Fuzzy Goal Programming Method Research Articles

Neutrosophic linear fractional optimization problem using fuzzy goal programming approach

This research paper develops an algorithm to solve a neutrosophic linear fractional optimization problem, where the cost of the objective functions, the technology coefficients, and the resources are neutrosophic numbers (triangular and trapezoidal numbers). Two defuzzification methods are used here to convert the neutrosophic linear fractional optimization problem into a multi-objective linear fractional optimization problem (MOLFOP). The fractional objective function is defuzzified using the component-wise optimization method, and the linear constraints are defuzzified using the aggregation ranking function strategy. Hence, the MOLFOP is then solved using the fuzzy goal programming method. In order to further explain our suggested algorithm, two numerical examples are solved at the end, and the outcomes obtained by our method are compared with the outcomes obtained using the other algorithm.

A Sustainable Multi-Objective Model for Capacitated-Electric-Vehicle-Routing-Problem Considering Hard and Soft Time Windows as Well as Partial Recharging.

Due to the high pollution of the transportation sector, nowadays the role of electric vehicles has been noticed more and more by governments, organizations, and environmentally friendly people. On the other hand, the problem of electric vehicle routing (EVRP) has been widely studied in recent years. This paper deals with an extended version of EVRP, in which electric vehicles (EVs) deliver goods to customers. The limited battery capacity of EVs causes their operational domains to be less than those of gasoline vehicles. For this purpose, several charging stations are considered in this study for EVs. In addition, depending on the operational domain, a full charge may not be needed, which reduces the operation time. Therefore, partial recharging is also taken into account in the present research. This problem is formulated as a multi-objective integer linear programming model, whose objective functions include economic, environmental, and social aspects. Then, the preemptive fuzzy goal programming method (PFGP) is exploited as an exact method to solve small-sized problems. Also, two hybrid meta-heuristic algorithms inspired by nature, including MOSA, MOGWO, MOPSO, and NSGAII_TLBO, are utilized to solve large-sized problems. The results obtained from solving the numerous test problems demonstrate that the hybrid meta-heuristic algorithm can provide efficient solutions in terms of quality and non-dominated solutions in all test problems. In addition, the performance of the algorithms was compared in terms of four indexes: time, MID, MOCV, and HV. Moreover, statistical analysis is performed to investigate whether there is a significant difference between the performance of the algorithms. The results indicate that the MOSA algorithm performs better in terms of the time index. On the other hand, the NSGA-II-TLBO algorithm outperforms in terms of the MID, MOCV, and HV indexes.

A location-inventory model for the sustainable supply chain of perishable products based on pricing and replenishment decisions: A case study.

In recent decades, changes in people's lifestyles and occupations have led to new food consumption patterns around the world, with a notable growth in the demand for ready meals and meat products. Accordingly, the food industry has tried to transform the global food culture by promoting its more profitable products to become able to set a higher price for meat. Considering the short lifetime of products in perishable food supply chains, inventory decisions are considered crucial. In addition, the demand for perishable food products is greatly affected by their freshness. In this paper, we develop a multi-objective mixed-integer non-linear programming model for a four-level sustainable supply chain (SC) of a perishable product with price-dependent demand and deterioration rates. The SC consists of suppliers, a production center (PC), distribution centers (DCs), and retailers. We aim to ascertain the optimal pricing policy and cycle length to maximize profit, achieve specific social objectives, and minimize the total cost and adverse environmental impacts. The proposed model determines the deterioration rate of each product according to its expiration date, the optimal location of supply-side facilities, and the flow rate between the facilities based on the selected mode of delivery. The products are delivered to the retailers by a mechanized transportation system either directly from the PC or indirectly through the DCs. Finally, an actual case study is provided to demonstrate the applicability of the model and our theoretical results under real-world conditions. We solve the case study by a preemptive fuzzy goal programming method and perform several sensitivity analyses on the results. By performing simultaneous sensitivity analyses on the demand and expiration dates, the optimal values of the problem's parameters are determined. The optimal values help decision-makers make optimal decisions regarding the selling price of products and replenishment times. The model is applicable to supply chains of any perishable items with expiration dates.

