Fuzzy Linear Programming Method Research Articles

The equilibrium of maritime transport under disaster effects: The case of COVID-19

Ensuring traffic flows remain in equilibrium is crucial in preventing congestion and disruptions in maritime transport chains. Using the fuzzy linear programming method, this article examines how COVID-19 risks have affected the concentration and capacity of maritime cargo flows. The study presents the model, the computational process, and its applications, assessing the transport system's degree of imbalance in 2020-2021 compared to 2018-2019. The model allows for the evaluation of multiple dimensions to obtain an aggregative result. The model provides insights into the dynamics of changes in maritime traffic under the influence of COVID-19. Keywords: Intuitionistic Fuzzy Rough, maritime transport, transport equilibrium, seaborne trade, port calls

FUZZY LINEAR PROGRAMMING MODEL FOR INVERSE MULTIPLE CRITERIA SORTING PROBLEM: AN APPLICATION IN A PUBLIC TRANSPORTATION COMPANY

Multi-criteria decision making (MCDM) techniques are among the methods used by the decision maker in the decision phase in practice, as in the literature. MCDM problems are grouped as classifications and sorting problems according to the type of inclusion or ranking in existing classes. Inverse multi-criteria sorting problem, a new topic in recent years, is defined as choosing among existing actions in order to improve the status of alternatives. In this study, in order to find out which action plan should be chosen for providing the minimum cost for the improvement of public transportation vehicles in case the boundaries of the classes to be assigned are uncertain, the inverse multi-criteria ranking problem is used. Because the boundaries of the classes to be assigned are fuzzy, fuzzy linear programming method will be used to solve the problem.

FUZZY LINEAR PROGRAMMING METHOD IN PRODUCTION PLANNING: AN APPLICATION IN THE METAL INDUSTRY

Günümüzde hızla artan rekabet ortamı işletmelerin sahip olduğu kaynakları daha verimli kullanması ihtiyacını ortaya çıkarmıştır. İşletmelerin sahip oldukları kaynakları maksimum kâr sağlayacak bir şekilde müşterinin talep ve istekleri doğrultusunda doğru zamanda ve doğru miktarda sağlayabilmeleri hayati önem taşımaktadır. Bu sebeple rekabet ortamında başarılı olmak ve kâr sağlamak amacıyla işletmeler üretim planlama alanına odaklanmışlardır. İşletmeler bu sayede üretim planlama ile olası talep artışlarına önceden çözüm bularak minimum maliyet ve maksimum kâr ile rakip işletmeler içerisinde en önde yer almaktadır. Üretim planlama konusu fazla kısıt ve kaynak bulundurması nedeni ile işletmelerin karar vermesi gereken önemli bir problemdir. Üretim planlama problemlerinde detaylı çözüme ulaşmak için en etkili ve hızlı yöntem yöneylem araştırmasının bir uygulaması olan doğrusal programlamadır. Doğrusal programlama ile işletmeler üretim planlama alanında karşılaştığı problemlere hızlı çözüm bularak karmaşık bir sistem de bile uygun optimal değere ulaşmaktadır. Bu çalışmada metal sektöründe faaliyet gösteren bir firmada üretim planlama problemi incelenmiş olup çalışmayı en iyi ifade eden model olan yöneylem araştırmasının bir yöntemi olan doğrusal programlama ile çözülmüştür. Model gerçek hayat problemlerinde verilerin kesin olmaması nedeniyle bulanık doğrusal programlamanın Verdegay yaklaşımı ile de çözülmüştür. Son olarak, Lingo bilgisayar programı yardımıyla çözüm sonucu bulunarak duyarlılık analizi yapılmıştır.

Implementation of Fuzzy Linear Programming Approach for More Accurate Demand Forecasting in a Make-to-Stock Company

Demand forecasting is of crucial importance for make-to-stock companies because product demand is uncertain and it changes with time. Fuzzy linear programming (FLP) can be an optimum approach for such uncertain situations. In this study, the FLP model was used for more accurate demand forecasting in a make-to-stock company. Demand forecasting study was carried out according to the FLP method and linear programming (LP) method. Solutions of FLP and LP were compared in terms of imputed shortage cost, inventory carrying cost, and net profit. Results show that the applied FLP method is more advantageous than LP as it provides a 67% decrease in costs and a 15% increase in net profit.

