An application of the fuzzy ELECTRE method for supplier selection

Supplier selection is vital to the success of a manufacturing firm. Supplier selection is a multi-criteria decision-making problem and is of strategic importance for most companies. As the conventional methods for supplier selection are inadequate for dealing with the imprecise or vague nature of linguistic assessment, a new method called the fuzzy technique for ELECTRE (ELimination Et Choix Traduisant la REalité) is proposed. The aim of this study is to compare and contrast crisp and fuzzy ELECTRE methods for supplier selection. The proposed methods are applied to a manufacturing company in Turkey. After determining the criteria that affect the supplier selection decisions, the results for both crisp and fuzzy ELECTRE methods are presented.     

Lexicographic fuzzy multi-objective model for minimisation of exceptional and void elements in manufacturing cell formation

This research proposes a lexicographic fuzzy multi-objective model based on perfect grouping for concurrent solving the part-family and machine-cell formation problems in a cellular manufacturing system. New simplified mathematical expressions of exceptional and void elements are proposed, opposing conventional quadratic and absolute functions. The main objectives of the proposed solution model, that is, the minimisation of both the number of exceptional elements and the number of void elements is defined by fuzzy goals as pre-emptive ordering. A lexicographic fuzzy goal model is developed to enhance cell performance and machine utilisation simultaneously. A satisfactory efficient solution can easily be obtained, and alternative solutions can also be generated by capturing flexibility of the proposed fuzzy multi-objective programming model. The formulated model can be solved by existing integer programming solvers. Finally, the evaluation of cell formation problems is briefly discussed to show the performance of the proposed model.     

Multi-site production planning integrating procurement and distribution plans in multi-echelon supply chains: an interactive fuzzy goal programming approach

Motivated by a real case of an automobile company, this study proposes a multi-objective, multi-site production planning model integrating procurement and distribution plans in a multi-echelon supply chain network with multiple suppliers, multiple manufacturing plants and multiple distribution centres. The model incorporates four important conflicting objectives simultaneously: minimisation of the total cost of logistics, maximisation of the total value of purchasing, minimisation of defective items and minimisation of late deliveries subject to some realistic constraints. Due to the imprecise/fuzzy nature of the objectives’ aspiration levels and some critical data, an interactive fuzzy goal programming formulation is first developed. Then, a novel fuzzy approach is proposed to convert the FGP model into an auxiliary crisp formulation to find an efficient compromise solution. The proposed model and solution method are validated through some numerical tests. Computational results indicate the practicality and tractability of the proposed model and also the superiority of the proposed auxiliary crisp formulation in contrast to the current alternative fuzzy approaches.     

Distance-based fuzzy MCDM approach for evaluating flexible manufacturing system alternatives

Considering the high required capital outlay and moderate risk of a flexible manufacturing system (FMS) investment, economic justification techniques are insufficient by themselves since they cannot cope with the benefits such as flexibility and enhanced quality offered by advanced manufacturing technologies. A robust decision-making procedure for evaluating FMS requires the consideration of both economic and strategic investment measures. A distance-based fuzzy multicriteria decision-making (MCDM) framework based on the concepts of ideal and anti-ideal solutions is presented for the selection of an FMS from a set of mutually exclusive alternatives. The proposed method provides the means for integrating the economic figure of merit with the strategic performance variables. The multicriteria decision approach presented here enables us to incorporate data in the forms of linguistic variables, triangular fuzzy numbers and crisp numbers into the evaluation process of FMS alternatives. Linguistic variables are also used to indicate the criteria's importance weights assigned by the decisionmakers. A comprehensive example illustrates the application of the multicriteria decision analysis.     

Applying fuzzy logic and constraint networks to a problem of manufacturing flexibility

The primary contribution is to present an application of fuzzy logic and constraint networks to a problem of manufacturing flexibility. The paper begins with a literature review showing the different approaches when measuring manufacturing flexibility. Next, it provides a brief review of fuzzy logic and its applications, explaining how it enhances the ability to model flexibility strategies. Then, the application is presented and its utility is demonstrated with an example from the production of printed circuit boards. Finally, the paper concludes with comments on how this model could be expanded to other applications.     

