Fuzzy Goal Programming Technique Research Articles

A cost-efficient relocation model minimizing economic and social disruption of the disaster-affected population of the Kedarnath considering uncertainty

In 2013, Kedarnath, India, faced a devastating landslide-induced flood, causing substantial damage, loss of life, and displacement. This event highlights a gap in post-disaster relocation models, hindering efficient transportation to preferred locations. The challenge intensifies as coordinating relocation with individual preferences, coupled with post-disaster data uncertainty, complicates efforts and triggers a series of effects on community acceptance, psychological well-being, and overall resilience. The study addresses post-disaster relocation gaps by introducing a multi-objective transportation model (MOTM) with psychological support, optimizing resettlement to minimize budget impact, distance, and economic and social disruption (ESD). The proposed interval-valued pentagonal neutrosophic number (IVPN) and defuzzification technique advances disaster management theory and offers a practical solution for uncertainty in data, bridging theory, and practical application in the disaster response phase. The MOTM efficiently minimizes transportation, psychological intervention, and rental costs through fuzzy goal programming (FGP), global criterion method (GCM), and neutrosophic compromise approach (NCA), implemented with LINGO optimization software. The values of parameters considered in the MOTM are captured in IVPN format and converted to crisp values, availing the proposed defuzzification technique. The performance evaluation of the defuzzification technique is carried out through a comparative analysis of past literature. The proposed MOTM and IVPN were implemented in the 2013 Kedarnath flood case study to generate diverse relocation options. GCM provides relocation options at a higher cost and distance but with minimal ESD by providing a preferred location to a family count as high as 3324 out of 3491 families. The FGP technique provides results similar to NCP that reduce the costs and distance of the relocation process by 6.95% and 0.88%, respectively; however, it increases ESD by allocating preferred locations to only 2623 out of 3491 families. The study provides Pareto optimal solutions for the smooth application of MOTM for diverse post-disaster instances.

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

Optimizing system reliability through selective maintenance allocation: A novel multi‐objective programming approach using neutrosophic fuzzy concept

AbstractSelective maintenance refers to the problem of decision‐making on how to maintain a multi‐component complex system that can be repaired or replaced. The goal is generally to plan ahead in order to improve the likelihood of success for future maintenance tasks. In this article, we proposed a multi‐objective decision‐making model for maximizing the system reliability of a multi‐component systems. The objective functions represent the reliability of the sub‐systems arranged in series comprising of components arranged in parallel forms. The cost and total time incurred in the repair/replacement activities are considered as two sets of constraints in the proposed model. Fuzzy logic is incorporated to deal with the inherent uncertainty that exists in the parameters involved in the proposed model. To solve the uncertain multi‐objective selective maintenance model, we have proposed four‐valued neutrosophic technique. The proposed solution methodology combines the concept of four‐valued neutrosophic fuzzy set with fuzzy goal programming technique. Four linear membership functions for the degrees of truth, uncertainty, contradiction, and false are used to obtain the compromise solution through the proposed technique. To determine the feasibility and applicability of the proposed model and solution methodology, a case problem of multi‐component system of an aircraft gas turbine engine is studied.

Application of fuzzy goal programming approach in the real-life problem of agriculture sector

Goal: The present study aimed to demonstrate the applicability of the fuzzy goal programming to frame the decision support system for the decision-makers to deal with the real-life problem of the agriculture sector namely the apple cultivation planning problem and to obtain an optimum solution. Design / Methodology / Approach: The proposed method occurred within the apple-producing sector in the Kashmir valley of India and included the collection of data through interviews and surveys with various farmers. Also, the results were drawn with the help of LINGO 18.0. Results: The current finding implies that all of the desired objectives have been met, as well as an optimal solution. The proposed model offers a significant approach for designing plans to determine various agricultural activities in a fuzzy decision environment. Finally, the current study conducts a case study in the apple cultivation sector to obtain various competing objectives. Sensitivity analysis was also performed on its preferential weight parameters. Limitations of the investigation: It should be noted that the parameters related to production cost, transportation cost, and cost of material may change over the years. The selling price may also vary according to the quality of apples and over the years. Because of natural factors, the annual production of apples may also vary. Practical implication: The current study shows that using fuzzy goal programming techniques in an apple production process has a huge potential to increase farmers' income. It can be concluded that the current study can help decision-makers to deal with real-life planning issues in the agricultural sector. Future research can also take advantage of other initiation strategies. Originality/Value: The study looks at the applicability of the fuzzy goal programming paradigm in a new field of apple production in the agriculture sector. According to our knowledge, this is the first time the optimization model has been used in the apple cultivation sector.

