Chance-constrained programming with fuzzy stochastic coefficients

International audienceWe consider fuzzy stochastic programming problems with a crisp objective function and linear constraints whose coefficients are fuzzy random variables, in particular of type L-R. To solve this type of problems, we formulate deterministic counterparts of chance-constrained programming with fuzzy stochastic coefficients, by combining constraints on probability of satisfying constraints, as well as their possibility and necessity. We discuss the possible indices for comparing fuzzy quantities by putting together interval orders and statistical preference. We study the convexity of the set of feasible solutions under various assumptions. We also consider the case where fuzzy intervals are viewed as consonant random intervals. The particular cases of type L-R fuzzy Gaussian and discrete random variables are detailed

Improved two-phase solution strategy for multiobjective fuzzy stochastic linear programming problems with uncertain probability distribution

Multiobjective Fuzzy Stochastic Linear Programming (MFSLP) problem where the linear inequalities on the probability are fuzzy is called a Multiobjective Fuzzy Stochastic Linear Programming problem with Fuzzy Linear Partial Information on Probability Distribution (MFSLPPFI). The uncertainty presents unique difficulties in constrained optimization problems owing to the presence of conflicting goals and randomness surrounding the data. Most existing solution techniques for MFSLPPFI problems rely heavily on the expectation optimization model, the variance minimization model, the probability maximization model, pessimistic/optimistic values and compromise solution under partial uncertainty of random parameters. Although these approaches recognize the fact that the interval values for probability distribution have important significance, nevertheless they are restricted by the upper and lower limitations of probability distribution and neglected the interior values. This limitation motivated us to search for more efficient strategies for MFSLPPFI which address both the fuzziness of the probability distributions, and the fuzziness and randomness of the parameters. The proposed strategy consists two phases: fuzzy transformation and stochastic transformation. First, ranking function is used to transform the MFSLPPFI to Multiobjective Stochastic Linear Programming Problem with Fuzzy Linear Partial Information on Probability Distribution (MSLPPFI). The problem is then transformed to its corresponding Multiobjective Linear Programming (MLP) problem by using a-cut technique of uncertain probability distribution and linguistic hedges. In addition, Chance Constraint Programming (CCP), and expectation of random coefficients are applied to the constraints and the objectives respectively. Finally, the MLP problem is converted to a single-objective Linear Programming (LP) problem via an Adaptive Arithmetic Average Method (AAAM), and then solved by using simplex method. The algorithm used to obtain the solution requires fewer iterations and faster generation of results compared to existing solutions. Three realistic examples are tested which show that the approach used in this study is efficient in solving the MFSLPPFI

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Analysis of Decision Support Systems of Industrial Relevance: Application Potential of Fuzzy and Grey Set Theories

The present work articulates few case empirical studies on decision making in industrial context. Development of variety of Decision Support System (DSS) under uncertainty and vague information is attempted herein. The study emphases on five important decision making domains where effective decision making may surely enhance overall performance of the organization. The focused territories of this work are i) robot selection, ii) g-resilient supplier selection, iii) third party logistics (3PL) service provider selection, iv) assessment of supply chain’s g-resilient index and v) risk assessment in e-commerce exercises. Firstly, decision support systems in relation to robot selection are conceptualized through adaptation to fuzzy set theory in integration with TODIM and PROMETHEE approach, Grey set theory is also found useful in this regard; and is combined with TODIM approach to identify the best robot alternative. In this work, an attempt is also made to tackle subjective (qualitative) and objective (quantitative) evaluation information simultaneously, towards effective decision making. Supplier selection is a key strategic concern for the large-scale organizations. In view of this, a novel decision support framework is proposed to address g-resilient (green and resilient) supplier selection issues. Green capability of suppliers’ ensures the pollution free operation; while, resiliency deals with unexpected system disruptions. A comparative analysis of the results is also carried out by applying well-known decision making approaches like Fuzzy- TOPSIS and Fuzzy-VIKOR. In relation to 3PL service provider selection, this dissertation proposes a novel ‘Dominance- Based’ model in combination with grey set theory to deal with 3PL provider selection, considering linguistic preferences of the Decision-Makers (DMs). An empirical case study is articulated to demonstrate application potential of the proposed model. The results, obtained thereof, have been compared to that of grey-TOPSIS approach. Another part of this dissertation is to provide an integrated framework in order to assess gresilient (ecosilient) performance of the supply chain of a case automotive company. The overall g-resilient supply chain performance is determined by computing a unique ecosilient (g-resilient) index. The concepts of Fuzzy Performance Importance Index (FPII) along with Degree of Similarity (DOS) (obtained from fuzzy set theory) are applied to rank different gresilient criteria in accordance to their current status of performance. The study is further extended to analyze, and thereby, to mitigate various risk factors (risk sources) involved in e-commerce exercises. A total forty eight major e-commerce risks are recognized and evaluated in a decision making perspective by utilizing the knowledge acquired from the fuzzy set theory. Risk is evaluated as a product of two risk quantifying parameters viz. (i) Likelihood of occurrence and, (ii) Impact. Aforesaid two risk quantifying parameters are assessed in a subjective manner (linguistic human judgment), rather than exploring probabilistic approach of risk analysis. The ‘crisp risk extent’ corresponding to various risk factors are figured out through the proposed fuzzy risk analysis approach. The risk factor possessing high ‘crisp risk extent’ score is said be more critical for the current problem context (toward e-commerce success). Risks are now categorized into different levels of severity (adverse consequences) (i.e. negligible, minor, marginal, critical and catastrophic). Amongst forty eight risk sources, top five risk sources which are supposed to adversely affect the company’s e-commerce performance are recognized through such categorization. The overall risk extent is determined by aggregating individual risks (under ‘critical’ level of severity) using Fuzzy Inference System (FIS). Interpretive Structural Modeling (ISM) is then used to obtain structural relationship amongst aforementioned five risk sources. An appropriate action requirement plan is also suggested, to control and minimize risks associated with e-commerce exercises