Aplikasi Fuzzy Linier Programming dengan Metode Branch and Bound untuk Mengoptimalkan Jumlah Produksi dan Keuntungan Penjualan Roti di Italia Bakery Bandar Lampung

Italia Bakery is one of the bakeries in Bandar Lampung that produces various types of sandwiches, namely meat bread, and green bean bread. The Italian Bakery factory has difficulty in determining the optimal amount of bread production as well as controlling the right amount of raw materials. This causes losses for the factory because bread that is not worth the market will be thrown away, as a result of which the profits obtained do not reach the maximum limit. This problem can be solved by planning the optimal production amount based on the amount of raw material supply and the amount of demand with fuzzy linear programming methods. Results that have been completed with fuzzy linear programming that is still a fractional number can be rounded using the branch and bound method. Based on the results of research conducted, it is known that the use of both methods can increase the company's profits by 8,17%.

Economic-Environment-Energy (3E) objective-driven integrated municipal waste management under deep complexities – A novel multi-objective approach

• WtE technologies compatible with recycling are integrated into the MSW system; • Multi-objective-driven integrated MSW management is optimized to achieve sustainable goals; • An interval-valued fuzzy linear programming method is developed to address uncertainties; • The subsidy is still required to encourage anaerobic digestion from the environmental aspect. Waste-to-energy technologies compatible with recycling are promising solutions for sustainable municipal waste management from both economic and environmental perspectives. This study focuses on the economic-environment-energy (3E) objective-driven integrated waste management optimization problems under deep complexities. A novel multi-objective programming model is developed to assist the optimal decision-making with the consideration of system profit, greenhouse gas emission, and energy recovery simultaneously. Besides, it advances existing optimization methods by incorporating interval-valued fuzzy numbers to tackle the ambiguity and the essential fuzziness in experts’ judgment. It was verified by a case study from an urban district of Beijing, China. The optimum waste treatment facility planning and waste stream allocation strategies with multi-objective tradeoffs were obtained to support decision-making considering different preferences of importance ranking. In general, incineration and anaerobic digestion would be the main technologies for waste disposal in the study area. Recycling would be greatly encouraged when pursuing more economic profits and greenhouse gas emission reduction. With withdrawing the subsidy in the future, the investment in anaerobic digestion would become less attractive. Meanwhile, the landfill with gas recovery would even become economically infeasible if there is no further reduction in cost. In addition, waste source separation is also a crucial factor for successful integrated waste management. It is suggested that a proper government subsidy and public participation in waste source separation would guarantee the sustainable development of the integrated waste management system.

Making the optimal decision for production by using the fuzzy linear programming method

Deciding on a fuzzy environment faces many difficulties due to the lack of accuracy in data or permanently changing data. Fuzzy linear programming is one of the best methods used in a fuzzy environment which has a big role in making the right decision to solve a problem. This paper aims to identify the method of Fuzzy Linear Programming (FLP) to take the optimal decision and reach the optimal production for crude oil products of the North Refineries Company, This paper constructs the FLP model and solves the model to reach a production decision that contributes to maximizing profit and solves the model by using the methods of FLP. The fuzziness was removed from the model by using five methods. Comparison between the methods of removing fuzzy in a linear programming model to get maximum profit. The paper results that the highest maximum profit is (993423791) million dinars when using the bounded and decomposition method for the linear programming problem, which is higher than the profits achieved by the research company by (50%). The results were implemented by the software package python 3.9.

An Application Model for Linear Programming with an Evolutionary Ranking Function

One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This method is simple in structure and is based on crisp linear programming. To solve the fuzzy linear programming problem (FLPP), a new ranking function (RF) with the trapezoidal fuzzy number (TFN) is devised in this study. The fuzzy quantities are de-fuzzified by applying the proposed ranking function (RF) transformation to crisp value linear programming problems (LPP) in the objective function (OF). Then the simplex method (SM) is used to determine the best solution (BS). To demonstrate our findings, we provide a numerical example (NE).

Exploring the Optimal Allocation Decision-Making of Expenditure Budget in Hospitals Under Multi-Objective Constraints: Evidence from Urban Public Hospitals, China

Hospitals in many countries face the need for balancing different categories of expenditures to achieve multiple goals within a limited budget. This study established a two-stage fuzzy linear programming (FLP) estimation model to explore the optimal allocation decision-making of expenditure budget under the multi-objective constraints. Taking all urban public hospitals in Henan province of China as a sample, the optimal allocation decision-making of total expenditure budget was tested with the human resources expenditures (HE) as the dependent variable. And the outcome was compared with the actual expenditure data of these hospitals between 2010 and 2016. The study found that when the HE achieves the maximum and minimum feasible scale, the expenditure scales of the budget allocation categories including pharmaceutical expenditures, medical supplies expenditures, and other expenditures were all within a reasonable range. Among them, the observed promoting space for HE was 3.78 billion yuan. The results show that the FLP method can help urban public hospitals to make better total expenditure budget allocation decisions, which can maintain their reasonable expenditure structure under the hospitals’ development goals and the government’s regulatory requirements.

Truck dispatching in surface mines -Application of fuzzy linear programming

Material handling in surface mines accounts for around 50% of the operational cost. Optimum truck dispatching plays a critical role in the reduction of this operational cost in truck and shovel surface mines. Researchers in this field have presented several mathematical models to solve the truck dispatching problem optimally. However, a critical survey of the literature has shown that three significant drawbacks exist in the available truck dispatching models. The published models underestimate the importance of the interaction between truck fleet, shovel fleet, and the processing plants. They also disregard goals set by strategic-level plans. Moreover, none of the available models account for the uncertainty associated with the input parameters. In this paper we present a new truck dispatching model that covers all of these drawbacks, using a fuzzy linear programming method. The performance of the developed model was evaluated through implementatin in an active surface mining operation. The results show a significant improvement in production and fleet utilization.

Wetland Restoration Planning Approach Based on Interval Fuzzy Linear Programming under Uncertainty.

When planning wetland restoration projects, the planting area allocation and the costs of the restoration measures are two major issues faced by decision makers. In this study, a framework based on the interval fuzzy linear programming (IFLP) method is introduced for the first time to plan wetland restoration projects. The proposed framework can not only effectively deal with interval and fuzzy uncertainties that exist in the planning process of wetland restorations but also handle trade-offs between ecological environment benefits and economic cost. This framework was applied to a real-world wetland restoration planning problem in the northeast of China to verify its validity and examine the credibility of the constraints. The optimized results obtained from the framework that we have developed indicate that higher ecological and social benefits can be obtained with optimal restoration costs after using the wetland restoration decision-making framework. The optimal restoration measure allocation schemes obtained by IFLP under different credibility levels can help decision makers generate a range of alternatives, which can also provide decision suggestions to local managers to generate a satisfactory decision-making plan. Furthermore, a comparison was made between the IFLP model and ILP model in this study. The comparison results indicate that the IFLP model provides more information regarding ecological environment and economic trade-offs between the system objective, certainty, and reliability. This framework provides managers with an effective way to plan wetland restoration projects, while transference of the model may help solve similar problems.

Research on Inter-Provincial Transfer of CO2 Emissions from Transportation by Considering Fuzzy Parameter

CO2 reduction from transportation is exerting significant effects on global CO2 reduction. This industry contributes 23.96% of global CO2 emissions. In this research, an ecological network input–output interval fuzzy linear programming (EIFP) method is developed to clarify CO2 reduction responsibilities and depict transfer relationships of transportation. This method integrates input–output analysis (IOA), inexact rough interval fuzzy linear programming (IRFLP) and ecological network analysis (ENA) into a general framework. The proposed method is employed for calculating inter-provincial CO2 transfer under different situations in 30 provinces of China and further supporting the formulation of regional reduction policies. Results demonstrate that transportation energy demand of Beijing is dependent on imports, which indirectly increases CO2 reduction pressure in energy supply areas. Therefore, CO2 reduction responsibility should be traced to source and included in emission reduction plan of energy demand areas. In inter-provincial CO2 transfer relationships of natural gas, positive relationships account for a higher proportion; therefore, it is feasible to consider raising the proportion of natural gas in the future development direction of transportation. The achievements of this paper can provide scientific references for decision makers to formulate CO2 reduction policies in transportation.

