Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input \u2013 output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

A Methodology for Assessing Eco-efficiency in Logistics Networks

Recent literature on sustainable logistics networks points to two important questions: (i) How to spot the preferred solution(s) balancing environmental and business concerns? (ii) How to improve the understanding of the trade-offs between these two dimensions? We posit that a complete exploration of the efficient frontier and trade-offs between profitability and environmental impacts are particularly suitable to answer these two questions. In order to deal with the exponential number of basic efficient points in the frontier, we propose a formulation that performs in exponential time for the number of objective functions only. We illustrate our findings by designing a complex recycling logistics network in Germany.Eco-efficiency;Environmental impacts;Profitability;Recycling logistics network

Methodological review of multicriteria optimization techniques: aplications in water resources

Multi-criteria decision analysis (MCDA) is an umbrella approach that has been applied to a wide range of natural resource management situations. This report has two purposes. First, it aims to provide an overview of advancedmulticriteriaapproaches, methods and tools. The review seeks to layout the nature of the models, their inherent strengths and limitations. Analysis of their applicability in supporting real-life decision-making processes is provided with relation to requirements imposed by organizationally decentralized and economically specific spatial and temporal frameworks. Models are categorized based on different classification schemes and are reviewed by describing their general characteristics, approaches, and fundamental properties. A necessity of careful structuring of decision problems is discussed regarding planning, staging and control aspects within broader agricultural context, and in water management in particular. A special emphasis is given to the importance of manipulating decision elements by means ofhierarchingand clustering. The review goes beyond traditionalMCDAtechniques; it describes new modelling approaches. The second purpose is to describe newMCDAparadigms aimed at addressing the inherent complexity of managing water ecosystems, particularly with respect to multiple criteria integrated with biophysical models,multistakeholders, and lack of information. Comments about, and critical analysis of, the limitations of traditional models are made to point out the need for, and propose a call to, a new way of thinking aboutMCDAas they are applied to water and natural resources management planning. These new perspectives do not undermine the value of traditional methods; rather they point to a shift in emphasis from methods for problem solving to methods for problem structuring. Literature review show successfully integrations of watershed management optimization models to efficiently screen a broad range of technical, economic, and policy management options within a watershed system framework and select the optimal combination of management strategies and associated water allocations for designing a sustainable watershed management plan at least cost. Papers show applications in watershed management model that integrates both natural and human elements of a watershed system including the management of ground and surface water sources, water treatment and distribution systems, human demands,wastewatertreatment and collection systems, water reuse facilities,nonpotablewater distribution infrastructure, aquifer storage and recharge facilities, storm water, and land use

Robust optimization in data envelopment analysis: extended theory and applications.

Performance evaluation of decision-making units (DMUs) via the data envelopment analysis (DEA) is confronted with multi-conflicting objectives, complex alternatives and significant uncertainties. Visualizing the risk of uncertainties in the data used in the evaluation process is crucial to understanding the need for cutting edge solution techniques to organizational decisions. A greater management concern is to have techniques and practical models that can evaluate their operations and make decisions that are not only optimal but also consistent with the changing environment. Motivated by the myriad need to mitigate the risk of uncertainties in performance evaluations, this thesis focuses on finding robust and flexible evaluation strategies to the ranking and classification of DMUs. It studies performance measurement with the DEA tool and addresses the uncertainties in data via the robust optimization technique. The thesis develops new models in robust data envelopment analysis with applications to management science, which are pursued in four research thrust. In the first thrust, a robust counterpart optimization with nonnegative decision variables is proposed which is then used to formulate new budget of uncertainty-based robust DEA models. The proposed model is shown to save the computational cost for robust optimization solutions to operations research problems involving only positive decision variables. The second research thrust studies the duality relations of models within the worst-case and best-case approach in the input – output orientation framework. A key contribution is the design of a classification scheme that utilizes the conservativeness and the risk preference of the decision maker. In the third thrust, a new robust DEA model based on ellipsoidal uncertainty sets is proposed which is further extended to the additive model and compared with imprecise additive models. The final thrust study the modelling techniques including goal programming, robust optimization and data envelopment to a transportation problem where the concern is on the efficiency of the transport network, uncertainties in the demand and supply of goods and a compromising solution to multiple conflicting objectives of the decision maker. Several numerical examples and real-world applications are made to explore and demonstrate the applicability of the developed models and their essence to management decisions. Applications such as the robust evaluation of banking efficiency in Europe and in particular Germany and Italy are made. Considering the proposed models and their applications, efficiency analysis explored in this research will correspond to the practical framework of industrial and organizational decision making and will further advance the course of robust management decisions

