Fuzzy Goal Research Articles

Optimizing Manufacturing Supplier Selection and Order Allocation Processes using Fuzzy-QFD and Goal Programming: A Case Study in Indonesian Chemical Industry

This empirical study aims to implement an optimal methodology of a supplier selection process by integrating Fuzzy Quality Function Deployment (FQFD) and Goal Programming (GP). We apply the method to a company engaged in chemical industry, under multi item, multi supplier, and multi period environments. Problems encountered in this study are how to select suppliers and determine the optimal order allocation in accordance with company requirements. We use FQFD and GP to evaluate and allocate orders to suppliers. Four objectives are incorporated, including maximization of good products, on time delivery, and supplier scoring, along with minimization of material purchasing cost. We seek to find an optimal solution considering several constraints, such as material requirement and cost estimation, supplier and warehouse capacity, and safety stock. Our results provide insights that the most and the least important technical responses in chemical supplier selection are “supplier experience” and “response to customer order”, respectively. Whereas, the most important criteria are “product quality”, “product price”, and “delivery performance”, while the least important criteria are “return & repair service” and “documents”. The result also shows that the proposed method can achieve better solution compared to the past decision, in term of cost and supplier scoring.

A chance constrained fuzzy goal programming approach for perishable pharmaceutical supply chain network design

In this paper, a bi-objective mixed-integer linear programming model is formulated for designing a perishable pharmaceutical supply chain network under demand uncertainty. The objectives of the proposed model are to simultaneously minimize the total cost of the network and lost demand amount. The proposed model is multi-product and multi-period and includes simultaneous facilities location, vehicle routing, and inventory management; hence, it is considered an operational-strategic model. Procurement discounts, the lifetime of products, storing products for future periods, lost demand, and soft and hard time windows are the main assumptions of the proposed model. A novel hybrid approach, based on fuzzy theory, chance constrained programming, and goal programming approach, is developed for solving the proposed bi-objective model. The validity of the proposed model and developed solution approach is evaluated using data from Avonex, a prefilled syringe distribution chain serving 11 health centers in Tehran. The proposed model indicates that some lost sales exist, and to overcome the lost sales, the case company needs to invest a little more in addition to the initial investment of around 2 billion tomans. The results obtained from implementing the model and the sensitivity analysis, using real-world data, confirm the efficiency and validity of the proposed mathematical model and solution approach.

A PRODUCT DESIGN BY FUZZY AXIOMATIC DESIGN AND GOAL PROGRAMMING APPROACHES

Bu çalışmada, içecek sektöründe faaliyet gösteren bir firmanın ürün tasarım problemi ele alınarak, literatürde ilk kez Bulanık Aksiyomatik Tasarım (BAT) ve Hedef Programlama yaklaşımlarının birlikte kullanılmasıyla çözülmüştür. Problemde tasarlanacak olan ürünün mevcut hat spesifikasyonlarında değişikliğe neden olmaması, üretim hızını belirli bir seviyede tutması ve aynı zamanda müşteri beğenisine de hitap etmesi hedeflenmektedir. Bu hedeflerden müşteri beğenisi, insanın doğal karar verme süreçlerini daha iyi ifade edebilmesi bakımından bulanık verilerle ifade edilmiştir. Çalışmada müşteri beğenisine ait bulanık veriler BAT tekniği ile durulaştırılmıştır ve elde edilen değerler, söz konusu üç hedefi de dikkate alan bir 0-1 karma tam sayılı doğrusal olmayan hedef programlama modeline parametre olarak girilmiştir. Modelin çözümünde nihai ürünün belirli parametrelerinin değerleri elde edilmiştir. Bu değerlere göre tasarımı yapılan şişenin silme hacmi hesaplanmaktadır. Silme hacme göre de, yeni tasarımın üretim hattı spesifikasyonlarını sağlayıp sağlamadığı, üretim hızının ortalama değeri ve müşteri beğenisine hitap edip etmediği anlaşılabilmektedir. Önerilen çözüm yaklaşımı sayesinde, problem analitik olarak ele alınmış, firmanın ürün tasarımında başvurduğu deneme yanılma yöntemi terk edildiği için de hem zamandan, hem iş gücünden, hem de kalıp ve preform maliyetlerinden tasarruf sağlanmıştır.

