Fuzzy linear programming models for new product design using QFD with FMEA

Quality function deployment (QFD) is a customer-driven approach in processing new product developments in order to maximize customer satisfaction. Determining the fulfillment levels of design requirements (DRs) and parts characteristics (PCs) is an important decision problem during QFD activity processes for new product development. Unlike the existing literature, which mainly focuses on the determination of DRs, this paper proposes fuzzy linear programming models to determine the fulfillment levels of PCs under the requirement to achieve the determined contribution levels of DRs for customer satisfaction. In addition, considering the design risk, this paper incorporates failure modes and effect analysis (FMEA) into QFD processes, which is treated as the constraint in the models. To cope with the vague nature of product development processes, fuzzy approaches are used for both FMEA and QFD. The illustration of the proposed models is performed with a numerical example to demonstrate the applicability in practice.     

Fuzzy linear programming models for NPD using a four-phase QFD activity process based on the means-end chain concept

Quality function deployment (QFD) is a customer-driven approach in processing new product development (NPD) to maximize customer satisfaction. Determining the fulfillment levels of the “hows”, including design requirements (DRs), part characteristics (PCs), process parameters (PPs) and production requirements (PRs), is an important decision problem during the four-phase QFD activity process for new product development. Unlike previous studies, which have only focused on determining DRs, this paper considers the close link between the four phases using the means-end chain (MEC) concept to build up a set of fuzzy linear programming models to determine the contribution levels of each “how” for customer satisfaction. In addition, to tackle the risk problem in NPD processes, this paper incorporates risk analysis, which is treated as the constraint in the models, into the QFD process. To deal with the vague nature of product development processes, fuzzy approaches are used for both QFD and risk analysis. A numerical example is used to demonstrate the applicability of the proposed model.     

Rating technical attributes in fuzzy QFD by integrating fuzzy weighted average method and fuzzy expected value operator

Quality function deployment (QFD) is a planning and problem-solving tool that is gaining acceptance for translating customer requirements into the technical attributes of a product. Deriving the rating order of technical attributes from input variables is a crucial step in applying QFD. When the relative weights of customer requirements and the relationship measures between customer requirements and technical attributes are expressed as fuzzy numbers, calculating the importance of each technical attribute falls into the category of fuzzy weighted average, in which the derived membership function of the fuzzy importance of each technical attribute is not explicitly known. Thus, most ranking methods are not suitable under these circumstances. A method is proposed in this paper using fuzzy weighted average method in the fuzzy expected value operator in order to rank technical attributes in fuzzy QFD. An example of a flexible manufacturing system design is cited to demonstrate the application of the proposed approach.     

服务管理目标优化配置的Fuzzy-QFD线性规划模型构建与求解

由于服务管理的复杂性和模糊性,现有方法难以有效解决基于主观语言评价的服务质量改进问题。本文拓展了质量功能展开(QFD)方法在服务业中的应用,通过构建一个模糊线性规划模型,以求解最大化提高顾客需求综合满意度的企业能力优化配置问题。首先基于顾客感知-期望差距的模糊评估确定顾客需求、需求权重和边界约束等模型参数,接着运用模糊线性回归和非对称三角模糊数的隶属函数,将含有模糊变量的模糊线性规划问题转化为经典线性规划问题,进而求得不同模糊条件下的模型解。最后通过网购平台的实例验证了模型的有效性和可行性。     

Product design and selection using fuzzy QFD and fuzzy MCDM approaches

Quality function deployment (QFD) is a useful analyzing tool in product design and development. To solve the uncertainty or imprecision in QFD, numerous researchers have applied the fuzzy set theory to QFD and developed various fuzzy QFD models. Three issues are investigated by examining their models. First, the extant studies focused on identifying important engineering characteristics and seldom explored the subsequent prototype product selection issue. Secondly, the previous studies usually use fuzzy number algebraic operations to calculate the fuzzy sets in QFD. This approach may cause a great deviation in the result from the correct value. Thirdly, few studies have paid attention to the competitive analysis in QFD. However, it can provide product developers with a large amount of valuable information. Aimed at these three issues, this study integrates fuzzy QFD and the prototype product selection model to develop a product design and selection (PDS) approach. In fuzzy QFD, the α-cut operation is adopted to calculate the fuzzy set of each component. Competitive analysis and the correlations among engineering characteristics are also considered. In prototype product selection, engineering characteristics and the factors involved in product development are considered. A fuzzy multi-criteria decision making (MCDM) approach is proposed to select the best prototype product. A case study is given to illustrate the research steps for the proposed PDS method. The proposed method provides product developers with more useful information and precise analysis results. Thus, the PDS method can serve as a helpful decision-aid tool in product design.     