Application of Multi-Objective Optimization Based on Genetic Algorithm for Sustainable Strategic Supplier Selection under Fuzzy Environment

Purpose: The incorporation of environmental objective into the conventional supplier selection practices is crucial for corporations seeking to promote green supply chain management (GSCM). Challenges and risks associated with green supplier selection have been broadly recognized by procurement and supplier management professionals. This paper aims to solve a Tetra “S” (SSSS) problem based on a fuzzy multi-objective optimization with genetic algorithm in a holistic supply chain environment. In this empirical study, a mathematical model with fuzzy coefficients is considered for sustainable strategic supplier selection (SSSS) problem and a corresponding model is developed to tackle this problem. Design/methodology/approach: Sustainable strategic supplier selection (SSSS) decisions are typically multi-objectives in nature and it is an important part of green production and supply chain management for many firms. The proposed uncertain model is transferred into deterministic model by applying the expected value measure (EVM) and genetic algorithm with weighted sum approach for solving the multi-objective problem. This research focus on a multiobjective optimization model for minimizing lean cost, maximizing sustainable service and greener product quality level. Finally, a mathematical case of textile sector is presented to exemplify the effectiveness of the proposed model with a sensitivity analysis. Findings: This study makes a certain contribution by introducing the Tetra ‘S’ concept in both the theoretical and practical research related to multi-objective optimization as well as in the study of sustainable strategic supplier selection (SSSS) under uncertain environment. Our results suggest that decision makers tend to select strategic supplier first then enhance the sustainability. Research limitations/implications: Although the fuzzy expected value model (EVM) with fuzzy coefficients constructed in present research should be helpful for solving real world problems. A detailed comparative analysis by using other algorithms is necessary for solving similar problems of agriculture, pharmaceutical, chemicals and services sectors in future. Practical implications: It can help the decision makers for ordering to different supplier for managing supply chain performance in efficient and effective manner. From the procurement and engineering perspectives, minimizing cost, sustaining the quality level and meeting production time line is the main consideration for selecting the supplier. Empirically, this can facilitate engineers to reduce production costs and at the same time improve the product quality. Originality/value: In this paper, we developed a novel multi-objective programming model based on genetic algorithm to select sustainable strategic supplier (SSSS) under fuzzy environment. The algorithm was tested and applied to solve a real case of textile sector in Pakistan. The experimental results and comparative sensitivity analysis illustrate the effectiveness of our proposed model.Peer Reviewe

The role of multiplier bounds in fuzzy data envelopment analysis

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The non-Archimedean epsilon ε is commonly considered as a lower bound for the dual input weights and output weights in multiplier data envelopment analysis (DEA) models. The amount of ε can be effectively used to differentiate between strongly and weakly efficient decision making units (DMUs). The problem of weak dominance particularly occurs when the reference set is fully or partially defined in terms of fuzzy numbers. In this paper, we propose a new four-step fuzzy DEA method to re-shape weakly efficient frontiers along with revisiting the efficiency score of DMUs in terms of perturbing the weakly efficient frontier. This approach eliminates the non-zero slacks in fuzzy DEA while keeping the strongly efficient frontiers unaltered. In comparing our proposed algorithm to an existing method in the recent literature we show three important flaws in their approach that our method addresses. Finally, we present a numerical example in banking with a combination of crisp and fuzzy data to illustrate the efficacy and advantages of the proposed approach