Fuzzy goal programming for biodiesel production

ABSTRACT The energy consumed around the world and especially in Morocco is dominated by oil products. The latter; whether in the global or the national context; are mainly due to diesel, whose climate impacts are well established, suggesting the search for a greener alternative. Despite its virtues, biodiesel is struggling to impose itself for purely economic reasons. Thus, in order to offer a sustainable solution, while keeping in mind the unpredictable fluctuations (price, demand …). This work proposes a generalization of fuzzy goal programming into fully fuzzy goal programming and a relative application, where the aim is to have a final product at a competitive price.

A reverse supply chain for medical waste: A case study in Babol healthcare sector

Medical waste generation is rapidly rising, which may cause a serious risk for both humans and environment if it is not properly managed. Designing an efficient and reliable medical waste reverse supply chain (MWRSC) is extremely beneficial to society. Most studies on this issue have only considered the generated waste and have not reported the uncertainty in the amount of medical waste generation and other MWRSC parameters. Sustainability criteria and environmental issues in choosing treatment technology are rarely considered as well. In this research, a linear programming model under uncertainty is developed to design an MWRSC. The proposed model is multi-item and multi-period with three objective functions. The first objective function minimizes total costs, the second objective function is relevant to the best treatment technology selection and the third objective function minimizes the total medical waste stored. A robust possibilistic programming approach is utilized to handle imprecise parameters in the model and a fuzzy goal programming method is employed to build up a multi-objective model. A real case study is conducted to illustrate the potential of the proposed model which involves different attributes and problems, such as the location and capacity of facilities, and the type of treatment technology. Furthermore, the transferring amount of medical waste among different nodes is calculated.

Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a real-life application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.

A fuzzy goal programme–based sustainable Greenfield supply network design for tyre retreading industry

The rising global concerns and the tightening of the government legislations, the supply networks are compelled to consider the three dimensions—economic, environmental and social in their operations. This study proposed a sustainable Greenfield tyre retreading supply network design model under uncertainty and group decision-making environment to incorporate economics dimension-maximum profit, coverage and capacity flexibility, carbon cost as environmental dimension and social benefit indicator as social dimension. To solve the proposed fuzzy multi-objective mixed integer programme model, a methodology is designed using Jimeniz’s uncertainty approach, Chang’s fuzzy AHP approach to determine weights, Mirakhorli’s membership function formulation approach, Liou and Wang’s desirable achievement degree computation of each goal approach and Chen and Tsai’s Fuzzy goal programming. Numerical experiments imparts important policy intelligence for industry specialists and the government: (1) formulated human-regional forwardness index to decide regional carbon tax for economic growth of backward areas, (2) formulated social benefit weight of a region and social benefit indicator of facilities in various regions for social dimension assessment, (3) analysed the possible influence of carbon tax rate with various carbon emission policies on sustainable strategic tyre retreading supply network planning, (4) suggested appropriate carbon emission policies for tyre retreading supply network and government, (5) suggested the admissible national carbon tax rate in a country on tyre retreading supply network and (6) decided an appropriate regional tax rate in a country for carbon emission using human-regional forwardness index to promote economic growth of backward areas.

A bi-level programming approach for improving relief logistics operations: A real case in Kermanshah earthquake