Bi-criteria optimization of cleaner biofuel supply chain model by novel fuzzy goal programming technique

In engineering, the biofuel supply chain (BSC) is a significant supply chain optimization challenge. Here, the multi-objective optimization problem for biofuel distribution is based on the life cycle energy consumption (LCEC) and the emission of CO2 involve in supply network of a biofuel. It includes numerous feedstocks, means of transportation, and locations for biofuel plant construction, as well as multiple technologies, the number of feedstocks in the agricultural system, transportation capabilities, crop yields, and market needs. To provide a modelling framework for optimization issues with multi-fold uncertainty, different reduction approaches to turn a Type-2 Fuzzy variable into a Type-1 Fuzzy variable through the expected value method are described. The deterministic BSC model is then solved utilizing Goal Programming and Weighted Sum Method using Generalized Reduced Gradient Technique. The goal BSC models are (i) Minimization of life cycle energy consumption (ii) total emission of CO2 in uncertain environment. The numerical experiments demonstrated with different optimistic labels by which managers can control their objects by choosing optimistic values. Here, we have developed a systematic optimization approaches for the advancement of biofuel transportation, supply and process chain analysis, sustainability, and industrial optimization. Finally, a real-world case study is used to demonstrate the applicability of the suggested approach. The findings show that the proposed solutions are successful in reducing logistical expenses.

Estimation and Optimization for System Availability Under Preventive Maintenance

Engineers design systems to be reliable and work to fulfil their missions without failure for a specific period. However, the system components deteriorate with time and lead to its failures. A frequent system failure increases the management costs, hence posing a challenge to decision-makers. Therefore, for the avoidance of frequent system failures, preventive maintenance is necessary. The objective of any manufacturing firm is to maximize profit and minimize costs. The interval for preventive maintenance can be optimized if the system’s availability is maximized and its cost function minimized. This study evaluates the availability and cost function for a continuous operating series-parallel system under a fixed time environment. A multiobjective model is formulated to maximize the availability and minimize the cost function of the system. The study illustrated a numerical example and solved using goal programming (GP), fuzzy goal programming (FGP), genetic algorithm (GA), and particle swarm optimization (PSO) techniques. The results are compared using a robust statistical test and, the PSO proves to be better. A simulation study was carried out further to evaluate the availability and cost function using R and MATLAB packages.

Solving multi-level multiobjective fractional programming problem with rough interval parameter in neutrosophic environment

In this study, a novel algorithm is developed to solve the multi-level multiobjective fractional programming problems, using the idea of a neutrosophic fuzzy set. The co-efficients in each objective functions is assumed to be rough intervals. Furthermore, the objective functions are transformed into two sub-problems based on lower and upper approximation intervals. The marginal evaluation of pre-determined neutrosophic fuzzy goals for all objective functions at each level is achieved by different membership functions, such as truth, indeterminacy/neutral, and falsity degrees in neutrosophic uncertainty. In addition, the neutrosophic fuzzy goal programming algorithm is proposed to attain the highest degrees of each marginal evaluation goals by reducing their deviational variables and consequently obtain the optimal solution for all the decision-makers at all levels. To verify and validate the proposed neutrosophic fuzzy goal programming techniques, a numerical example is adressed in a hierarchical decision-making environment along with the conclusions.

