Fuzzy Linear Programming Model Research Articles

A fuzzy multi-criteria decision-making for optimizing supply chain aggregate production planning based on cost reduction and risk mitigation

In an increasingly complex and uncertain business environment, decision makers require robust strategies for supply chain aggregate production planning that account for the interdependencies and coordination across multiple echelons of the supply chain network. Traditional approaches often inadequately address the uncertainties and risks inherent in supply chain operations, leading to suboptimal performance and increased costs. This study introduces a business model incorporating open innovation dynamics to achieve cost-effectiveness and resilient supply chain performance in the face of uncertainties. A Multi-Objective Fuzzy Linear Programming model was proposed by integrating the Chance-Constraint Programming and Zimmermann’s approach designed to assist decision makers in optimizing the production plan, material flows and resource allocation across the entire supply chain network. The model focuses on both cost and risk minimization based on unsymmetrical triangular fuzzy numbers. Specifically, it targets the downside risk of uncertainty, aiming to reduce the likelihood of negative outcomes or financial losses due to fluctuations, unpredictability, and unforeseen circumstances, which can drive-up supply chain operation costs. The efficacy of the model is demonstrated through a case study. It highlights various imprecise factors such as costs, customer demands, and machine operating hours. The findings underscore the model's capability to provide decision makers with a comprehensive supply chain aggregate production plan that not only optimizes the supply chain network and enhances operational efficiency and reliability but also significantly reduces costs and mitigates unsymmetrical skewness of risks associated with operational uncertainties.

Sensitivity Analysis for Fuzzy Linear Programming Problem by Mehar Method

Numerous manufacturing companies face significant financial setbacks due to excessive raw material costs, low profits, and no taxes on imported goods. The production companies also suffer from uncertainty concerning expenses, production levels, sales figures, and the accessibility of raw materials. Therefore, in our study, we developed an innovative method to design a fuzzy linear programming model customised for the Doura Refinery of the Middle Refineries Company. We emphasised five essential products: white oil, naphtha, light puffs, heavy Jet, and liquid gas. The main goal of our approach was to achieve optimal decision-making by identifying the most favourable production quantities and evaluating the corresponding net income derived from product sales. Following the Mehar method, we employed a methodology that converts the fuzzy linear programming problem into a standard linear programming problem. Subsequently, we conducted a sensitivity analysis, focusing only on the impact of fuzzy cost changes, and successfully derived optimal solutions for this case. Therefore, we aim to resolve the challenges of fuzzy linear programming and explore how

Multi‐objective interval type‐2 fuzzy linear programming problem with vagueness in coefficient

AbstractOne of the most widely used fuzzy linear programming models is the multi‐objective interval type‐2 fuzzy linear programming (IT2FLP) model, which is of particular importance due to the simultaneous integration of multiple criteria and objectives in a single problem, the fuzzy nature of this type of problems, and thus, its closer similarity to real‐world problems. So far, many studies have been done for the IT2FLP problem with uncertainties of the vagueness type. However, not enough studies have been done regarding the multi‐objective interval type‐2 fuzzy linear programming (MOIT2FLP) problem with uncertainties of the vagueness type. As an innovation, this study investigates the MOIT2FLP problem with vagueness‐type uncertainties, which are represented by membership functions (MFs) in the problem. Depending on the localisation of vagueness in the problem, that is, vagueness in the objective function vector, vagueness in the technological coefficients, vagueness in the resources vector, and any possible combination of them, various problems may arise. Furthermore, to solve problems with MOIT2FLP, first, using the weighted sum method as an efficient and effective method, each of the MOIT2FLP problems is converted into a single‐objective problem. In this research, these types of problems are introduced, their MFs are stated, and different solution methods are suggested. For each of the proposed methods, the authors have provided an example and presented the results in the corresponding tables.

Forest Carbon Sequestration Based on Time Series Analysis and Fuzzy Linear Programming Model

Forest Carbon Sequestration Based on Time Series Analysis and Fuzzy Linear Programming Model

Analyzing the Importance of International Law in Current International Relations Based on Linear Programming Models

Abstract International law is mainly the law between countries, which is the code of conduct for countries to conduct international interactions, and this paper researches the role of international law in international relations interactions. First of all, this paper combines the fuzzy set on the basis of the classical linear regression model algorithm, establishes the fuzzy linear programming model, and explores the fuzzy correlation analysis. Then, taking EU law as an example, the role of EU law in EU relations is analyzed through the theory of EU law, EU and the role of EU law in the EU embodied. Finally, based on the role of EU law, the importance of international law in international relations is studied through a fuzzy linear programming model, and the role of strengthening international law is considered. The results show that the countries consider the legitimacy of EU law to be above 0.9, and the countries’ participation in EU law also ranges from 0.9 to 1.0, and the countries’ self-identification increases by about 0.1 to 0.2 after the enactment of EU law. The correlation coefficients of international law on the construction of the identities of the 10 countries are all greater than 0.75, and the interests of the countries have increased by about 2.3, and international law promotes the order of international relations.