Sustainable supply chain network design integrating logistics outsourcing decisions in the context of uncertainties

Les fournisseurs de services logistiques (3PLs) possèdent des potentialités pour activer les pratiques de développement durables entre les différents partenaires d’une chaîne logistique (Supply Chain SC). Il existe un niveau optimal d'intégration des 3PLs en tant que fournisseurs, pour s’attendre à des performances opérationnelles élevées au sein de toute la SC. Ce niveau se traduit par la distinction des activités logistiques à externaliser de celles à effectuer en interne. Une fois que les activités logistiques externalisés sont stratégiquement identifiées, et tactiquement dimensionnées, elles doivent être effectuées par des 3PLs appropriés afin d’endurer les performances économiques ; sociales ; et environnementales de la SC. La présente thèse développe une approche holistique pour concevoir une SC durable intégrant les 3PLs, dans un contexte incertain d’affaires et politique de carbone. Premièrement, une approche de modélisation stochastique en deux étapes est suggérée pour optimiser à la fois le niveau d'intégration des 3PLs, et le niveau d'investissement en technologies sobres au carbone, et ce dans le contexte d’une SC résiliente aux changements climatiques. Notre SC est structurée de façon à capturer trois principales préoccupations du Supply Chain Management d’une entreprise focale FC (e. g. le fabricant) : Sécurité d’approvisionnement, Segmentation de distribution, et Responsabilité élargie des producteurs. La première étape de l'approche de modélisation suggère un plan stochastique basé sur des scenarios plus probables, afin de capturer les incertitudes inhérentes à tout environnement d’affaires (e. g. la fluctuation de la demande des différents produits ; la qualité et la quantité de retour des produits déjà utilisés ; et l’évolution des différents coûts logistiques en fonction du temps). Puis, elle propose un modèle de programmation stochastique bi-objectif, multi-période, et multi-produit. Le modèle de programmation quadratique, et non linéaire consiste à minimiser simultanément le coût logistique total espéré, et les émissions de Gaz à effet de Serre de la SC fermée. L'exécution du modèle au moyen d'un algorithme basé sur la méthode Epsilon-contraint conduit à un ensemble de configurations Pareto optimales d’une SC dé- carbonisée, avant tout investissement en technologie sobre au carbone. Chacune de ces configurations sépare les activités logistiques à externaliser de celles à effectuer en interne. La deuxième étape de l'approche de modélisation permet aux décideurs de choisir la meilleure configuration de la SC parmi les configurations Pareto optimales identifiées. Le concept de Prix du Carbone Interne est utilisé pour établir un plan stochastique du prix de carbone, dans le cadre d'un régime de déclaration volontaire du carbone. Nous proposons un ensemble des technologies sobres au carbone, dans le domaine de transport des marchandises, disposées à concourir pour contrer les politiques incertaines de carbone. Un modèle stochastique combinatoire, et linéaire est développé pour minimiser le coût total espéré, sous contraintes de l’abattement du carbone; limitation du budget, et la priorité attribuée pour chaque Technologie Réductrice de carbone (Low Carbone Reduction LCR). L'injection de chaque solution Pareto dans le modèle, et la résolution du modèle conduisent à sélectionner la configuration de la SC, la plus résiliente aux changements climatiques. Cette configuration définit non seulement le plan d'investissement optimal en LCR, mais aussi le niveau optimal d’externalisation de la logistique dans la SC. Deuxièmement, une fois que les activités logistiques à externaliser sont stratégiquement définies et tactiquement dimensionnées, elles ont besoin d’être effectuées par des 3PL appropriées, afin de soutenir la FC à construire une SC durable et résiliente. Nous suggérons DEA-QFD / Fuzzy AHP- Conception robuste de Taguchi : Une approche intégrée & robuste, pour sélectionner les 3PL candidats les plus efficients. Les critères durables et les risques liés à l’environnement d’affaires, sont identifiés, classés et ordonnés. Le Déploiement de la Fonction Qualité (QFD) est renforcé par le Processus Hiérarchique Analytique (AHP), et par la logique floue pour déterminer avec consistance l'importance relative de chaque facteur de décision, et ce, conformément aux besoins logistiques réels, et stratégies d'affaires de la FC. L’Analyse d’Enveloppement des Données (DEA) Data Envelopment Analysis conduit à limiter la liste des candidats, uniquement à ceux d’efficiences comparables, et donc excluant tout candidat moins efficient. La technique de conception robuste Taguchi permet de réaliser un plan d'expérience qui détermine un candidat idéal nommé 'optimum de