Designing reverse logistics network for healthcare waste management considering epidemic disruptions under uncertainty

Population growth and recent disruptions caused by COVID-19 and many other man-made or natural disasters all around the world have considerably increased the demand for medical services, which has led to a rise in medical waste generation. The improper management of these wastes can result in a serious threat to living organisms and the environment. Designing a reverse logistics network using mathematical programming tools is an efficient and effective way to manage healthcare waste. In this regard, this paper formulates a bi-objective mixed-integer linear programming model for designing a reverse logistics network to manage healthcare waste under uncertainty and epidemic disruptions. The concept of epidemic disruptions is employed to determine the amount of waste generated in network facilities; and a Monte Carlo-based simulation approach is used for this end. The proposed model minimizes total costs and population risk, simultaneously. A fuzzy goal programming method is developed to deal with the uncertainty of the model. A simulation algorithm is developed using probabilistic distribution functions for generating data with different sizes; and then used for the evaluation of the proposed model. Finally, the efficiency of the proposed model and solution approach is confirmed using the sensitivity analysis process on the objective functions’ coefficients.

Sectoral growth dynamics of country groups: a country grouping suggestion

Purpose- In the study, the effects of sectors on the growth of OECD member countries were determined by using the Fuzzy Goal Programming method. These findings may help policymakers see sector impacts that help countries in their growth targets. The study aims to contribute to the literature in two ways. The first of these analyses are based on long-term economic growth and primary sector analysis. The second contribution is to propose an alternative empirical methodology with clustering analysis which is not used to obtain the basic assumption of homogeneity in the application of panel data analysis. Methodology- The effects of sectors on the growth of OECD member countries were determined by using the Fuzzy Goal Programming method. In the second step, countries were divided into groups using K-means clustering analysis according to these impact values. With the help of these weights, the growth dynamics of similar countries and the contributions of sectors to this dynamic were obtained. Findings- Countries analyzed in terms of the contribution of sectoral growth rates to the growth rate of the country were divided into groups by cluster analysis. It is determined that the countries grouped in terms of the contribution of sectors to growth are divided into 5 groups. The first group has 10 member countries. The second group has 12 countries and the third group it has 7 countries, the fourth group has 4 countries and only 1 country belongs to the fifth group. The countries in group 1 are Estonia, Turkey, Greece, Italy, Poland, Portugal, Lithuania, Latvia, Slovakia, and Slovenia. The countries in group 2 are Australia, Belgium, Czech Republic, Germany, Denmark, Hungary, Ireland, Mexico, Netherlands, Norway, Sweden, and New Zealand. The countries in group 3 are Austria, Spain, Finland, France, the Republic of Korea, Luxembourg, Switzerland, the USA, Israel, Costa Rica, the United Kingdom, and Japan. Conclusion- Countries that have similar sectoral structures can analyze growth with panel data analysis, but it is important to form homogeneous groups while doing this analysis. For this reason, another critical suggestion it is offered based on the study is the use of FGP methodology in the analysis method. Keywords: Economic growth, sectoral growth, Fuzzy Goal Programming, Cluster Analysis, Panel VAR JEL Codes: N10, C61, C38, C33

Designing an IoT-enabled supply chain network considering the perspective of the Fifth Industrial Revolution: Application in the medical devices industry

The rapid growth of technology, environmental concerns, and disruptions caused by the COVID-19 pandemic have led researchers to pay more attention to an emerging concept called the fifth industrial revolution (I5.0). Despite the high importance of the I5.0, the literature shows that no study investigated the supply chain network design problem based on the I5.0 pillars. Hence, this research develops a multi-stage decision-making framework to configure a closed-loop supply chain based on I5.0 dimensions to cover this gap. In the first stage, the score of technologies that utilized in the supply chain is calculated using the analytic hierarchy process method. Afterwards, in the second stage, a mathematical model is proposed to configure the supply chain. Then, Furthermore, an efficient solution method, named the fuzzy lexicographic multi-choice Chebyshev goal programming method, is developed to obtain the optimal solution. In general, the main contributions of the current study can be divided into two major parts as follows: (i) the current study is the first research that incorporates the dimensions of the I5.0 into the supply chain network design problem, and (ii) this work develops a novel and efficient solution method. In this regard, the major problems and challenges that existed include the limitation of available resources in relation to Industry 5, especially in the field of the supply chain, as well as quantifying the elements of Industry 5.0 in the form of a mathematical programming model.

A branch and efficiency algorithm to design a sustainable two-echelon supply chain network considering traffic congestion and uncertainty.

This work aims to design a sustainable two-echelon supply chain not only based on the widely used cost perspective, but also based on the efficient use and preservation of limited resources. For this purpose, a branch and efficiency (B&E) algorithm is developed, which includes an optimization model and an evaluation model. The proposed tri-objective optimization model simultaneously minimizes the total cost of the supply chain, maximizes the sustainability score, and minimizes inequity among customers. The solutions obtained from the optimization model are then evaluated by extended data envelopment analysis (EDEA) models based on common criteria (i.e., cost and service) and traffic congestion criterion. To take into account real-world conditions, parameters related to labor and demand are assumed under uncertainty. Since the presented models consist of more than one objective function, fuzzy goal programming (FGP) method is utilized to tread the multi-objectiveness. The obtained results from tackling a case study problem demonstrate that considering sustainability issues can positively affect both the economic and social aspects of the problem. Furthermore, the developed B&E algorithm is able to reduce costs in each iteration; this is what supply chain managers are interested in. On the other hand, this algorithm can provide more services to applicants compared to one of the competing algorithms.