A Hybrid Grid Partitioning and Fuzzy Goal Programming Model for Enhanced Performance and Decision Support

This study introduces an innovative Hybrid Grid Partitioning and Fuzzy Goal Programming Model for Enhanced Performance and Decision Support. The proposed model combines grid partitioning and fuzzy goal programming techniques in order to address the challenges of complex systems and optimize performance while taking into account subjective preferences and uncertainties. Using grid partitioning, the hybrid model divides the problem space into smaller grid cells, facilitating localized analysis and efficient processing. Fuzzy goal programming handles ambiguous objectives and uncertain constraints, providing decision-making flexibility and robustness. The effectiveness of the model is demonstrated through a numerical example, highlighting enhanced performance and decision support for complex problems. The applicability of the hybrid paradigm to diverse fields, including transportation, logistics, and resource management, is discussed. The study also acknowledges limitations, such as computational complexity and the need for validation in the actual world. In the future, it will be necessary to resolve these limitations and improve the hybrid model. Overall, the research advances optimization methodologies and decision support systems by providing a comprehensive framework for confronting complex systems and facilitating well-informed decision making.

Optimizing Design of Smart Workplace through Multi-Objective Programming

Smart environments have proven very supportive to the improvement of the performance of people in different workplaces. Plenty of applications have been introduced spanning different settings including healthcare, ambient assisted living, homes, offices, and manufacturing environment, etc. However, subjectivity and ambiguity prevail in the majority of research, and still, up to date, rare approaches found quantitatively and objectively constructing or assessing the impact of smart enabling technologies on the performance of the subject environment. Further, no approaches have considered optimizing the adoption of those smart technologies with respect to objectives achievement. This article presents a novel optimization methodology for designing a smart workplace environment in conditions of ambiguity or fuzziness. The methodology begins with defining and weighing the overall goals and objectives of the workplace. The Prometthe multi-criterion decision-making technique is used to weigh the operational objectives with respect to the overall workplace goals. Next, the relation among basic building blocks of the model; namely: the operational objectives, smartness features, and smart enabling technologies are quantified, utilizing fuzzy relations. Then, the fuzzy goal programming techniques will be utilized to optimize the impact relation values while considering the budget constraint. The proposed optimization methodology is implemented on the development and optimization of the smart clinic, as a typical instance of the workplace.

Revenue optimization modeling for renewable energy resource mix for sustainable development

The adoption and attainment of sustainable development goals have diverted developing nations like India towards the use of renewable resource for meeting the growing need for electricity. With the advancement in technology for generating electricity, the concern is to develop such renewable energy mix that can help satisfy the electricity demand and be environment friendly. In this paper, one such problem wherein the three conflicting criterion such as maximization of energy savings, maximization of efficiency and minimization of the cost of installation has been considered for designing a multi-objective optimization model to meet the growing demand of electricity. Interactive fuzzy goal programming technique with three different functional forms of membership function namely linear, exponential, and hyperbolic have been used to solve the proposed problem. The results have shown substantial adequacy in meeting the desired load demand and at the same time reduction in installation cost has been seen which in turn will impact the revenue generation.

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.

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.

Multi-Objective Two Echelon Supply Chain Inventory Model with Lot Size and Customer Demand Dependent Purchase Cost and Production Rate Dependent Production Cost

This paper develops an integrated production inventory model for a two echelon supply chain consisting of one manufacturer and one retailer. Purchase cost for the manufacturer is dependent on inventory lot size, production cost of the manufacturer is dependent on production rate. Purchase cost of the retailer is dependent on demand rate of the customer. Idle time cost has been considered. Multi-item has been considered in this supply chain inventory model. Average cost in integrated inventory model has been calculated per unit time. The formulated problem 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 provided to justify the proposed model. Finally graphical illustrations are considered and its sensitivity analysis is provided to test feasibility of the model.

Fermented mulberry leaf meal as fishmeal replacer in the formulation of feed for carp Labeo rohita and catfish Heteropneustes fossilis-optimization by mathematical programming.

Search for cost-effective, eco-friendly and sustainable plant resources as potential feedstuff to replace fishmeal in the formulation of feed for fish has been in the forefront of aquaculture researches since the last few years. In this study, experiments were conducted to evaluate if replacement of fishmeal by the fermented leaf meal of mulberry (Morus indica) was viable in the formulation of feed for carp fish Labeo rohita and catfish Heteropneustes fossilis. Four iso-proteinous, iso-lipidic and iso-energetic experimental feed were formulated by replacing 0, 25, 50 and 75% of fishmeal by the fermented mulberry leaf meal (FMLM), and both species were grown on these feeds for 8weeks. Since the results revealed differences in response to fishmeal replacement level between parameters, we determined optimum fishmeal replacement level (OFRL) for each parameter from the polynomial curve equation. While maximum weight gain and specific growth rate and minimum feed conversion ratio was found at 30-32% OFRL for L. rohita and at 52-53% OFRL for H. fossilis, other parameters responded differently in both fish. Therefore, we applied a two-phase fuzzy goal programming technique using all parameters, which showed overall OFRL for L. rohita and H. fossilis as 30.95% and 52%, respectively. We also applied the concept of 'decision tree' to identify the key factor behind utilization of FMLM. It was concluded that activity of amylase and subsequent utilization of carbohydrate was the key factor in utilizing FMLM. Interestingly, H. fossilis was found more efficient in utilizing carbohydrate of FMLM than L. rohita.

An interactive weighted fuzzy goal programming technique to solve multi-objective reliability optimization problem

This paper presents an application of interactive fuzzy goal programming to the nonlinear multi-objective reliability optimization problem considering system reliability and cost of the system as objective functions. As the decision maker always have an intention to produce highly reliable system with minimum cost, therefore, we introduce the interactive method to design a high productivity system here. This method plays an important role to maximize the worst lower bound to obtain the preferred compromise solution which is close to the best upper bound of each objective functions. Until the preferred compromise solution is reached, new lower bounds corresponding to each objective functions will be determined based on the present solution to develop the updated membership functions as well as aspiration levels to resolve the proposed problem. Considering judgmental vagueness of decision maker, here we consider the resources as trapezoidal fuzzy numbers and apply total integral value of fuzzy number to transform into crisp one. To illustrate the methodology and performance of this approach, numerical examples are presented and evaluated by comparing with the other method at the end of this paper.

Maximizing profit and responsiveness of a closed-loop supply chain in presence of product exchange offer

Designing an effective collection process is strategically important due to its impact on product-recovery, profit and responsiveness of overall closed-loop supply chain (CLSC). In this paper, we propose a product-recovery framework which models consumers’ willingness to accept a product exchange offer (PEO) as non-linear function of discount amount offered to them on returning used product and utility they obtain on receiving the new product. The proposed recovery framework is then integrated with a multi-objective optimization model, which takes into account the responsiveness of both forward and reverse supply chain, in order to maximize profit and responsiveness of the overall CLSC. The optimization model is solved using a modified interactive fuzzy goal programming technique, which allows the decision makers to adjust lower and/or upper bound of the objective functions during the interactive decision making process. The developed optimization model determines optimal value of discount, optimal return and remanufacturing quantity of used products, and optimal manufacturing quantity of fresh-new products. The analysis suggests a trade-off between amount of discount offered to consumers on returning used products and perceived quality of the new product while accepting the PEO.

A model for two-stage fixed charge transportation problem with multiple objectives and fuzzy linguistic preferences

In this paper, a multi-objective model for two-stage fixed charge transportation planning problem is studied. The transportation process is considered to occur from manufacturing plants to the distributers and then from distributers to the customers. The availabilities at the manufacturing plants, capacities of the distributers and demand of the customers, all are considered to be fuzzy numbers. The proposed model is formulated with three conflicting goals or objective functions. The first objective is to minimize the total transportation cost involved in the whole transportation process. The second objective is to maximize the total quantity of the products to be transported, whereas minimizing the total deterioration that occurred during the transportation process is considered to be the third objective function. Fuzzy linguistic relations or preferences among the three objective functions are studied. A linear membership function is used to represent the fuzzy relative preferences between the objective functions. For solving the multi-objective problem, fuzzy goal programming technique is adopted with some linear and nonlinear membership functions. Finally, the proposed model is illustrated and solved for some simulated numerical data and some sensitivity analysis for the problem is also discussed. The best results for the solved numerical problem are found when hyperbolic membership functions are considered to model the aspiration levels for objective functions, whereas comparatively less significant results are found when linear membership functions are used to model the aspiration levels for objective functions.