How to promote sustainable land use in Hangzhou Bay, China? A decision framework based on fuzzy multiobjective optimization and spatial simulation

Rapid economic development has a significant impact on both regional land use/cover change (LUCC) and ecosystem services. In this paper, we present a decision framework based on fuzzy multiobjective optimization and spatial simulation to achieve sustainable land use development. Specifically, we first investigate the evolution of LUCC in Hangzhou Bay, China, and assess its ecosystem service value (ESV) using the equivalence coefficient table method based on land use data in 2000, 2010 and 2020. Then, we construct a multiobjective fuzzy linear programming model to optimize the land use decision that can balance the ESV and economic benefits of the land. Finally, a future land use simulation model is established to perform spatial simulation to find the most likely land use scenario for Hangzhou Bay in 2030 using the optimization results as input. Our results show that the LUCC in Hangzhou Bay became more frequent between 2000 and 2020, especially the area of built-up land, which increased by 179.74%. The ESV in Hangzhou Bay shows an accelerated decreasing trend, with a total decrease of 1.22 × 108 yuan. We observe spatial heterogeneity in both LUCC and ESV in Hangzhou Bay, with LUCC occurring more frequently in the coastal area, while high ESV areas are concentrated in the eastern coastal area and southern forest. The land use decisions obtained through land use structure optimization and spatial simulation can significantly slow down the decreasing trend of ESV (from −14.5% to −0.17%), effectively reduce the fragmentation of the landscape, prevent the disorder of LUCC, and help the government formulate sustainable land use policies.

Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models

Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models

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.

Multiobjective Intuitionistic Fuzzy Optimization Approach in Optimal Irrigation Planning and Operation of Reservoir

A Multiobjective Intuitionistic Fuzzy Linear Programming model is developed to get an optimal cropping pattern in the command area of the Ukai-Kakrapar Irrigation project in Gujarat, India. Four conflicting objectives, namely, maximization of net irrigation benefits (NIB), maximization of employment (EG), minimization of cultivation cost (CC), and maximization of revenue generation on account of industrial and municipal supplies (MI) were optimized for their crisp linear programming (LP) solutions. Intuitionistic Fuzzy Optimization Multi-objective fuzzy linear programming (IFO MOFLP), IFO MOFLP with hesitation index, and two-phase IFO MOFLP models were developed from their LP solutions. The TPIFO MOFLP model has been found to perform better than other variant of IFO MOFLP models and the MOFLP model (Average operator Case-I) developed by Mirajkar and Patel in J Water Resour Plan Manag 142(11):1–16, 2016 for the same command area with reference to the uncertainty parameters like degree of acceptance (α), rejection (β), and hesitation index (π) for 75% dependable inflow condition. The recommended TPIFO MOFLP model also gives higher irrigation intensity (112.19%) than Average Operator Case-I (104.60%) for the whole command area. The implementation of TPIFO MOFLP model in the command area is likely to give the values of NIB, EG, CC, and MI as Rs 10,836.19 million, 34,980.4 thousand workdays, Rs 5,672.23 million, and Rs 2,314.03 million, respectively, with α = 0.68, β = 0.19, and π = 0.13. The suggested model with new parameters like α, β, and, π, would assist the decision makers to apply the same on real world problems with greater certainty.

Multi-objective optimization model for uncertain crop production under neutrosophic fuzzy environment: A case study

<abstract> <p>In real world uncertainty exist in almost every problem. Decision-makers are often unable to describe the situation accurately or predict the outcome of potential solutions due to uncertainty. To resolve these complicated situations, which include uncertainty, we use expert descriptive knowledge which can be expressed as fuzzy data. Pakistan, a country with a key geographic and strategic position in South Asia, relies heavily on irrigation for its economy, which involves careful consideration of the limits. A variety of factors can affect yield, including the weather and water availability. Crop productivity from reservoirs and other sources is affected by climate change. The project aims to optimize Kharif and Rabbi crop output in canal-irrigated areas. The optimization model is designed to maximize net profit and crop output during cropping seasons. Canal-connected farmed areas are variables in the crop planning model. Seasonal crop area, crop cultivated area, crop water requirement, canal capacity, reservoir evaporation, minimum and maximum storage, and overflow limits affect the two goals. The uncertainties associated with the entire production planning are incorporated by considering suitable membership functions and solved using the Multi-Objective Neutrosophic Fuzzy Linear Programming Model (MONFLP). For the validity and effectiveness of the technique, the model is tested for the wheat and rice production in Pakistan. The study puts forth the advantages of neutrosophic fuzzy algorithm which has been proposed, and the analyses derived can be stated to deal with yield uncertainty in the neutrosophic environments more effectively by considering the parameters which are prone to abrupt changes characterized by unpredictability.</p> </abstract>

Fuzzy linear programming approach for the capacitated vehicle routing problem

In recent years, with both technological advances and the effect of globalization, businesses have entered a very intense competition. In this harsh competitive environment, customer satisfaction has become a critical concept. Firms implement costs reducing strategies in order to increase profitability levels and gain competitive advantage in the market. Researches show that a significant ratio of the cost of a product is derived from the transport activities. Therefore, it has become important for companies to find the optimal route during transportation. In this study, it is addressed as capacity constrained vehicle routing. First, a deterministic model is proposed for the addressed problem. Second, in accordance with real life conditions, a fuzzy linear programming model has been developed in case of the vehicle capacities are uncertain. The Verdegay approach has been adopted for the fuzzy linear programming model. The proposed model was implemented to a real life problem in the food sector. The results are compared with the results of a deterministic model and they show that the fuzzy linear programming model proposed in this study gives cost effective results in uncertain environment.