Due to its location on the world dry belt, Iran is known as a disaster-prone country. Regarding such a problem, planning for relief operations in disaster situations seems significant and undeniable. The literature on disaster management has mostly defined their problems in a single-level framework, ignoring the bi-level aspect of such problems in both preparedness and response phases. However, in the context of disaster in the real world, there is normally more than one decision-maker that each of them may have their own objective. In this study, a bi-level multi-objective programming approach is extended to design a pre-positioning and distribution network under disastrous conditions considering both preparedness and response phases. The extended framework takes into account simultaneous planning for the distribution of drug, blood and relief items among disaster victims, and transferring the injured to hospital in order to diminish the adverse effects of potential disasters in the response phase. Additionally, to determine suitable candidate places for locating relief centers in the preparedness phase, a modified version of data envelopment analysis model is utilized, something that is not frequently done for facility location planning in the disaster management field. On the other hand, to solve the bi-level multi-objective programming problem with decision-makers at the upper level (the affected country) and the lower level (the international organization), a fuzzy goal programming algorithm is proposed. Furthermore, a consolidated method with respect to a novel fuzzy measure is developed to keep the considered network safe against the inherent uncertainty. Finally, the extended framework is utilized to solve a case study in Kermanshah, the province of Iran.

Study of Achievement Stability Set for Parametric Linear FGP Problems

Goal Programming has numerous advances, especially in the zone of brilliant modeling and it is a functional and powerful technique in the formulation, solution, and investigation of issues containing varied and conflicting objectives. The previous studies presented in this era focused on making the solution be stable. In addition, the achievement stability set introduced by Osman et al. [16] assumed a deterministic case even though real world problems possess uncertain natures which lead us to present the current study. In this research we introduce the achievement stability set for parametric linear fuzzy goal programming issues when the objective coefficients have a parametric nature. Firstly, the membership goals of each fuzzy goal were formulated then α-cut methodology is applied to obtain the deterministic feasible region. Secondly, the complete attainment problem is worked out and solved by utilizing the lexicographical approach. Finally, notions and strategies for finding the achievement stability set for parametric linear fuzzy goal programming issue and numerical examples are presented.

Modified two-phase fuzzy goal programming integrated with IF-TOPSIS for green supplier selection

The environmental consciousness of society and globally competitive market have considerably increased thanks to the scientific studies, media, governmental and non-governmental organizations. In this regard, environmental factors have been considered within the supplier selection process which is a major decision point in supply chains. Hence, in addition to the optimization of the traditional criteria, green criteria have also started to take its place in the supplier selection problem. In this study, an integrated methodology including the Intuitionistic Fuzzy Technique for Order Preference by Similarity to Ideal Solution (IF-TOPSIS) and a modified two-phase fuzzy goal programming model are proposed to better address this selection problem in a multi-item/multi-supplier/multi-period environment. The detailed steps are explicitly provided within the proposed methodology. In this respect, the criteria importance weights are determined via IF-TOPSIS which enables the opportunity to handle the vagueness within the evaluation process of decision-makers. Afterward, the obtained importance weights are used in the modified two-phase fuzzy goal programming model for selecting the best suppliers. An application in the air filter industry is performed to demonstrate the validation of the proposed methodology. Consequently, the proposed methodology successfully provides the best selection of suppliers by satisfying both classic and green criteria.

Algorithmic Improvements of the KSU-STEM Method Verified on a Fund Portfolio Selection

The topic of this article is inspired by the problem faced by many people around the world: investment portfolio selection. Apart from the standardly used methods and approaches, non-traditional multiple objective programming methods can also be significant, providing even more efficient support for making a satisfactory investment decision. A more suitable method for this purpose seems to be a concept working with an interactive procedure through the portfolio that may gradually be adapted to the investor’s preferences. Such a method is clearly the Step Method (STEM) or the more suitable improved version KSU-STEM. This method is still burdened by partial algorithmic weaknesses or methodical aspects to think about, but not as much as the other methods. The potentially stronger application power of the KSU-STEM concept motivates its revision. Firstly, an unnecessarily negative principle to determine the basal value of the objectives is revised. Further, the fuzzy goals are specified, which leads to a reformulation of the revealed defuzzified multi-objective model. Finally, the imperfect re-setting of the weights (importance) of unsatisfactory objectives is revealed. Thus, the alternative approaches are proposed. The interventions to the algorithm are empirically verified through a real-life selection of a portfolio of the open unit trusts offered by CONSEQ Investment Management traded on the Czech capital market. This application confirms a significant supporting power of the revised multiple objective programming approach KSU-STEM in a portfolio-making process.