Multi-site integrated production-distribution planning with trans-shipment: a fuzzy goal programming approach

In multi-site (parallel) manufacturing systems, each selling region (SR) is usually allocated to a specific manufacturing site (MS) in order to minimise the transportation costs, simplify the planning process, etc. However, such manufacturing systems usually encounter great drawbacks in terms of over-achievement or under-achievement of the forecasted demand due to isolation of the MSs. To cope with this drawback, this paper proposes a novel framework for preparing an optimal aggregate production plan by interconnecting the MSs through lateral trans-shipment. In the presence of fluctuating and dynamic demands, we apply some classic strategies including the inventory holding, back-ordering, and additional capacity options (i.e. overtime and changing workforce level) as well as lateral trans-shipment of products among MSs as the feasible strategies undertaken. Maximising the total profit and minimising the manufacturing lead time are considered as two managerial goals. Due to ambiguousness of some critical parameters as well as vagueness of objectives’ target values, a fuzzy goal programming (FGP) approach with imprecise goal hierarchy is developed for modelling the aggregate production-distribution planning (APDP) problem with trans-shipment. The proposed FGP model is then converted to an equivalent crisp one by combining the two recently developed fuzzy programming approaches. An illustrative example inspired by a real case study is provided to show the usefulness and applicability of the proposed model.     

Modeling and analysis of a manufacturing cell formation problem with fuzzy mixed-integer programming

Cell formation (CF) has received much attention from academicians and practitioners because of its strategic importance to modern manufacturing practice. In this paper a sophisticated mixed-integer programming (MIP) model is proposed to simultaneously form manufacturing cells and minimize the cost of dealing with exceptional elements. Also, we illustrate how a fuzzy mixed-integer programming (FMIP) approach can be used to solve the CF problem in a fuzzy environment, propose a new fuzzy operator, and examine the impact of different membership functions and operators on computational performance. Our study shows that FMIP not only provides a better and more flexible way of representing the problem domain, it also leads to improved overall performance.     

Development of a component-based machining centre selection model using AHP

Machining centres are widely used in manufacturing companies all over the world. Since investments in machining centres are long-term and expensive, selection of the most appropriate machining centre is an important decision for manufacturing companies. There has been considerable effort spent in developing crisp and fuzzy multi-criteria decision-making (MCDM) models that use technical specifications provided by machining-centre manufacturers such as, axis size, power, spindle speed, tolerance, repeatability, cutting-tool change time, and number of cutting tools along with other economical and commercial factors. However, the technical specifications are directly taken from machining-centre manufacturers’ catalogues without checking their correctness, adequacies, or ability to represent the areas that are used for measurement. In such a case, one cannot be sure whether the outcomes are sound or not without a detailed check of the technical specifications, which can only be performed after actual usage of the machine itself. To overcome all such problems, an analytic hierarchy process (AHP) model that evaluates the machining centre components is developed in this paper. The new component-based AHP model is then compared with two MCDM models that use only technical specification values.     

Multi-objective cell formation and production planning in dynamic virtual cellular manufacturing systems

This article presents a fuzzy goal programming-based approach for solving a multi-objective mathematical model of cell formation problem and production planning in a dynamic virtual cellular manufacturing system. In a dynamic environment, the product mix and part demand change over a planning horizon decomposed into several time periods. Thus, the cell formation done for one period may be no longer efficient for subsequent periods and hence reconfiguration of cells is required. Due to the variation of demand and necessity of reconfiguration of cells, the virtual cellular manufacturing (VCM) concept has been proposed by researchers to utilise the benefits of cellular manufacturing without reconfiguration charges. In a VCM system, machines, parts and workers are temporarily grouped for one period during which machines and workers of a group dedicatedly serve the parts of that group. The only difference of VCM with a real CM is that machines of the same group are not necessarily brought to a physical proximity in VCM. The virtual cells are created periodically depending on changes in demand volumes and mix, as new parts accumulate during a planning horizon. The major advantage of the proposed model is the consideration of demand and part mix variation over a multi-period planning horizon with worker flexibility. The aim is to minimise holding cost, backorder cost and exceptional elements in a cubic space of machine–part–worker incidence matrix. To illustrate the applicability of the proposed model, an example has been solved and computational results are presented.     

A rolling horizon approach for material requirement planning under fuzzy lead times

This paper proposes a fuzzy multi-objective integer linear programming (FMOILP) approach to model a material requirement planning (MRP) problem with fuzzy lead times. The objective functions minimise the total costs, back-order quantities and idle times of productive resources. Capacity constraints are included by considering overtime resources. Into the crisp MRP multi-objective model, we incorporate the possibility of occurrence of each uncertain lead time using fuzzy numbers. Then FMOILP is transformed into an auxiliary crisp mixed-integer linear programming model by a fuzzy goal programming approach for each fuzzy lead time combination. In order to defuzzify the set of solutions associated with each fuzzy lead time combination, a solution method based on the centre of gravity concept is addressed. Model validation with a numerical example is carried out by a novel rolling horizon procedure where uncertain lead times are updated during each planning period according to the centre of gravity obtained. For illustration purposes, the proposed solution approach is satisfactorily compared to a rolling horizon approach in which lead times are allocated when the possibility of occurrence is established at one.     