A Novel Fuzzy SIMUS Multicriteria Decision-Making Method. An Application in Railway Passenger Transport Planning

To increase the level of adequacy in multi-criteria decision-making in the case of uncertainty, it is essential to reduce the subjectivism and to increase the reality of obtained results. The study aims to propose a novel fuzzy multi-criteria method based on the fuzzy linear programming method and sequential interactive model for urban systems method (SIMUS), named fuzzy SIMUS. This paper is something completely different because it links the power of fuzzy with the advantage of the SIMUS method. Indeed, not using weights, it works with optimal values. Here, this procedure is presented for the first time. The methodology consists of three stages. The first stage includes forming the parameters of a multi-criteria model in the case of uncertainty. The initial matrix has three values: lower, medium, and upper. In the second stage, the fuzzy SIMUS model for each objective is formed based on fuzzy linear programming method. The third stage deals with the ranking of the alternatives. The methodology was experimented for planning railway intercity passenger transport in Bulgarian’s railway network. Nine alternative transport plans and eight criteria were studied. It was found that the objectives which influence ranking the most are the frequency of train stops (15%), direct operational costs (15%), train’s capacity (14.7%), and reliability (14.3%). A transport plan for railway passenger transport is proposed. A verification of the results was performed. It was found that the stability of the choice presented a suitable alternative.

Methodology of ensuring ecological safety of radio-electronic and instrument-making production in territorial natural production complexes

The production of electronics and instrumentation is currently based on technologies that can be harmful to the environment. The strategy for the modernization and development of electronic and instrument-making industries in accordance with the requirements of modern environmental legislation includes the development of technological standards based on the best available techniques. The work analyzes the status and development prospects of radio electronics and instrument-making enterprises according to environmental indicators and criteria of the best available techniques. A method for assessing the life cycle of an electronic device is considered as a tool for obtaining data on the environmental impact of its production. In order to develop environmental standards for permissible impacts of electronic and instrument-making industries, a fuzzy linear programming method with probabilistic restrictions has been proposed. On the basis of this method, a model has been formed for a water management system within territorial natural-production complexes, taking the impact on water objects of all water-using enterprises into account. The proposed decision-making algorithm for load normalization allows the company to develop a strategy for planning the volumes of water consumption and water disposal, while considering regional conditions and the influence of other entities of the territorial natural production complex.

A grey production planning model on a ready-mixed concrete plant

ABSTRACTThe parameters of decision models are not clearly known and they are not exact for most real-life problems. Therefore, this article presents a model of linear programming with grey interval numbers for right-hand-side parameters under an uncertainty case. The purpose of this article is to compare the results of a fuzzy linear programming model and those of four proposed grey linear programming models and to find effective solutions for alternative production planning. The results produced a more effective plan to use as an industrial solution according to a fuzzy linear programming model. The objective function value is about 3% more effective than with the fuzzy linear programming method, and the customer satisfaction of total demand is about 25% more effective for the number of served customers.

Multi-Objective Fuzzy Linear Programming for Land Allocation under Different Crops in Bhagwanpur Distributary

A study was undertaken in Bhagwanpur distributary of Vaishali Branch Canal in Gandak Canal Command Area, Bihar to optimally allocate land area under different crops (rice and maize in kharif, wheat, lentil, potato in rabi and green gram in summer) in such a manner that maximizes net return, maximizes crop production and minimizes labour requirement employing simplex linear programming method and Multi-Objective Fuzzy Linear Programming (MOFLP) method. Maximum net return, maximum agricultural production, and minimum labour required under defined constraints (including 10% affinity level of farmers to rice and wheat crops) as obtained employing Simplex method were ` 3.7 × 108, 5.06 × 107 Kg and 66,092 man-days, respectively, whereas Multi-Objective Fuzzy Linear Programming (MOFLP) method yielded compromised solution with net return, crop production and labour required as ` 2.4 × 108, 3.3 × 107Kg and 1,79,313 man-days, respectively. As the affinity level of farmers to rice and wheat crops increased from 10% to 40%, maximum net return and maximum production as obtained from simplex linear programming method and MOFLP followed a decreasing trend and minimum labour required followed an increasing trend. MOFLP may be considered as one of the best capable ways of providing a compromised solution, which can fulfill all the objectives at a time.