Decision Support System for Managing Reverse Supply Chain

Reverse logistics are becoming more and more important in the overall Industry area because of the environment and business factors. Planning and implementing a suitable reverse logistics network could bring more profit, customer satisfaction, and an excellent social picture for companies. But, most of the logistics networks are not equipped to handle the return products in reverse channels. Reverse logistics processes and plans rely heavily on reversing the supply chain so that companies can correctly identify and categorize returned products for disposition, an area that offers many opportunities for additional revenue. The science of reverse logistics includes return policy administration, product recall protocols, repairs processing, product repackaging, parts management, recycling, product disposition management, maximizing liquidation values and much more. The focus of this project is to develop a reverse logistics management system/ tools (RLMS). The proposed tools are demonstrated in the following order. First, we identify the risks involved in the reverse supply chain. Survey tool is used to collect data and information required for analysis. The methodologies that are used to identify key risks are the six sigma tools, namely Define, Measure, Analyse, Improve and Control (DMAIC), SWOT analysis, cause and effect, and Risk Mapping. An improved decision-making method using fuzzy set theory for converting linguistic data into numeric risk ratings has been attempted. In this study, the concept of ‘Left and Right dominance approach’(Chen and Liu, 2001) and Method of ‘In center of centroids’ (Thoran et al., 2012a,b) for generalized trapezoidal fuzzy numbers has been used to quantify the ‘degree of risk’ in terms of crisp ratings. After the analysis, the key risks are identified are categorized, and an action requirement plan suggested for providing guidelines for the managers to manage the risk successfully in the context of reverse logistics. Next, from risk assessment findings, information technology risk presents the highest risk impact on the performance of the reverse logistics, especially lack of use of a decision support system (DSS). We propose a novel multi-attribute decision (MADM) support tool that can categorizes return products and make the best alternative selection of recovery and disposal option using carefully considered criteria using MADM decision making methodologies such as fuzzy MOORA and VIKOR. The project can be applied to all types of industries. Once the returned products are collected and categorized at the retailers/ Points of return (PoR), an optimized network is required to determine the number of reprocessing centres to be opened and the optimized optimum material flow between retailers, reprocessing, recycling and disposal centers at minimum costs. The research develops a mixed integer linear programming model for two scenarios, namely considering direct shipping from retailer/ PoR to the respective reprocessing centers and considering the use of centralized return centers (CRC). The models are solved using LINGO 15 software and excel solver tools respectively. The advantage of the implementation of our solution is that it will help improve performance and reduce time. This benefits the company by having a reduction in their cost due to uncertainties and also contributes to better customer satisfaction. Implementation of these tools at ABZ computer distributing company demonstrates how the reverse logistics management tools can used in order to be beneficial to the organization. The tool is designed to be easily implemented at minimal cost and serves as a valuable tool for personnel faced with significant and costly decisions regarding risk assessment, decision making and network optimization in the reverse supply chain practices

Multiple Criteria Assessment of Insulating Materials with a Group Decision Framework Incorporating Outranking Preference Model and Characteristic Class Profiles

We present a group decision making framework for evaluating sustainability of the insulating materials. We tested thirteen materials on a model that was applied to retrofit a traditional rural building through roof's insulation. To evaluate the materials from the socio-economic and environmental viewpoints, we combined life cycle costing and assessment with an adaptive comfort evaluation. In this way, the performances of each coating material were measured in terms of an incurred reduction of costs and consumption of resources, maintenance of the cultural and historic significance of buildings, and a guaranteed indoor thermal comfort. The comprehensive assessment of the materials involved their assignment to one of the three preference-ordered sustainability classes. For this purpose, we used a multiple criteria decision analysis approach that accounted for preferences of a few tens of rural buildings' owners. The proposed methodological framework incorporated an outranking-based preference model to compare the insulating materials with the characteristic class profiles while using the weights derived from the revised Simos procedure. The initial sorting recommendation for each material was validated against the outcomes of robustness analysis that combined the preferences of individual stakeholders either at the output or at the input level. The analysis revealed that the most favorable materials in terms of their overall sustainability were glass wool, hemp fibres, kenaf fibres, polystyrene foam, polyurethane, and rock wool