Multi-objective capacitated transportation: a problem of parameters estimation, goodness of fit and optimization

This paper discusses a solution procedure of a multi-objective capacitated transportation problem (MOCTP) in an uncertain environment. In MOCTP, the primary objective is to find the optimum quantity of the shipment subject to some capacitated restriction on each route. Due to uncertainty in MOCTP, the formulated problem cannot be solved directly for the optimum allocation. The uncertainty in MOCTP has been presented by the multi-choices and probabilistic distributions, respectively. The multi-choice and probabilistic distributions have been transformed into an equivalent deterministic form using the binary variable and stochastic programming approach, respectively. It has been assumed that the demand and supply parameter of the formulated problem follows different kinds of probabilistic distributions, namely, Pareto, Weibull, Normal, Extreme value, Cauchy and Logistic distribution, respectively. The maximum likelihood estimation approach has been used to estimate the unknown parameters of the probabilistic distributions with specified probability level. Finally, Akaike’s information criterion and Bayesian information criterion have been used to identify the goodness-of-fit of probability distributions for the given scenarios. The fuzzy goal-programming technique has been used to obtain the best optimum compromise solution for an equivalent crisp MOCTP model. A case study has been given to illustrate the computational procedure.

A unified method of defuzzification for type-2 fuzzy numbers with its application to multiobjective decision making

This paper introduces a process of defuzzification for ranking of type-2 trapezoidal fuzzy numbers. A two-phase defuzzification method has been developed using probability density function of the random variables associated with the fuzzy numbers. This method finds an equivalent defuzzified value of type-2 fuzzy numbers through phasewise reduction. The process reduces the computational complexities for using type-2 fuzzy numbers significantly and it is applicable to not only type-2 fuzzy numbers but also to any types of fuzzy numbers for ranking them properly. To illustrate the proposed defuzzification process, the method is applied on a set of type-2 trapezoidal fuzzy numbers and ranked them according to their defuzzified values. The achieved results are compared with other existing ranking methods. Furthermore, a multiobjective linear programming model having type-2 fuzzy numbers as parameters is solved using the proposed defuzzification process. Fuzzy goal programming technique is used for achieving the highest degree of each of the defined membership goals to the extent possible in the decision-making context. A numerical example is provided to demonstrate the efficiency of the proposed methodology.

An enhanced reliability-oriented workforce planning model for process industry using combined fuzzy goal programming and differential evolution approach

This paper draws on the “human reliability” concept as a structure for gaining insight into the maintenance workforce assessment in a process industry. Human reliability hinges on developing the reliability of humans to a threshold that guides the maintenance workforce to execute accurate decisions within the limits of resources and time allocations. This concept offers a worthwhile point of deviation to encompass three elegant adjustments to literature model in terms of maintenance time, workforce performance and return-on-workforce investments. These fully explain the results of our influence. The presented structure breaks new grounds in maintenance workforce theory and practice from a number of perspectives. First, we have successfully implemented fuzzy goal programming (FGP) and differential evolution (DE) techniques for the solution of optimisation problem in maintenance of a process plant for the first time. The results obtained in this work showed better quality of solution from the DE algorithm compared with those of genetic algorithm and particle swarm optimisation algorithm, thus expressing superiority of the proposed procedure over them. Second, the analytical discourse, which was framed on stochastic theory, focusing on specific application to a process plant in Nigeria is a novelty. The work provides more insights into maintenance workforce planning during overhaul rework and overtime maintenance activities in manufacturing systems and demonstrated capacity in generating substantially helpful information for practice.