Leveraging tacit knowledge for shipyard facility layout selection using fuzzy set theory

A shipyard's layout contributes significantly to manufacturing performance. The practitioners based on experience can provide feasible alternative layouts by considering qualitative factors. However, no study in the shipyard layout context has leveraged their valuable subjective knowledge.This study addresses the above research gap. It proposes a two-stage approach using the Fuzzy similarity index (FSI) and the Fuzzy goal programming model (FGPM). The first stage elicits alternative layouts and relationship (REL) charts from practitioners. REL's fuzzy proximity ratings are assigned by subjective assessment of shipbuilding process flow, inter-shop material flow, distance, cost per unit distance, sharing of material handling equipment. Thereafter, the FSI of each alternative layout with respect to the ideal layout is evaluated. However, implementing the alternative layout with the highest FSI may not be feasible due to practical constraints. Therefore, in the second stage, FGPM is formulated incorporating practical constraints related to site factors, harmful gases emission, environmental, and safety to yield an optimal selection of layout.

Optimizing sustainable and renewable energy portfolios using a fuzzy interval goal programming approach

Determining the most sustainable renewable energy (RE) source portfolio that meets decision-maker preferences is a complicated and uncertain multi-criteria decision-making (MCDM) problem. The RE selection process involves meeting decision-makers’ (DMs) preferences wherein several conflicting criteria are present, such as environmental, societal, and economic. Fuzzy goal programming (FGP) is one of the most well-known techniques for dealing with uncertainty existing in MCDM problems. However, conventional FGP techniques suppose only one single coefficient (or parameter) for each decision variable. This paper proposes a novel multi-objective decision-making model called fuzzy interval goal programming (FIGP) to release the restrictions of FGP with single-coefficient modeling. The proposed model can formulate an interval coefficient for each decision variable. To formulate such a model, this study adopts the concept of multi-choice aspiration levels (MCALs) from the revised multi-choice goal programming (RMCGP) technique. Specifically, the integrated model considers various types of fuzzy goals in real-world problems and offers DMs more flexibility to express and formulate their preferences in terms of fuzzy interval goals. The proposed method is illustrated by selecting the optimal RE portfolio for electricity generation in Italy. The relevant renewables are biomass, solar photovoltaic (PV), tidal currents, and wind energy. An empirical analysis shows that the proposed methodology is capable of assisting the DMs in ascertaining the optimal portfolio of RE under a high level of uncertainty and in imprecise environments.

A Fuzzy Goal Programming Approach to Multiobjective Transportation Problems

The current paper focuses on a multiobjective transportation problem which is a special type of vector minimum problem. In order to deal with such a problem, a new model based on fuzzy goal programming is suggested. Different solutions are obtained according to the priorities of the decision maker in the proposed model. With respect to its properties, at least a weakly efficient solution is yielded by solving the new model. To demonstrate the validity and strengths of the suggested model, some numerical examples are given. Further, a comparison is made with different existing methods.

Allocation of Maltodextrin Raw Material Orders by Fuzzy Analytic Network Process (FANP) and Goal Programming Methods (Study Case: PT. Neopangan Selaras Indonesia)

PT. Neopangan Selaras Indonesia is a food company that produces seasoning. One of the raw materials with the most frequent problems with delays and wrong allocation is maltodextrin, which is 72%. To determine the need for evaluation for each maltodextrin supplier using the Fuzzy Analytical Network Process (FANP) and Goal Programming methods. The existence of a method of merging these two studies. Determination of the proportion of the criteria and sub-criteria in the company by minimizing changes in each assessment. The FANP method in this study produced criteria and assessments of each supplier that could be considered in the allocation of the purchase of raw materials. The best supplier of weights was obtained by PT. Indo Asia Tirta Manunggal (0.4421). The Goal Programming method provides a solution by minimizing total costs by considering the price of each supplier, maximizing the purchase value by considering the weight generated. This method produces a solution that produces a total cost of 0.134%, increasing the purchase value of 1.143%.