The supplier selection problem of a manufacturing company using the weighted multi-choice goal programming and MINMAX multi-choice goal programming

This paper presents two methods of decision making, Weighted multi-choice goal programming (MCGP) and MINMAX MCGP. With the proposed Weighted MCGP method, decision makers can set different weights w_i for each goal with linguistic terms, such as high, average and low, which can be transformed into trapezoidal fuzzy numbers. Meanwhile, with the proposed MINMAX MCGP method, this study also let decision makers set the satisfaction membership function for each goal according to their preference in order to eliminate the effect of different scales in each goal.This paper also investigates the relationship between Weighted multi-choice goal programming and MINMAX multi-choice goal programming. According to the sensitivity analysis, decision makers can get the solution with the minimum aggregate deviation for all multiple goals from the Weighted multi-choice goal programming. Meanwhile, decision makers can get the solution with the most balanced solution between all multiple goals from the MINMAX multi-choice goal programming method. The weight variable is introduced to the above two methods to provide decision-makers with a mechanism to evaluate the discrepancy between the maximum aggregate achievement and the most balanced solution, enabling decision-makers to reach the preferable decision for their situation. A real-world problem of supplier selection by the purchasing and sales managers of a manufacturing company is used to illustrate the differing solutions given by the two models.     

A fuzzy goal programming method with imprecise goal hierarchy

Two most widely used approaches to treating goals of different importance in goal programming (GP) are: (1) weighted GP, where importance of goals is modelled using weights, and (2) preemptive priority GP, where a goal hierarchy is specified implying infinite trade-offs among goals placed in different levels of importance. These approaches may be too restrictive in modelling of real life decision making problems. In this paper, a novel fuzzy goal programming method is proposed, where the hierarchical levels of the goals are imprecisely defined. The imprecise importance relations among the goals are modelled using fuzzy relations. An additive achievement function is defined, which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations. Examples are given to illustrate the proposed method.     

An advanced quality function deployment model using fuzzy analytic network process

Quality function deployment (QFD) is a customer-oriented design tool used to ensure that the voice of customers is employed throughout the product planning and design stages. QFD uses the house of quality (HOQ), which is a matrix that provides a conceptual map for inter-functional planning and communication. In this paper, an advanced QFD model, based on fuzzy analytic network process (ANP) approach, is proposed to systematically take into account the interrelationship between and within the QFD components. The proposed method is aimed at expanding the current research scope from the product planning phase to the part deployment phase to provide product developers with more valuable information (ex. the importance and bottleneck level of part characteristics). Both customer requirements and the company’s production demands will be used as the inputs for the QFD process to enhance the completeness and accuracy of the QFD analysis results. A case study is presented to illustrate the application of the proposed method.     

Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing

Assembly line balancing generally requires a set of acceptable solutions to the several conflicting objectives. In this study, a binary fuzzy goal programming approach is applied to assembly line balancing. Models for balancing straight and U-shaped assembly lines with fuzzy goals (the number of workstations and cycle time goals) are proposed. The binary fuzzy goal programming models are solved using the methodology introduced by Chang [Chang, C.T., 2007. Binary fuzzy goal programming. European Journal of Operational Research 180 (1), 29–37]. An illustrative example is presented to demonstrate the validity of the proposed models and to compare the performance of straight and U-shaped line configurations.     

Modeling customer satisfaction with new product design using a flexible fuzzy regression-data envelopment analysis algorithm

The success of new products depends greatly on customer satisfaction and meeting the customer needs is vital for new product development. By incorporating customer needs in the design and development process, organizations can improve productivity for their new products and reduce the risks associated with new product markets. Hence, design teams require methods to model customer satisfaction when setting the associated product design attributes. Thus, different approaches have been developed for modeling the relationship between customer satisfaction and product design parameters. In this study, 16 well-known fuzzy regression (FR) models are considered to understand the relationship between customer satisfaction and new product design. The design of FR models is based on the 4Ps marketing mix (product, price, place, and promotion) concept in fuzzy environments. A flexible algorithm is then presented based on the index of confidence, error measures, and data envelopment analysis for selecting the best FR model. The applicability and usefulness of the proposed algorithm is demonstrated experimentally based on an actual case study, where the flexible algorithm is employed to predict customer satisfaction with a new product design in the freezer/refrigerator industry.     

Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility

This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.     

A combined approach for fuzzy multi-objective multiple knapsack problems for defence project selection

In this study, a model representing military requirements as scenarios and capabilities is offered. Pair-wise comparisons of scenarios are made according to occurrence probabilities by using the Analytical Hierarchy Process (AHP). The weights calculated from AHP are used as the starting weights in a Quality Function Deployment (QFD) matrix. QFD is used to transfer war fighter requirements into the benefit values of projects. Two levels of QFD matrices are used to evaluate new capability areas versus capabilities and capabilities versus projects. The benefit values of the projects are used in a multi-objective problem (multi-objective multiple knapsack problem) that considers the project benefit, implementation risks and environmental impact as multiple objectives. Implementation risk and environmental impact values are also calculated using the same combined AHP and QFD methodology. Finally, the results of the fuzzy multi-objective goal programming suggest a list of projects that offers optimal benefit when carried out within multiple budgets.     

Capturing and prioritizing students’ requirements for course design by embedding Fuzzy-AHP and linear programming in QFD

Customer requirements play a vital and important role in the design of products and services. Quality Function Deployment (QFD) is a popular, widely used method that helps translate customer requirements into design specifications. Thus, the foundation for a successful QFD implementation lies in the accurate capturing and prioritization of these requirements. This paper proposes and tests the use of an alternative framework for prioritizing students’ requirements within QFD. More specifically, Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) and the linear programming method (LP-GW-AHP) based on Data Envelopment Analysis (DEA) are embedded into QFD (QFD-LP-GW-Fuzzy AHP) in order to account for inherent subjectivity of human judgements. The effectiveness of the proposed framework is assessed in capturing and prioritizing students’ requirements regarding courses’ learning outcomes within the process of an academic course design. Sensitivity analysis evaluates the robustness of the prioritization solution and implications for course design specifications are discussed.     

Binary fuzzy goal programming

Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model.     

Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization

This paper considers Stackelberg solutions for two-level linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random two-level linear programming problem, an α-stochastic two-level linear programming problem is defined through the introduction of α-level sets of fuzzy random variables. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through fractile criterion optimization in stochastic programming, the transformed stochastic two-level programming problem can be reduced to a deterministic two-level programming problem. An extended concept of Stackelberg solution is introduced and a numerical example is provided to illustrate the proposed method.     

Fuzzy goal programming for inventory management: A bacterial foraging approach

An efficient inventory planning approach in today’s global trading regime is necessary not only for increasing the profit margin, but also to maintain system flexibility for achieving higher customer satisfaction. Such an approach should hence be comprised of a prudent inventory policy and clear satisfaction of stakeholder’s goals. Relative significance given to various objectives in a supply chain network varies with product as well as time. In this paper, a model is proposed to fill this void for a single product inventory control of a supply chain consisting of three echelons. A generic modification proposed to the membership functions of the fuzzy goal-programming approach is used to mathematically map the aspiration levels of the decision maker. The bacterial foraging algorithm has been modified with enhancement of the algorithms’ capability to map integer solution spaces and utilised to solve resulting fuzzy multi-objective function. An illustrative example comprehensively covers various decision scenarios and highlights the underlying managerial insights.     

Tackling an MCDM-problem with the help of some results from fuzzy set theory

The problem to be addressed and tackled in this paper arose as a byproduct from some efforts at solving problems involving multiple goals by linking linear and goal programming models. The critical issue was that some forms for interdependence among the goals could not be handled in the programming models. Here we will deal with a set of goals — with realistic counterparts in a Finnish plywood industry — in which a subset of the goals are (i) conflicting, another subset (ii) unilaterally supporting and a third subset (iii) mutually supporting. It is furthermore observed that the elements of a studied set of goals may be partly independent and partly interdependent, which makes the context a fullfledged MCDM-problem. It is tackled with a technique which is based on the theory of fuzzy sets, the conceptual framework for fuzzy decisions and the algorithms developed for fuzzy mathematical programming. The resulting fuzzy multiobjective programming model is simplified and tested with the help of a fairly complex numerical example.     

Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach

In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem; so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers.     

考虑预算约束的旅游服务质量提升决策方法

通过对Kano模型的定量化分析,从最大化顾客满意视角提出考虑预算约束的旅游服务质量提升决策方法。采用问卷调查方式获取顾客旅游服务质量因素的评价信息;依据Kano模型,对评价信息进行处理并建立顾客满意度与旅游服务质量满足水平的关系函数(S-CR);基于S-CR函数构建考虑预算约束条件下、顾客满意最大化的旅游服务质量提升决策模型,通过求解确定最优的预算分配方案。最后,通过实证验证模型的可行性与有效性。     

Nonlinear goal programming using multi-objective genetic algorithms

Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. This procedure has a number of known difficulties. First, the obtained solution to the goal programming problem is sensitive to the chosen weight vector. Second, the conversion to a single-objective optimization problem involves additional constraints. Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods. In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals and then suggest an evolutionary optimization algorithm to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem. The proposed approach alleviates all the above difficulties. It does not need any weight vector. It eliminates the need of having extra constraints needed with the classical formulations. The proposed approach is also suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region. The efficacy of the proposed approach is demonstrated by solving a number of nonlinear goal programming test problems and an engineering design problem. In all problems, multiple solutions (each corresponding to a different weight vector) to the goal programming problem are found in one single simulation run. The results suggest that the proposed approach is an effective and practical tool for solving real-world goal programming problems.