Taguchi' ; un Benchmark pour comparer les 3PLs candidats. Par suite, le 3PL le plus efficient est celui le plus proche de cet optimum. Nous conduisons actuellement une étude de cas d’une entreprise qui fabrique et commercialise les fours à micro-ondes pour valider la modélisation stochastique en deux étapes. Certains aspects concernant l’application de l’approche sont reportés. Enfin, un exemple de sélection d’un 3PL durable pour s’occuper de la logistique inverse est fourni, pour démontrer l'applicabilité de l'approche intégrée & robuste, et montrer sa puissance par rapport aux approches populaires de sélection.The Third-Party Logistics service providers (3PLs) have the potentialities to activate sustainable practices between different partners of a Supply Chain (SC). There exists an optimal level of integrating 3PLs as suppliers of a Focal Company within the SC, to expect for high operational performances. This level leads to distinguish all the logistics activities to outsource from those to perform in-house. Once the outsourced logistics activities are strategically identified, and tactically dimensioned, they need to be performed by appropriate 3PLs to sustain economic, social and environmental performances of the SC. The present thesis develops a holistic approach to design a sustainable supply chain integrating 3PLs, in the context of business and carbon policy uncertainties. First, a two-stage stochastic modelling approach is suggested to optimize both the level of 3PL integration, and of Low Carbon Reduction LCR investment within a climate change resilient SC. Our SC is structured to capture three main SC management issues of the Focal Company FC (e.g. The manufacturer) : Security of Supplies; Distribution Segmentation; and Extended Producer Responsibility. The first-stage of the modelling approach suggests a stochastic plan based scenarios capturing business uncertainties, and proposes a two-objective, multi-period, and multi-product programming model, for minimizing simultaneously, the expected logistics total cost, and the Green House Gas GHG emissions of the whole SC. The run of the model by means of a suggested Epsilon-constraint algorithm leads to a set of Pareto optimal decarbonized SC configurations, before any LCR investment. Each one of these configurations distinguishes the logistics activities to be outsourced, from those to be performed in-house. The second-stage of the modelling approach helps the decision makers to select the best Pareto optimal SC configuration. The concept of internal carbon price is used to establish a stochastic plan of carbon price in the context of a voluntary carbon disclosure regime, and we propose a set of LCR technologies in the freight transportation domain ready to compete for counteracting the uncertain carbon policies. A combinatory model is developed to minimize the total expected cost, under the constraints of; carbon abatement, budget limitation, and LCR investment priorities. The injection of each Pareto optimal solution in the model, and the resolution lead to select the most efficient climate resilient SC configuration, which defines not only the optimal plan of LCR investment, but the optimal level of logistics outsourcing within the SC as well. Secondly, once the outsourced logistics are strategically defined they need to be performed by appropriate 3PLs for supporting the FC to build a Sustainable SC. We suggest the DEA-QFD/Fuzzy AHP-Taguchi Robust Design: a robust integrated selection approach to select the most efficient 3PL candidates. Sustainable criteria, and risks related to business environment are identified, categorized, and ordered. Quality Function Deployment (QFD) is reinforced by Analytic Hierarchic Process (AHP), and Fuzzy logic, to consistently determine the relative importance of each decision factor according to the real logistics needs, and business strategies of the FC. Data Envelopment Analysis leads to shorten the list of candidates to only those of comparative efficiencies. The Taguchi Robust Design technique allows to perform a plan of experiment, for determining an ideal candidate named ‘optimum of Taguchi’. This benchmark is used to compare the remainder 3Pls candidates, and the most efficient 3PL is the closest one to this optimum.We are currently conducting a case study of a company that manufactures and markets microwave ovens for validating the two-stage stochastic approach, and certain aspects of its implementation are provided. Finally, an example of selecting a sustainable 3PL, to handle reverse logistics is given for demonstrating the applicability of the integrated & robust approach, and showing its power compared to popular selection approaches. Keywords:Third Party Logistics; Green Supply Chain design; Stochastic Multi-Objective Optimization; Carbon Pricing; Taguchi Robust Design

