of information content on the selection of a plan. In papers I and II, plans were selected using an a posteriori method of preference elicitation. For paper III, preference elicitation was done in an interactive fashion, to develop an acceptable forest plan using both a priori and a posteriori preference elicitation methods. The second objective is to develop techniques for incorporating preference information into optimization methods. In paper IV, a series of goal programming models were used to incorporate the preference information from several DMs to generate a number of potentially desirable forest plans. Paper V develops a goal programming formulation which separates the treatment of different goals into two partitions; one strives to maintain the difference from the target for the goals in balance, the other strives to obtain the most efficient aggregate solution.Nykyaikainen metsäsuunnittelu keskittyy usein sellaisille käsitteellisille tasoille kuin strateginen, taktinen ja operatiivinen suunnittelu. Suunnitelmat on toteutettu käyttämällä simulointi- ja optimointiohjelmistoja, jotka perustuvat tieteellisiin malleihin ja matemaattiseen ohjelmointiin. Kuitenkin päätöksentekijän /jien (PT) preferenssit määrittelevät optimaalisen aikataulun metsänhoidolle. Metsäsuunnitelmia tuotettaessa menetelmän tulisi olla mahdollisimman vapaa suunnittelijan omista arvoista ja mielipiteistä. Jotta lähestymistapa olisi mahdollisimman PT-ystävällinen, pitäisi päätöksentekijälle esittää useita metsänsuunnittelun vaihtoehtoja, joiden perusteella PT voi tehdä aidosti henkilökohtaisen valintansa. Tuotettujen metsäsuunnitelmien tulisi vastata metsänomistajan sen hetkisiä toiveita ja mieltymyksiä. Jotta suunnitelmien kustannusten ja laadun välille saadaan tasapaino, tarvitsemme työkaluja joilla muokata metsäsuunnittelua paremmin asiakaslähtöiseksi. Tämän tutkimuksen ensimmäinen tavoite oli analysoida eri preferenssien hankintamenetelmiä, sekä selvittää saadun tiedon määrän vaikutus suunnitelman valintaan. Artikkeleissa I ja II suunnitelma valittiin a posteriori menetelmän avulla. Artikkelissa III preferenssien hankinta toteutettiin interaktiivisesti, siten, että hyväksyttävä metsäsuunnitelma saatiin aikaiseksi hyödyntämällä sekä a priori, että a posteriori preferenssien valintamenetelmiä. Tutkimuksen toinen tavoite oli kehittää tekniikoita, joilla sisällytetään preferenssitietoa osaksi optimointimenetelmiä. Artikkelissa IV on käytetty sarjaa tavoiteohjelmointimalleja, joiden tavoitteena oli sisällyttää preferenssitietoja useilta eri päätöksentekijöiltä, joiden pohjalta sitten tuotettiin useita PT:itä potentiaalisesti kiinnostavia metsäsuunnitelmia. Artikkeli V kehitti uuden tavan formuloida tavoiteohjelmoinnin tehtävä, , joka erottaa tavoitteiden käsittelyn kahteen osaan; toinen pyrkii löytämään mahdollisimman tasapainoisen ratkaisun ja toinen pyrkii löytämään kaikista tehokkaimman ratkaisuyhdistelmän

A Multicriteria Model to Evaluate Strategic Plans for the Nautical and Naval Industry in Cartagena de Indias, Colombia

[EN] The evaluation of urban development plans is a key concern of the strategic planning of the city of Cartagena de Indias (Colombia) due to the pressure exerted by both public and private sectors. Any strategic planning requirement deserves the inclusion of clear terms of coordination and cooperation among sectors, including local communities and the scientific sector. In this paper, we present a methodology for the sustainable evaluation of strategic nautical and naval projects for the development of the city of Cartagena de Indias. The methodology is based on the multicriteria technique Analytic Network Process, which allows considering political, socio-cultural and environmental aspects. The aim is to provide answers and guide the decision makers towards the optimal selection of strategies. Results provide some important insights into the overall conception of what sustainable evaluation means for the experts consulted. The procedure enhances participation and transparency and becomes a support for their decisions.The authors would like to thank the "Bolivar Gana con Ciencia" project from the Gobernacion de Bolivar (Colombia) for the financial support. Special thanks are also extended to the experts for their enthusiastic cooperation, which made this study possible.Gonzalez-Urango, H.; García-Melón, M. (2017). A Multicriteria Model to Evaluate Strategic Plans for the Nautical and Naval Industry in Cartagena de Indias, Colombia. Sustainability. 9(4). https://doi.org/10.3390/su9040653S9

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems