Determining design requirements in QFD using fuzzy mixed-integer goal programming: application of a decision support system

In product development, the identification of critical design requirements (DRs) is key to satisfying customer needs because it helps produce more successful products in a shorter time. Quality function deployment (QFD) is a tool used in product development to systematically determine the DRs so as to attain higher customer satisfaction. In the QFD process, the simultaneous optimisation of more than one conflicting objective is generally required. However, it is very difficult for decision makers to determine the goal value of each objective in imprecise and uncertain environments. In order to overcome this problem, the present study proposes a fuzzy mixed-integer goal programming model that determines a combination of optimal DR values. Different from the existing fuzzy goal programming models, the values of the DRs in the proposed model are taken as discrete. Finally, a new Decision Support System is developed. The new system integrates QFD and mathematical programming, enabling the design team to effectively compare product design alternatives and make product development easier and faster. The proposed methodology is illustrated using a real-world application in the Turkish white goods industry.     

Quantification and integration of Kano’s model into QFD for optimising product design

With increasing concerns on customer needs in today’s competitive market, the issue of incorporating customer requirements into product design arises the interest of both researchers and practitioners. Quality Function Deployment (QFD) is a well-known methodology for customer-driven product design. However, conventionally, QFD analysis has a major challenge in understanding customer needs accurately. Kano’s model, which studies the nature of customer needs, provides a way for a better classification of customer needs. However, seldom research contributions are found in terms of integrating Kano’s model with QFD quantitatively. In this research, a novel integration approach is proposed. At first, Kano’s model is quantified by identifying relationship between customer needs and customer satisfaction (CS). Next, both qualitative and quantitative results from Kano’s model are integrated into QFD. Finally, a mixed non-linear integer programming model is formulated to maximise CS under cost and technical constraints. In this research, an illustrative example associated with the design of notebook computers is also presented to demonstrate the availability of the proposed approach.     

QFD optimization using linear physical programming

A new approach to quality function deployment (QFD) optimization is presented. The approach uses the linear physical programming (LPP) technique to maximize overall customer satisfaction in product design. QFD is a customer-focused product design method which translates customer requirements into product engineering characteristics. Because market competition is multidimensional, companies must maximize overall customer satisfaction by optimizing the design of their products. At the same time, all constraints (e.g. product development time, development cost, manufacturing cost, human resource in design and production, etc.) must be taken into consideration. LPP avoids the need to specify an importance weight for each objective in advance. This is an effective way of obtaining optimal results. Following a brief introduction to LPP in QFD, the proposed approach is described. A numerical example is given to illustrate its application and a sensitivity analysis is carried out. Using LPP in QFD optimization provides a new direction for optimizing the product design process.     

Modelling and a tabu search solution for the slab reallocation problem in the steel industry

This paper considers a slab reallocation problem arising from operations planning in the steel industry. The problem involves reallocating steel slabs to customer orders to improve the utilisation of slabs and the level of customer satisfaction. It can be viewed as an extension of a multiple knapsack problem. We firstly formulate the problem as an integer nonlinear programming (INLP) model. With variable replacement, the INLP model is then transformed into a mixed integer linear programming (MILP) model, which can be solved to optimality by MILP optimisers for very small instances. To obtain satisfactory solutions efficiently for practical-sized instances, a heuristic algorithm based on tabu search (TS) is proposed. The algorithm employs multiple neighbourhoods including swap, insertion and ejection chain in local search, and adopts solution space decomposition to speed up computation. In the ejection chain neighbourhood, a new and more effective search method is also proposed to take advantage of the structural properties of the problem. Computational experiments on real data from an advanced iron and steel company in China show that the algorithm generates very good results within a short time. Based on the model and solution approach, a decision support system has been developed and implemented in the company.     

Optimal scheduling for flexible job shop operation

This paper presents a new integer linear programming (ILP) model to schedule flexible job shop, discrete parts manufacturing industries that operate on a make-to-order basis. The model considers groups of parallel homogeneous machines, limited intermediate buffers and negligible set-up effects. Orders consist of a number of discrete units to be produced and follow one of a given number of processing routes. The model allows re-circulation to take place, an important issue in practice that has received scant treatment in the scheduling literature. Good solution times were obtained using commercial mixed-integer linear programming (MILP) software to solve realistic examples of flexible job shops to optimality. This supports the claim that recent advances in computational power and MILP solution algorithms are making this approach competitive with others traditionally applied in job shop scheduling.     

Prioritizing quality characteristics in dynamic quality function deployment

Due to the combination of rapid influx of new technology, high pressure on time-to-market and increasing globalization, the number of products that have highly uncertain and dynamic specifications or customer requirements might significantly increase. In order to deal with these inherently volatile products or services, we need to adopt a more pro-active approach in order not to produce an unwanted product or service. Thus, based on the idea of the quality loss function and the zero-one goal programming, an intuitively simple mathematical model is developed to prioritize the quality characteristics (QCs) in the dynamic quality function deployment (QFD). It incorporates a pro-active approach towards providing products and services that meet the future voice of the customer (FVOC). The aim is to determine and prioritize only the ‘important’ QCs with a greater confidence in meeting the FVOC. It is particularly useful when the number of the potentially dominant QCs is very large so that, by using the prioritization, the size of the QFD can be effectively reduced. Some constraints, such as minimum customer satisfaction level and limitation on budget are also taken into consideration. A sensitivity analysis is suggested to give an insight to the QFD users in the change of parameters of the proposed model.     

A three-phase heuristic approach for reverse logistics network design incorporating carbon footprint

Reverse logistics (RL) is emerging as a significant area of activity for business and industry, motivated by both commercial profitability and wider environmental sustainability factors. However, planning and implementing an appropriate RL network within existing supply chains for product recovery that increases customer satisfaction, decreases overall costs, and provides a competitive advantage over other companies is complex. In the current study, we developed a mixed integer linear programming (MILP) model for a reverse logistics network design (RLND) in a multi-period setting. The RL network consists of collection centres, capacitated inspection and remanufacturing centres and customer zones to serve. Moreover, the model incorporates significant characteristics such as vehicle type selection and carbon emissions (through transportation and operations). Since the network design problems are NP-hard, we first propose a solution approach based on Benders decomposition (BD). Then, based on the structure of the problem we propose a three-phase heuristic approach. Finally, to establish the performance and robustness of the proposed solution approach, the results are compared with benchmark results obtained using CPLEX in terms of both solution quality and computational time. From the computational results, we validated that the three-phase heuristic approach performs superior to the BD and Branch &Cut approach.     

Fuzzy multiple objective decision making approach to prioritize design requirements in quality function deployment

Quality function deployment (QFD) is a customer-oriented design tool for developing new or improved products to increase customer satisfaction by integrating marketing, design engineering, manufacturing, and other related functions of an organization. QFD focuses on delivering value by taking into account customer needs and then deploying this information throughout the development process. Although QFD aims to maximize customer satisfaction, technology and cost considerations limit the number and the extent of the possible design requirements that can be incorporated into a product. This paper presents a fuzzy multiple objective programming approach that incorporates imprecise and subjective information inherent in the QFD planning process to determine the level of fulfilment of design requirements. Linguistic variables are employed to represent the imprecise design information and the importance degree of each design objective. The fuzzy Delphi method is utilized to achieve the consensus of customers in determining the importance of customer needs. A pencil design example illustrates the application of the multiple objective decision analysis.     

原油处理过程短期生产计划优化

在原油处理过程短期生产计划的递阶求解方法中,原油处理短期生产计划问题分为上下两层,上层根据市场需求产生一个目标炼油计划;在此基础上,下层得到一个详细生产计划以实现目标炼油计划。研究了在上层目标炼油计划已知的情况下,下层详细生产计划的求解问题。为该问题建立了基于离散时间表示的混合整数线性规划模型,分析了问题的特点并将其进行转化,给出了基于启发式的求解方法,在保证目标炼油计划实现的前提下,对原油转运过程中油品切换及不同油品的罐底混合进行了优化,取得了一定的成果。用一个工业实例验证了启发式规则的可行性和有效性。     

A novel fuzzy linguistic model for prioritising engineering design requirements in quality function deployment under uncertainties

Quality function deployment (QFD) is a planning and problem-solving tool gaining wide acceptance for translating customer requirements (CRs) into the design requirements (DRs) of a product. Deriving the priority order of DRs from input variables is a crucial step in applying QFD. Due to the inherent vagueness or impreciseness in QFD, the use of fuzzy linguistic variables for prioritising DRs has become more and more important in QFD applications. Existing approaches make use of the associated fuzzy membership functions of linguistic labels based on the fuzzy extension principle. However, an inherent limitation of such fuzzy linguistic approaches is the information loss caused by approximation processes, which eventually implies a lack of precision in the final results. This paper proposes an alternative approach to prioritising engineering DRs in QFD based on the order-based semantics of linguistic information and fuzzy preference relations of linguistic profiles, under random interpretations of customers, design team and CRs. Ultimately, this approach enhances the fuzzy-computation-based models proposed in the previous studies by overcoming the mentioned limitations. A case study taken from the literature is used to illuminate the proposed technique and to compare with the previous techniques based on fuzzy computation.     

Multi-objective mixed integer programming and an application in a pharmaceutical supply chain

Multi-objective integer linear and/or mixed integer linear programming (MOILP/MOMILP) are very useful for many areas of application as any model that incorporates discrete phenomena requires the consideration of integer variables. However, the research on the methods for the general multi-objective integer/mixed integer model has been scant when compared to multi-objective linear programming with continuous variables. In this paper, an MOMILP is proposed, which integrates various conflicting objectives. We give importance to the imprecise nature of some of the critical factors used in the modelling that can influence the effectiveness of the model. The uncertainty and the hesitation arising from estimating such imprecise parameters are represented by intuitionistic fuzzy numbers. The MOMILP model with intuitionistic fuzzy parameters is first converted into a crisp MOMILP model, using appropriate defuzzification strategies. Thereafter, the MOMILP is transformed into a single objective problem to yield a compromise solution with an acceptable degree of satisfaction, using suitable scalarisation techniques such as the gamma-connective technique and the minimum bounded sum operator technique. The proposed solution method is applied to several test problems and a multi-objective pharmaceutical supply chain management model with self generated random data.     

Integrating production-transportation planning decision with fuzzy multiple goals in supply chains

This work presents a novel fuzzy multi-objective linear programming (f-MOLP) model for solving integrated production-transportation planning decision (PTPD) problems in supply chains in a fuzzy environment. The proposed model attempts to simultaneously minimise total production and transportation costs, total number of rejected items, and total delivery time with reference to available capacities, labor level, quota flexibility, and budget constraints at each source, as well as forecast demand and warehouse space at each destination. An industrial case demonstrates that the proposed f-MOLP model achieves an efficient compromise solution and overall decision maker satisfaction with determined goal values. Additionally, the proposed model provides a systematic framework that facilitates decision makers to interactively modify the fuzzy data and parameters until a satisfactory solution is obtained. Overall, the f-MOLP model offers a practical method for solving PTPD problems with fuzzy multiple goals, and can effectively improve producer–distributor relationships within a supply chain.     

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.     

Modelling of multi-period multi-product production planning considering production routes

The multi-period multi-product (MPMP) production planning problems, generally, deal with matching production levels of individual products with fluctuated demands over planning horizon. The conventional MPMP optimisation models suffer from insufficient utilisation of available capacity of machines. This fallacy is due to inappropriate formulation of machine capacity and material handling constraints. In this study, a novel mathematical model is proposed to simultaneously optimise production quantities and provide information about managerial decisions such as subcontracting, carrying inventory/backordering, and also hiring/layoff personnel. The problem is then formulated as a mixed integer linear programming (MILP) model by applying appropriate linearisation of non-linear components. The objective is to minimise production costs comprising of production, storage, shortage, subcontracting costs and costs associated with hiring/dismissing labourers. Superiority of the proposed model over existing ones, has been initially evaluated by solving the case presented by Byrne and Bakir [Byrne, M.D. and Bakir, M.A., 1999. Production planning using a hybrid simulation-analytical approach. International Journal of Production Economics, 59 (1), 305–311], and then evaluated by comparing the results obtained from solving both the proposed and the conventional MPMP production planning models using a 100-randomly-generated-test-problem.     

Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions

In this paper, we formulate the material requirements planning) problem of a first-tier supplier in an automobile supply chain through a fuzzy multi-objective decision model, which considers three conflictive objectives to optimise: minimisation of normal, overtime and subcontracted production costs of finished goods plus the inventory costs of finished goods, raw materials and components; minimisation of idle time; minimisation of backorder quantities. Lack of knowledge or epistemic uncertainty is considered in the demand, available and required capacity data. Integrity conditions for the main decision variables of the problem are also considered. For the solution methodology, we use a fuzzy goal programming approach where the importance of the relations among the goals is considered fuzzy instead of using a crisp definition of goal weights. For illustration purposes, an example based on modifications of real-world industrial problems is used.     

Systematical decision-making approach for quality function deployment based on uncertain linguistic term sets

A systematical decision-making approach is constructed for quality function deployment (QFD) in uncertain linguistic situations. The mathematical expression and operation of linguistic terms play important roles in the proposed approach in terms of customer requirements (CRs) and design requirements (DRs) in QFD. First, hesitant fuzzy linguistic term sets are designed to conveniently express uncertain linguistic terms and compute with words after the data derived from customers are pretreated and integrated in the decision-making process. Second, the tolerance deviation is defined to restrict innovatively the deviation range of fuzzy linguistic terms in the assessment stage of relative importance for CRs. Third, information entropy is originally designed to determine the final importance of DRs. Moreover, an empirical study on the research project called vortex recoil hydraulic retarder is conducted to demonstrate the performance of the systematical decision-making approach. The proposed approach can be applied to a wide variety of new product development problems in uncertainty settings.     

Assessing the relative importance weights of customer requirements using multiple preference formats and nonlinear programming

Quality function deployment (QFD) is a methodology to ensure that customer requirements (CRs) are deployed through product planning, part development, process planning and production planning. The first step to implement QFD is to identify CRs and assess their relative importance weights. This paper proposes a nonlinear programming (NLP) approach to assessing the relative importance weights of CRs, which allows customers to express their preferences on the relative importance weights of CRs in their preferred or familiar formats. The proposed NLP approach does not require any transformation of preference formats and thus can avoid information loss or information distortion. Its potential applications in assessing the relative importance weights of CRs in QFD are illustrated with a numerical example.     

An evaluation framework for product planning using FANP,QFD and multi-choice goal programming

Technological innovation and satisfaction of customer needs are the keys to survival and success for firms, especially in global competitive high-tech industries. Since new products are usually a source of new sales and profits, the success of new product development (NPD) is essential to maintain a competitive edge and to make a decent profit in a longer term. Therefore, how to develop products that deliver the quality and functionality customers demand while generating the desired profits becomes an important task for the manufacturers. In this paper, a framework with two phases is constructed for facilitating the selection of engineering characteristics (ECs) for product design. In the first phase, quality function deployment (QFD) is incorporated with the supermatrix approach of analytic network process (ANP) and the fuzzy set theory to calculate the priorities of ECs with the consideration of the interrelationship among factors and the impreciseness and vagueness in human judgments and information. In the second phase, multi-choice goal programming model is constructed by considering the outcome from the first phase and other additional goals, such as NPD cost and manufacturability, in the attempt to select the most suitable ECs. A case study of the product design process of backlight unit (BLU) in thin film transistor liquid crystal display (TFT-LCD) industry in Taiwan is carried out to verify the practicality of the proposed framework.     

Scheduling commercial advertisements for television

The problem of scheduling the commercial advertisements in the television industry is investigated. Each advertiser client demands that the multiple airings of the same brand advertisement should be as spaced as possible over a given time period. Moreover, audience rating requests have to be taken into account in the scheduling. This is the first time this hard decision problem is dealt with in the literature. We design two mixed integer linear programming (MILP) models. Two constructive heuristics, local search procedures and simulated annealing (SA) approaches are also proposed. Extensive computational experiments, using several instances of various sizes, are performed. The results show that the proposed MILP model which represents the problem as a network flow obtains a larger number of optimal solutions and the best non-exact procedure is one that uses SA.     

A data-driven approach to multi-product production network planning

The clearing function models the non-linear relationship between work-in-process and throughput and has been proposed for production planning in environments with queuing (congestion) effects. One approach in multi-product, multi-stage environments has been to model the clearing function at the bottleneck machine only. However, since the bottleneck shifts as the product release mix changes, this approach has its limitations. The other approach is the Alternative Clearing Function formulation, where the clearing function is first estimated at the resource level using piecewise linear regression from simulation experiments, and then embedded into a linear programme. This paper develops an alternative to the Allocated Clearing Function formulation, wherein system throughput is estimated at discrete work-in-process points. A mixed integer programming formulation is then presented to use these throughput estimates for discrete release choices. The strength of the formulation is illustrated with a numerical example and the new approach is compared with the ACF.