How managerial perspectives affect the optimal fleet size and mix model: a multi-objective approach

We examine the interplay between the business and logistical aspects of a heterogeneous vehicle mix and fleet size problem using inputs from a dairy cooperative in India. Five objective functions have been modelled and simultaneously solved using a mixed-integer linear fuzzy goal programming method. These include net profit as a maximization function, and transportation cost, transportation time, lost sales due to non-service, and in-transit damage or loss as minimization functions. Our paper contributes to the literature by evaluating critical business objectives such as net profits, lost sales due to non-service, and in-transit loss in conjunction with the typical heterogeneous fleet size and mix optimization decisions. The paper proposes two different solution methods: the Competing and the Compensatory method, which may be viewed as two extreme ends of the solution spectrum. Under the Competing method, all five objectives are assumed to be equally important, while the Compensating method allows the optimal solution to endogenously attach priorities to the different objectives. The two provide very different solutions since the Compensatory method considers the synergies between the objectives while the Competing method ignores them. The sensitivity analysis in the paper will also aid to managerial decision-making by evaluating different priorities for the multiple objectives during different periods. Given the impreciseness in the goal definitions and incomplete information available to a decision-maker, our paper the strengthens vehicle fleet size and mix decision modelling problems by adding other managerial perspectives.

A novel intuitionistic fuzzy goal programming method for heterogeneous MADM with application to regional green manufacturing level evaluation under multi-source information

The existed regional green manufacturing level assessment methods pay little attention to the multi-source information such as the expert’s psychological preference information, the preference information among regions, the heterogeneous information of regions on attributes and the interactions information between attributes at the same time, which is as a heterogeneous multi-attribute decision making (MADM) problems. A novel intuitionistic fuzzy goal programming is proposed for HMADM problems under multi-source information. The Choquet integral-based relative ratio is proposed on the basis of the Choquet integral measure. It is far away from the negative-ideal solution (NIS) and closeness to the positive-ideal solution (NIS) simultaneously with the interactions between attributes. Hereby the consistency and inconsistency indices with expert’s hesitation degrees are defined, the attribute weights are solved by using the developed intuitionistic fuzzy goal programming models with the optimistic, pessimistic and mixed methods. The Choquet integral-based relative ratios of alternatives can be calculated to generate their ranking orders. Finally, a regional green manufacturing level assessment example and compared with existed methods show that the superiority and validity of the proposed method, which improves the intuitionistic fuzzy goal programming methods, LINMAP methods and MADM methods with the interactions between attributes.

Multi-objective green 4-dimensional transportation problems for damageable items through type-2 fuzzy random goal programming

As per ECOFYS’s11https://ingmarschumacher.files.wordpress.com/2013/05/asn-ecofys-2013-world-ghg-emissions-flow-chart-2010.pdf. report, road transportation contributes 10.5% of the GHGE, which is the cause of global warming. With the infrastructural developments, there are several routes between different cities, even in developing countries. In a business, objectives’ goals are always uncertain. With these facts, in this investigation, a multi-objective green four-dimensional transportation problem for damageable items is formulated and solved. Here four objectives — minimization of operational cost, transportation time, carbon emission amount and maximization of retailers’ satisfaction, whose goals are type-2 fuzzy random are considered. There are several connecting paths between sources and destinations with varied traffic congestion and maximum possible velocities for different conveyances. To get a better compromise solution for multi-objectives, the type-2 fuzzy random goal programming method (T2FRGPM) is developed using the Enhanced Karnik-Mendel algorithm for type reduction of type-2 fuzzy set The model is solved by the proposed T2FRGPM and illustrated with some numerical data using Lingo 11.0. A real-life example and several particular models are presented. The effectiveness of the proposed method, the importance of the four-dimensional transportation problem, and the objectives are established. A trade-off between transportation time and carbon emission amount is presented.