Multi-item a supply chain production inventory model of time dependent production rate and demand rate under space constraint in fuzzy environment

In this paper, we have developed an integrated production inventory model for two echelon supply chain consisting of one vendor and one retailer. Production rate and demand rate of retailer and customer are time dependent. Idle time cost of the vendor has been considered. Multi-item inventory has been considered. In integrated inventory model average cost has been calculated under limitation on stroge space. Two echelon supply chain fuzzy inventory model has been solved by various techniques like as Fuzzy programming technique with hyperbolic membership functions (FPTHMF), Fuzzy non-linear programming technique (FNLP) and Fuzzy additive goal programming technique (FAGP), weighted Fuzzy non-linear programming technique (WFNLP) and weighted Fuzzy additive goal programming technique (WFAGP). A numerical example is illustrated to test the model. Finally to make the model more realistic, sensitivity analysis has been shown.

Compromise allocation problem in multivariate stratified sampling with flexible fuzzy goals

In a multivariate stratified sample survey, we assumed p-characteristics which are to be measured on each unit of the population and the population is further subdivided into L subpopulations. For estimating the p-population means of all characteristics, which are not known in advance usually, a random sample is taken out from the population with the help of simple random sampling. In a multivariate stratified sample survey, the optimum allocation of one character is not considered as optimum for others. Then a solution is needed to work out an allocation that may be optimum for all characteristics in some sense, called as compromise allocation in sampling literature. The estimation of p-population means in the presence of non-response, for a fixed cost, is discussed. The formulated integer non-linear programming problem is converted into a binary goal programming problem. The problem's solution is obtained by using the concept of flexible fuzzy goal programming.

Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.

A novel fuzzy bi-objective vehicle routing and scheduling problem with time window constraint for a distribution system: A case study

In the process of hazardous material transportation, the risk is a significant factor that should be considered due to the potential severe consequence of an incident. Regardless of risks, time is a paramount concern that should be considered in hazardous material transportation. In this way, this paper introduces a bi-objective model for a vehicle routing and scheduling problem of hazardous material distribution problems under the fuzzy condition to minimize both total distribution time and risks. In the proposed model, the fuzzy inference system and fuzzy failure mode and effects analysis are applied to identify and calculate the high-level risks instead of the previous simple methods for the first time. Moreover, Jimenez method and fuzzy goal programming are respectively utilized to convert the fuzzy bi-objective model into the same crisp and single-objective one. Besides, to cope with the NP-hardness of the large-sized problems, two meta-heuristic algorithms namely invasive weeds optimization and genetic algorithm is used, and several sensitivity analyses are performed to prove the efficiency of the proposed approach. The performance of the proposed algorithms is also assessed through a comparative study. Finally, the proposed model is implemented to a real case study to prove the validity of the model.

Green and Reliable Freight Routing Problem in the Road-Rail Intermodal Transportation Network with Uncertain Parameters: A Fuzzy Goal Programming Approach

In this study, the author focuses on modeling and optimizing a freight routing problem in a road-rail intermodal transportation network that combines the hub-and-spoke and point-to-point structures. The operations of road transportation are time flexible, while rail transportation has fixed departure times. The reliability of the routing is improved by modeling the uncertainty of the road-rail intermodal transportation network. Parameters that are influenced by the real-time status of the network, including capacities, travel times, loading and unloading times, and container trains’ fixed departure times, are considered uncertain in the routing decision-making. Based on fuzzy set theory, triangular fuzzy numbers are employed to formulate the uncertain parameters as well as resulting uncertain variables. Green routing is also discussed by treating the minimization of carbon dioxide emissions as an objective. First of all, a multiobjective fuzzy mixed integer nonlinear programming model is established for the specific reliable and green routing problem. Then, defuzzification, linearization, and weighted sum method are implemented to present a crisp linear model whose global optimum solutions can be effectively obtained by the exact solution algorithm run by mathematical programming software. Finally, a numerical case is given to demonstrate how the proposed methods work. In the case, sensitivity analysis is adopted to reveal the effects of uncertainty on the routing optimization. Fuzzy simulation is then performed to help decision makers to select the best crisp route plan by determining the best confidence level shown in the fuzzy chance constraints.