Confidence-based contractor, propagation and potential clouds for differential equations

A novel interval contractor based on the confidence assigned to a random variable is proposed in this paper. It makes possible to consider at the same time an interval in which the quantity is guaranteed to be, and a confidence level to reduce the pessimism induced by interval approach. This contractor consists in computing a confidence region. Using different confidence levels, a particular case of potential cloud can be computed. As application, we propose to compute the reachable set of an ordinary differential equation under the form of a set of confidence regions, with respect to confidence levels on initial value

A NEW INTEGRATED GREY MCDM MODEL: CASE OF WAREHOUSE LOCATION SELECTION

Warehouses link suppliers and customers throughout the entire supply chain. The location of the warehouse has a significant impact on the logistics process. Even though all other warehouse activities are successful, if the product dispatched from the warehouse fails to meet the customer needs in time, the company may face with the risk of losing customers. This affects the performance of the whole supply chain therefore the choice of warehouse location is an important decision problem. This problem is a multi-criteria decision-making (MCDM) problem since it involves many criteria and alternatives in the selection process. This study proposes an integrated grey MCDM model including grey preference selection index (GPSI) and grey proximity indexed value (GPIV) to determine the most appropriate warehouse location for a supermarket. This study aims to make three contributions to the literature. PSI and PIV methods combined with grey theory will be introduced for the first time in the literature. In addition, GPSI and GPIV methods will be combined and used to select the best warehouse location. In this study, the performances of five warehouse location alternatives were assessed with twelve criteria. Location 4 is found as the best alternative in GPIV. The GPIV results were compared with other grey MCDM methods, and it was found that GPIV method is reliable. It has been determined from the sensitivity analysis that the change in criteria weights causes a change in the ranking of the locations therefore GPIV method was found to be sensitive to the change in criteria weights

Clouds, p-boxes, fuzzy sets, and other uncertainty representations in higher dimensions

Uncertainty modeling in real-life applications comprises some serious problems such as the curse of dimensionality and a lack of sufficient amount of statistical data. In this paper we give a survey of methods for uncertainty handling and elaborate the latest progress towards real-life applications with respect to the problems that come with it. We compare different methods and highlight their relationships. We introduce intuitively the concept of potential clouds, our latest approach which successfully copes with both higher dimensions and incomplete information

Appropriate location for remanufacturing plant towards sustainable supply chain

© 2019 The Author(s). Confronted with the scarcity of natural resources, increase in product returns and government regulations on protection of environment, firms are implementing remanufacturing operations to achieve growth which is more sustainable and contribute to the millennium sustainable development goals. The challenge before the managers is to decide the appropriate location to establish the remanufacturing facilities in the reverse supply chain. Several conflicting criteria need to be considered before establishing a remanufacturing facility. In this paper, a framework is proposed to evaluate an ideal location for opening a remanufacturing plant, with the aid of ideal solution based multi criteria decision making (MCDM) tools, specifically TOPSIS, GRA and VIKOR. The suitable candidate location is then selected using the veto rule, which helps to overcome the limitation of using a single MCDM tool. An illustrative application in the Indian automotive sector is demonstrated to show the applicability of proposed framework. The approach is useful when there is a lack of quantitative data or the information is incomplete. The developed framework will help industries and economies to impact the use of eco-efficient and socio-economic systems and suggest pathways of transitioning to a more sustainable future