Quantifying data for group technology with weighted fuzzy features

The high potential of using group technology in manufacturing has attracted the interest of both practitioners and researchers. Group technology is based on clustering parts which have similar features. Very often it is very hard to quantify successfully data regarding these features. This is because in many real applications features are fuzzy. This paper identifies two types of fuzzy features: qualitative features, and quantitative ones with subjective meaning. The paper presents a methodology for quantifying the data that refer to the fuzzy features. The proposed methodology deals with crisp and fuzzy data in a unified manner. Finally, some clustering approaches which process the quantified features are also discussed     

Maintenance policy selection in manufacturing firms using the fuzzy MCDM approach

In manufacturing firms, there is a critical need for proper maintenance of manufacturing facilities. The maintenance process enhances customer satisfaction and reliability of the products, and increases the profit of the manufacturer. Therefore, a proper maintenance policy selection is a critical issue for manufacturers, as an inefficient maintenance policy affects not only the direct cost of the firm but also the other aspects. In the present study, maintenance policy selection at the level of the firm rather than the equipment level is shown, and for selection various criteria have been identified. The presented work not only provides the best alternatives but also provides an alternative ranking, which facilitates decision-makers in choosing alternatives according to their constraints. These selection criteria are different in nature, as some give a crisp value, whereas others are defined in linguistic terms. To select the appropriate maintenance policy, a distance-based fuzzy multicriteria decision-making (MCDM) approach has been employed. The proposed method provides the means for integrating the economic figure of merit with the strategic performance variables. The MCDM approach is efficient in incorporating data, in the form of linguistic variables, triangular fuzzy numbers, and crisp numbers, into the evaluation process of maintenance policy alternatives. A comprehensive example illustrates the application of the distance-based fuzzy MCDM approach.     

基于模糊神经网络的公差-成本模型研究

研究了面向制造环境的公差-成本模型。对制造环境中有关的加工因素进行分类及模糊化处理,构造了加工因素的成本模糊影响系数,并以此系数和零件公差作为输入,建立了基于模糊神经网络的公差-成本模型。此模型在表征加工成本、公差关系上的精度较高,更适应面向制造公差设计的要求。     

An integrated weighted fuzzy multi-objective model for supplier selection and order scheduling in a supply chain

This paper presents a new weighted fuzzy multi-objective model to integrated supplier selection, order quantity allocation and customer order scheduling problem to prepare a responsive and order-oriented supply chain in a make-to-order manufacturing system. Total cost and quality of purchased parts as well as the reliability of on-time delivery of customer orders are regarded as the objectives of the model. On the other hand, flexible suppliers can contribute to the responsiveness and flexibility of entire supply chain in the face of uncertain customer orders. Therefore, a mathematical measure is developed for evaluating the volume flexibility of suppliers and is considered as the other objective of the model. Furthermore, by considering the effect of interdependencies between the selection criteria and to handle inconsistent and uncertain judgments, a fuzzy analytic network process method is used to identify top suppliers and consider as the last objective. In order to optimise these objectives, the decision-maker needs to decide from which supplier to purchase parts needed to assemble the customer orders, how to allocate the demand for parts between the selected suppliers, and how to schedule the customer orders for assembled products over the planning time horizon. Numerical examples are presented and computational analysis is reported.     

The effects of product modularity on launch speed

Extant literature suggests that product modularity positively and directly impacts the timeliness and frequency of new products as well as manufacturing performance, particularly flexibility. Little is known about the nature of these relationships, however, since few empirical studies have been done. Important questions remain unanswered including whether the effect of modularity on launch speed is direct or indirect, and what role other constructs might play. This study explores these issues by examining the effects of product modularity on launch speed within a holistic framework that considers the roles of product platforms and manufacturing flexibility. Drawing upon dynamic capabilities theory in the resource-based view, the model depicts product modularity as antecedent to product platforms, product platforms as antecedent to manufacturing flexibility and manufacturing flexibility as antecedent to launch speed. The model is strongly supported by an analysis of 93 manufacturers. Results reveal a positive effect of product modularity on launch speed, but it is delivered through the mediating effects of product platforms and manufacturing flexibility. In contrast to earlier work, the findings show modularity alone is an insufficient condition for the timely and frequent introduction of new products. Rather, launch speed is engendered by a ‘gestalt’ of dynamic capabilities.     