On the flexibility of an eco-industrial park (EIP) for managing industrial water

In a recent paper, a generic model, based on a multiobjective optimization procedure, for water supply system for a single company and for an eco-industrial park was proposed and illustrated by a park involving three companies A, B and C. The best configuration was identified by simultaneously minimizing the fresh water flow rate, the regenerated water flow rate and the number of connections in the eco-industrial park. The question is now to know what the maximal increase/decrease in pollutant flow rates is, so that the eco-industrial park remains feasible, economically profitable and environmentally friendly. A preliminary study shows that the park can accept an increase of pollutant flow rates of 29% in company A, 12% in company B and only 1% in company C; beyond these limits the industrial symbiosis becomes not feasible. The proposed configuration is not flexible with a very limited number of connections. Indeed, the solution implemented for conferring some flexibility to this network is to increase the number of connections within the park. However, connections have a cost, so the increase of their number needs to remain moderate. The number of connections is augmented until the symbiosis becomes unfeasible, or until the gain for each company to participate to the park becomes lower than a given threshold. Several cases are studied by increasing the pollutant flow rates under two different scenarios: 1) in only one company, 2) in two or three companies simultaneously

A Methodology for Assessing Eco-efficiency in Logistics Networks

Recent literature on sustainable logistics networks points to two important questions: (i) How to spot the preferred solution(s) balancing environmental and business concerns? (ii) How to improve the understanding of the trade-offs between these two dimensions? We posit that a complete exploration of the efficient frontier and trade-offs between profitability and environmental impacts are particularly suitable to answer these two questions. In order to deal with the exponential number of basic efficient points in the frontier, we propose a formulation that performs in exponential time for the number of objective functions only. We illustrate our findings by designing a complex recycling logistics network in Germany

Multiple Criteria Decision Analysis: Classification Problems and Solutions

Multiple criteria decision analysis (MCDA) techniques are developed to address challenging classification problems arising in engineering management and elsewhere. MCDA consists of a set of principles and tools to assist a decision maker (DM) to solve a decision problem with a finite set of alternatives compared according to two or more criteria, which are usually conflicting. The three types of classification problems to which original research contributions are made are Screening: Reduce a large set of alternatives to a smaller set that most likely contains the best choice. Sorting: Arrange the alternatives into a few groups in preference order, so that the DM can manage them more effectively. Nominal classification: Assign alternatives to nominal groups structured by the DM, so that the number of groups, and the characteristics of each group, seem appropriate to the DM. Research on screening is divided into two parts: the design of a sequential screening procedure that is then applied to water resource planning in the Region of Waterloo, Ontario, Canada; and the development of a case-based distance method for screening that is then demonstrated using a numerical example. Sorting problems are studied extensively under three headings. Case-based distance sorting is carried out with Model I, which is optimized for use with cardinal criteria only, and Model II, which is designed for both cardinal and ordinal criteria; both sorting approaches are applied to a case study in Canadian municipal water usage analysis. Sorting in inventory management is studied using a case-based distance method designed for multiple criteria ABC analysis, and then applied to a case study involving hospital inventory management. Finally sorting is applied to bilateral negotiation using a case-based distance model to assist negotiators that is then demonstrated on a negotiation regarding the supply of bicycle components. A new kind of decision analysis problem, called multiple criteria nominal classification (MCNC), is addressed. Traditional classification methods in MCDA focus on sorting alternatives into groups ordered by preference. MCNC is the classification of alternatives into nominal groups, structured by the DM, who specifies multiple characteristics for each group. The features, definitions and structures of MCNC are presented, emphasizing criterion and alternative flexibility. An analysis procedure is proposed to solve MCNC problems systematically and applied to a water resources planning problem