PENERAPAN FUZZY GOAL PROGRAMMING DALAM PENGOPTIMALAN PERENCANAAN PRODUKSI

Production planning is a very important activity for companies in considering production factors ranging from the number of products that must be produced, when the product must be completed, and other things needed. Improper production planning risks causing losses to the company because the use of production costs and profit estimates are not optimized. One method that can be used in optimizing production planning is the fuzzy goal programming method. Fuzzy goal programming is an extension of linear programming that can solve problems of more than one goal in the presence of target constraints. This study aims to examine and apply the fuzzy goal programming method which is solved by the simplex method in Ayune Kitchen production planning by maximizing revenue and minimizing raw material costs. The data used in this study include product data (comb bread, dulce, brulee, mentai, lasagna, and briyani rice), production prices, and raw materials for making products from Ayune Kitchen which will be analyzed using linear programming and fuzzy goal programming methods. simplex. The result of this research is the optimal income that will be obtained by Ayune Kitchen is Rp. 8.830.000 and the optimal expenditure incurred by Ayune Kitchen to purchase raw materials is Rp. 6.687.821

Low-Carbon Supplier Selection Using Fuzzy AHP and Goal Programming Approach

It has become the leading world trend that all countries join hands to respond to climate change and promote green and low-carbon development. In this background, more and more enterprises seek to control carbon emissions from the source and reduce indirect carbon emissions, consequently paying increased importance to the carbon footprint of their suppliers. Most of the earlier studies concerning supplier selection mainly focus on traditional factors, such as quality, service, and lead time, but minimal importance to the carbon emission of supplies. This study fills this gap by incorporating carbon emission criteria into supplier selection and presenting a method of combining fuzzy analytic hierarchy process (AHP) and fuzzy goal programming (GP) to address the problem of supplier selection and order quota allocation. Firstly, we use fuzzy AHP to evaluate the relevance and importance of supplier selection criteria according to the experts’ opinions. Second, each objective is given weights according to the fuzzy AHP results, and then the fuzzy GP method is used for supplier selection and order quota allocation. Finally, we implement an example study with a data set from a realistic situation, and the results confirm the effectiveness of the proposed method in an uncertain environment.

Solving Multi-Objective Multilevel Programming problems using two-phase Intuitionistic Fuzzy Goal Programming method

This paper presents a two-phase intuitionistic fuzzy goal programming (two-phase IFGP) algorithm to solve Multi-Objective Multilevel Programming (MO-MLP) problems. The coefficient of each objective and constraint function is assumed to be triangular intuitionistic fuzzy parameters and the crisp MO-MLP problems are obtained using the accuracy function method. To avoid decision lock, the top levels set tolerance limits for decision variables to control the lower levels. The problem is modeled in the intuitionistic fuzzy environment using membership and non-membership functions for each objective function at all levels and decision variables controlled by the top levels. Then, we proposed an IFGP algorithm to achieve the highest degree of each membership and non-membership goal by minimizing unwanted deviational variables and generating compensatory solutions for all decision-makers at all levels. Moreover, in the proposed approach, two-phase IFGP is modeled to yield a compromise solution that satisfies both the MN-Pareto optimal solution and the Pareto optimal solution at each level. Also, verification of the proposed method is discussed with numerical examples.

Optimization of Microgrid Operation under the Diffusion of Solar and Wind Plant with Special Attention on Environment

This paper introduces a priority based Fuzzy Goal Programming (FGP) method for modelling and solving of microgrids using Genetic Algorithm (GA). The microgrid consider in this article consists of conventional and nonconventional power plants, such as wind and solar power plants. To incorporate the fluctuating outputs of solar and wind plants, the objectives of the problem are fuzzily described. In this article, optimal generation cost, total losses, and environmental ill-effect of power generation under the penetration of renewable energy resources (RES) are considered. In model formulation, the membership functions associated with fuzzy goals are transformed into membership goals and introducing under- and over-deviational variables to each of them. A GA scheme is used within the structure of FGP model to achieve the aspired levels of goals based on priorities in the decision environment. Then, a sensitivity analysis with variations of priority structure is performed and then the notion of Euclidean distance function is used to identify optimal power generation decision. To prove the usefulness of the intended method, three versions of a modified IEEE 30-bus and 6-generator system with renewable power generations are counted as the test systems. The model solution is also evaluated with the solutions obtained by using other approaches.