Uncertainty modeling in higher dimensions

Moderne Design Probleme stellen Ingenieure vor mehrere elementare Aufgaben. 1) Das Design muss die angestrebten Funktionalitäten aufweisen. 2) Es muss optimal sein in Hinsicht auf eine vorgegebene Zielfunktion. 3) Schließlich muss das Design abgesichert sein gegen Unsicherheiten, die nicht zu Versagen des Designs führen dürfen. All diese Aufgaben lassen sich unter dem Begriff der robusten Design Optimierung zusammenfassen und verlangen nach computergestützten Methoden, die Unsicherheitsmodellierung und Design Optimierung in sich vereinen. Unsicherheitsmodellierung enthält einige fundamentale Herausforderungen: Der Rechenaufwand darf gewisse Grenzen nicht überschreiten; unbegründete Annahmen müssen so weit wie möglich vermieden werden. Die beiden kritischsten Probleme betreffen allerdings den Umgang mit unvollständiger stochastischer Information und mit hoher Dimensionalität. Der niedrigdimensionale Fall ist gut erforscht, und es existieren diverse Methoden, auch unvollständige Informationen zu verarbeiten. In höheren Dimensionen hingegen ist die Anzahl der Möglichkeiten derzeit sehr begrenzt. Ungenauigkeit und Unvollständigkeit von Daten kann schwerwiegende Probleme verursachen - aber die Lage ist nicht hoffnungslos. In dieser Dissertation zeigen wir, wie man den hochdimensionalen Fall mit Hilfe von "Potential Clouds" in ein eindimensionales Problem übersetzt. Dieser Ansatz führt zu einer Unsicherheitsanalyse auf Konfidenzregionen relevanter Szenarien mittels einer Potential Funktion. Die Konfidenzregionen werden als Nebenbedingungen in einem Design Optimierungsproblem formuliert. Auf diese Weise verknüpfen wir Unsicherheitsmodellierung und Design Optimierung, wobei wir außerdem eine adaptive Aktualisierung der Unsicherheitsinformationen ermöglichen. Abschließend wenden wir unsere Methode in zwei Fallstudien an, in 24, bzw. in 34 Dimensionen.Modern design problems impose multiple major tasks an engineer has to accomplish. 1) The design should account for the designated functionalities. 2) It should be optimal with respect to a given design objective. 3) Ultimately the design must be safeguarded against uncertain perturbations which should not cause failure of the design. These tasks are united in the problem of robust design optimization giving rise to the development of computational methods for uncertainty modeling and design optimization, simultaneously. Methods for uncertainty modeling face some fundamental challenges: The computational effort should not exceed certain limitations; unjustified assumptions must be avoided as far as possible. However, the most critical issues concern the handling of incomplete information and of high dimensionality. While the low dimensional case is well studied and several methods exist to handle incomplete information, in higher dimensions there are only very few techniques. Imprecision and lack of sufficient information cause severe difficulties - but the situation is not hopeless. In this dissertation, it is shown how to transfer the high-dimensional to the one-dimensional case by means of the potential clouds formalism. Using a potential function, this enables a worst-case analysis on confidence regions of relevant scenarios. The confidence regions are weaved into an optimization problem formulation for robust design as safety constraints. Thus an interaction between optimization phase and worst-case analysis is modeled which permits a posteriori adaptive information updating. Finally, we apply our approach in two case studies in 24 and 34 dimensions, respectively

An overview of fuzzy techniques in supply chain management: bibliometrics, methodologies, applications and future directions

Every practice in supply chain management (SCM) requires decision making. However, due to the complexity of evaluated objects and the cognitive limitations of individuals, the decision information given by experts is often fuzzy, which may make it difficult to make decisions. In this regard, many scholars applied fuzzy techniques to solve decision making problems in SCM. Although there were review papers about either fuzzy methods or SCM, most of them did not use bibliometrics methods or did not consider fuzzy sets theory-based techniques comprehensively in SCM. In this paper, for the purpose of analyzing the advances of fuzzy techniques in SCM, we review 301 relevant papers from 1998 to 2020. By the analyses in terms of bibliometrics, methodologies and applications, publication trends, popular methods such as fuzzy MCDM methods, and hot applications such as supplier selection, are found. Finally, we propose future directions regarding fuzzy techniques in SCM. It is hoped that this paper would be helpful for scholars and practitioners in the field of fuzzy decision making and SCM