带有积压定单的最优模糊存储模型

本文提出一个新的具有积压定单的关于模糊总需求的模糊存储模型。在模糊函数原理下，给出了模糊总存储成本。为了寻找最优解，使用积分均值法白化模糊总存储成本，利用Lingo8．0求解不等式约束问题，我们发现最优解都是确定的实数。此外，当模糊总需求是确定的实数时，我们提出模型的最优解与经典的具有积压定单存储模型具有相同的结果。     

统一集论与人工智能

通过综合经典集合、模糊集合、可拓集合、Vague集合、粗糙集合、集对分析、FHW（模糊灰色物元空间）、FEEC（模糊可拓经济控制）等多种理论，提出了统一集概念，并详细讨论统一集的各种运算以及相关性质。从分析集合理论和人类思维形式之间的关系入手，把统一集理论初步应用到模式识别、聚类分析、逻辑推理、机器学习、智能决策等多种人工智能领域，指出了集合论及其运算系统与逻辑推理系统的等价关系。统一集能对现有的理论进行总结、统一，还为开辟崭新的集合论、逻辑推理方法提供很好的理论基础。     

Modelling and integration of customer flexibility in the order commitment process for high mix low volume production

With increasing product variety and dynamic demand fluctuation, manufacturing industry is moving towards a high product mix and low order volume production environment. Consequently, the order commitment process is becoming one of the most important processes for manufacturing firms to meet individual customer's needs with limited resources. However, demands for shortened delivery lead time, diverse customer requirements and more frequent customer orders have made the order commitment task more challenging. This paper attempts to tackle these new challenges by incorporating not only manufacturing flexibility but also flexibility from the demand side. Customer flexibility is characterised by customer indifference to certain product attributes and/or delivery schedules. Intuitively, with the consideration of customer flexibility, both manufacturers’ and customers’ interests can be better served since the solution space of matching demand and supply can be extended beyond the traditional domain purely from a manufacturing perspective. To this end, a systematic approach is developed to characterise and model customer flexibility. A mixed-integer-programming model is formulated to provide optimal order commitment decisions.     

A fuzzy multi-criteria decision-making approach for managing performance and risk in integrated procurement–production planning

Nowadays in Supply Chain (SC) networks, a high level of risk comes from SC partners. An effective risk management process becomes as a consequence mandatory, especially at the tactical planning level. The aim of this article is to present a risk-oriented integrated procurement–production approach for tactical planning in a multi-echelon SC network involving multiple suppliers, multiple parallel manufacturing plants, multiple subcontractors and several customers. An originality of the work is to combine an analytical model allowing to build feasible scenarios and a multi-criteria approach for assessing these scenarios. The literature has mainly addressed the problem through cost or profit-based optimisation and seldom considers more qualitative yet important criteria linked to risk, like trust in the supplier, flexibility or resilience. Unlike the traditional approaches, we present a method evaluating each possible supply scenario through performance-based and risk-based decision criteria, involving both qualitative and quantitative factors, in order to clearly separate the performance of a scenario and the risk taken if it is adopted. Since the decision-maker often cannot provide crisp values for some critical data, fuzzy sets theory is suggested in order to model vague information based on subjective expertise. Fuzzy Technique for Order of Preference by Similarity to Ideal Solution is used to determine both the performance and risk measures correlated to each possible tactical plan. The applicability and tractability of the proposed approach is shown on an illustrative example and a sensitivity analysis is performed to investigate the influence of criteria weights on the selection of the procurement–production plan.     

Waste treatment: an environmental,economic and social analysis with a new group fuzzy PROMETHEE approach

Most complex decisions involve several stakeholders and therefore need to be solved using a group multi-criteria decision method. However, stakeholders or decision-makers often have divergent views, especially in the environmental sector. In order to integrate this divergence, a new group fuzzy PROMETHEE approach is introduced to combine the traditional environmental criteria of life cycle assessments with social and economic criteria. The modelling of uncertainty within the group of decision-makers using a fuzzy approach makes this method unique. The proposed fuzzy approach differs significantly from the standard one. The decision-makers express their judgments in crisp forms. In order to take into account the intrinsic dispersion of judgments within the group, a posteriori fuzzification procedure is applied. The crisp values are not simply aggregated; they are converted into a triangular fuzzy number based on the given evaluations. As a consequence, the definition of fuzzy membership functions, as required in standard fuzzy logic, is not required, which simplifies the process and makes it more reliable. The new approach is illustrated with a real case study concerning the selection of the best waste treatment solution in a natural park from among a traditional incinerator and an innovative integrated plant.