Assessing employees’ job motivation using BWM method and fuzzy goal programming: a case study of a petrochemical company

PurposeRecognizing the factors affecting employees’ job motivation is one of the necessities that can improve people’s performance and increase their effectiveness. This study aims to determine the factors affecting job motivation and to examine effective strategies to increase motivation through identifying internal and external factors.Design/methodology/approachIn this descriptive study, the statistical population was the employees of the largest petrochemical company in Iran. The questionnaire was randomly distributed to the organization’s employees and managers based on Herzberg’s motivation-hygiene theory. To analyze the obtained data, first, the best and the worst factors were identified using SPSS software and then were ranked using best–worst method (BWM).FindingsThe results demonstrated that the highest rank among the motivational factors of employees is related to working environment conditions and the lowest rank is related to career advancement and development indicator. In the second stage, the best strategies for motivational factors were determined using the fuzzy goal programming method. The findings showed that 12 out of the 17 proposed solutions have the highest motivation among employees, the implementation of which can increase employee productivity in the petrochemical company under study.Originality/valueFurther to the best of the authors’ knowledge, job motivation factors in the petrochemical industry have never been examined and ranked by using the BWM method so far. Also, the goal programming approach has never been applied to determine strategies for increasing job motivation and ultimately productivity.

MULTI-OBJECTIVE TRANSPORTATION PROBLEM UNDER TYPE-2 TRAPEZOIDAL FUZZY NUMBERS WITH PARAMETERS ESTIMATION AND GOODNESS OF FIT

The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

Ecotourism supply chain during the COVID-19 pandemic: A real case study

The coronavirus (COVID-19) disease has caused serious and irreversible damage to the ecotourism industry, posing serious challenges to all parts of the ecotourism supply chain. The ecotourism supply chain is made up of various components, the most important of which are ecotourism centers. During these pandemic times, the primary concerns of these centers are to improve their deplorable economic conditions and retain customers for the post-coronavirus era. As a result, an investigation should be conducted to address these concerns and provide appropriate solutions to help them overcome the challenges that have emerged. To achieve the research goal, a bi-objective mathematical model for the ecotourism supply chain in an uncertain environment is developed, accounting for the effects of COVID-19. The first objective function minimizes the total cost of the supply chain, while the second maximizes customer satisfaction. The proposed mathematical model is solved using a fuzzy goal programming (FGP) method. A sensitivity analysis study is also carried out to examine the performance of some basic parameters. Furthermore, the model is tested in a real case study to determine its efficacy. Finally, some effective managerial insights are proposed to improve the situation of the centers during the pandemic.

Hayat Dışı Sigorta Sektöründe Kârı Etkileyen Firma İçi Faktörlerin İncelenmesi: Bulanık Hedef Programlama Örneği

People and companies face uncertainties and risks throughout their lives. A cost arises because of every risk arising from their activities. The size of the risk concept should be well calculated and managed in this case. Therefore, insurance steps in to manage risks effectively and efficiently. In this study, the effects of firm variables on period profit / loss in non-life insurance companies were examined. To obtain maximum profit, which is an important element in ensuring the continuity of the activities of insurance companies, the effects of intra-firm variables that have an impact on profit have been investigated using fuzzy goal programming model. The variables of the insurance companies selected in this study used in the model are financial variables, premium total variables and operating expense variables. These variables are given in detail later in study. Annual data between 2014-2020 were used in the study. According to the results obtained from the study, the profit of insurance companies was estimated using the financial variables, operating expenses, and total premiums, respectively. In addition, it has been observed that the fuzzy goal programming method gives effective results in calculating the amount of variables that affect the profit of companies.

Multimarket competition effects on product line decisions – A multi-objective decision model in fast moving consumer goods industry

In a multimarket competition, firms experience increased contacts with competitors under various product-geographic markets, exhibiting mutual forbearance, which in turn deters firms to venture into product proliferation. However, firms do engage in the same through horizontal product differentiation through 'brand extensions.' Since marketers face imprecise goals, we propose a multi-objective product line decision model for pruning or continuing product lines. Specifically, this is done by using a fuzzy goal-programming method while validating it using a dataset (comprising of eighty thousand households) from the Indian tea industry. Our findings reveal that in the festive season, a firm should only focus on limited brands and prune the rest to maximize its revenue while increasing the spending on advertising and the sales and distribution overheads. However, during the end of the financial quarter, the focus should be on achieving targets by maintaining a broader product portfolio.

The fuzzy goal programming approach to production planning of intermediate gear spare parts: a case study

Production planning has an important role in the company's business processes. A company engaged in the manufacture of intermediate gear parts has a problem in optimizing its production system. The production planning system that occurs is still based on predictions from decision-makers. This study aims to optimize the production planning system to maximize the 15T intermediate gear spare parts' production capacity and the 30T intermediate gear spare parts. Optimization of production planning uses the fuzzy goal programming method to optimize objectives based on existing constraints such as working hours, profit tolerance values, and demand tolerance values. The results showed that the use of fuzzy goal programming was able to increase the production level by 2.765, with an increase in profit of 2.57%. Fuzzy goal programming implementation provides an optimal solution in increasing profits in accordance with company goals based on the constraints that occur.