Process variation-aware gate sizing with fuzzy geometric programming

Limitations of manufacturing process in nanometer dimensions have led to large discrepancies between the circuit design and the manufactured chip known as process variation. In this paper, a new gate sizing method based on fuzzy geometric optimization approach is introduced for power minimization of digital circuits subjected to timing constraints under process variations. In the proposed geometric optimization approach, an accurate gate delay model is applied in which the delay variation is represented by fuzzy numbers; therefore, the subsequent optimization problem is a fuzzy geometric programing problem. In order to efficiently solve the fuzzy geometric programing problem, firstly, the problem is converted into a fuzzy linear programming problem and then, using the expected value and Mellin transform, it is converted into a non-fuzzy problem which is solved by traditional solution techniques. Experimental results show that, the proposed technique achieve more power reduction compared to a fuzzy linear programming method.

An interval type-2 fuzzy stochastic approach for regional-scale electric power system under parameter uncertainty

ABSTRACTIn this study, an interval type-2 fuzzy stochastic linear programming method (IT2FSLP) is developed to support regional-scale electric power system (REM) planning. The IT2FSLP-REM model is based on an integration of interval type-2 fuzzy sets boundary programming and stochastic linear programming techniques enable it to have robust abilities to the deal with uncertainties expressed as type-2 fuzzy intervals and probabilistic distributions within a general optimization framework. Moreover, it can reflect dynamic decisions for energy supply and energy conversion processes, as well as provide capacity expansion options with multiple periods. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability. Based on a two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs among economic cost, environmental requirements, and energy-supply security. Thus, the lower and upper solutions of IT2FSLP-REM would then help energy authorities adjust or justify allocation patterns of regional energy resources and services.

A robust inexact trapezoidal T2 fuzzy approach coupling possibility degrees for solid waste disposal allocation with integrated optimal greenhouse gas control under uncertainty

In this study, a new municipal solid waste (MSW) management approach was developed by grafting the robust inexact trapezoidal T2 fuzzy method to a conventional fuzzy linear programming (FLP) framework. Waste managers or authorities could utilize the degree of possibility to compare two different uncertain information sources, which are rendered as fuzzy sets (FSs). This approach improves upon previous interval linear programming (ILP), FLP and T2 FLP methods through further in-depth analyses and solves the ambiguity issues in the field of MSW management. A clear optimal allocation plan for MSW would lead to a lower cost budget under limited processing capacities. The applicability of the proposed MSW system with integrated waste flow allocation planning and facility expansion regarding greenhouse gas (GHG) emissions demonstrate the validity of this innovative approach. The results from the robust inexact trapezoidal T2 fuzzy approach coupling possibility degrees (RITT2FLP-CPDs) model indicate that, compared with other methods, more uncertain information can be incorporated into this RITT2FLP-CPDs model, and the range of cost for the objective function is decreased based on the extension principle of the inexact trapezoidal T2 fuzzy approach. Thus, the processing efficiency of the solid waste capacity would be improved. Therefore, the proposed RITT2FLP-CPDs model is a promising approach for improving the fitness of engineering problems in the scope of MSW management.

Research on IFLP optimization model for carbon emission reduction

This study proposed an optimization model combined with Binding Interval Linear Programming (ILP) and Fuzzy linear programming (FLP) Methods and further analyzed from the views of economic output, energy consumption, carbon dioxide emission and emission cost. The optimization model results demonstrated that the heavy energy consumption industries will significantly reduce, and the target of the carbon dioxide emissions per unit of GDP reduction decrease by 40%-45% from 2005 to 2020. In addition, the economic development model will trend to optimize the allocation of resources and green economy. However, a single low-carbon economic policy will always have shortcomings and low efficiency in emission reduction. Hence, the government should combine all emission reduction policies together and establish a lowcarbon economy system that practice production activities need.