Fuzzy Regression Analysis with a proposed model

Regression analysis refers to methods by which estimates are made for the model parameters from the knowledge of the values of a given input-output data set. The aim of this research this research is to find a suitable model and determine the ‘best’ values of the parameters of the model from the given data. In the statistical regression analysis, deviations between the observed output values and corresponding values predicted by the model are attributed to random errors. It is often assumed that the distribution of these random errors is Gaussian. On the other hand, in fuzzy regression analysis the deviations (errors) are attributed to the imprecision or the vagueness of the system structure or data. The research proposed a new fuzzy linear programming model. The new proposed model is compared with the models used in the literature which are Tanaka, Hojati and Tansu regression models. The results are presented and comparison has been done for each model. Eleven different applications have been mentioned. Then the comparison of results of all the application regarding each similarity measure of goodness of fit is stated in the paper.

Optimal reservoir operation policy determination for uncertainty conditions

In recent years, optimising reservoir operations has emerged as a hot topic in the field of water resources management. Heuristic approaches to reservoir operation that incorporate rule curves and, to some extent, operator discretion have been the norm in the past. With so many stakeholders involved in water management, it can be difficult to strike a happy medium between everyone's needs and wants. The dissertation proposes a method for transforming traditional reservoir operation into optimal strategies, allowing users to take advantage of the rapid development of computational techniques. This research creates and applies a Multi Objective Fuzzy Linear Programming (MOFLP) model to the monthly operating policies of the stage-I Jayakwadi reservoir located on the Godavari, the largest river in the Indian state of Maharashtra. In order to formulate the problem, we use two objective functions—maximizing irrigation releases and maximising power production releases. The constraints of the study are considered, including turbine release, irrigation demand, reservoir storage capacity, and continuity of reservoir storage. Utilizing linear membership functions, the objective functions are fuzzily defined. All other model parameters except for the goals are assumed to be hard and fast rules. Maximum Happiness Operating Policy (MOFLP) was used to determine the best course of action.

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.

Multi-objective Intuitionistic Fuzzy Linear Programming model for optimization of industrial closed-loop supply chain network

The urge to remanufacture and address environmental concerns in various industrial processes has drawn the attention of academics as well as practitioners towards Closed-loop Supply Chain Networks (CLSC). Although everchanging and complex external factors including social and economic ones, adversely impact the sustainable development of closed-loop supply chain networks. The basic aim of the research is to optimize the functioning of CLSC networks. For the above-said, two objective functions are made. The first objective is to minimize the cost of production and assembly expenses of the forward and reverse logistics. Secondly, an endeavour has been made to reduce the fixed costs associated with plants and retailers. For the sake of achieving two objective functions, two methods are employed: triangular fuzzy numbers and triangular intuitionistic fuzzy numbers. Among the two methods, triangular intuitionistic fuzzy numbers achieved the said objectives with greater optimization substantiated by statistics. This method can deal with uncertain external factors without undermining the optimization of the CLSC networks.

A novel fuzzy network DEA model to evaluate efficiency of Iran’s electricity distribution network with sustainability considerations

Iran’s electricity distribution network (EDN) includes three stages of generation, transmission, and distribution, with different types of input and output criteria and complex communications with both parallel and serial structures. This study formulates a Fuzzy Network DEA (FNDEA) model for assessing the efficiency of Iran’s EDNs components with sustainability considerations and uncertain data. In order to utilize all input and output criteria, this study also proposes a fuzzy linear programming model to determine the optimal lower bound for all input and output weights. Furthermore, appropriate policies are suggested based on the strengths and weaknesses of each EDN to improve its efficiency. Finally, a sensitivity analysis has been implemented to validate the proposed model. The results of the present study reveal that the transmission stage performed better than the generation and distribution stages. It also shows that the distribution stage has the greatest impact on the overall performance of Iran's EDN.

A Fuzzy Prescriptive Analytics Approach to Power Generation Capacity Planning

This study examines the long-term energy capacity investment problem of a power generation company (GenCo), considering the drought threat posed by climate change in hydropower resources in Turkey. The mid-term planning decisions such as maintenance and refurbishment scheduling of power plants are also considered in the studied investment planning problem. In the modeled electricity market, it is assumed that GenCos conduct business in uncertain market conditions with both bilateral contracts (BIC) and day-ahead market (DAM) transactions. The problem is modeled as a fuzzy mixed-integer linear programming model with a fuzzy objective and fuzzy constraints to handle the imprecisions regarding both the electricity market (e.g., prices) and environmental factors (e.g., hydroelectric output due to drought). Bellman and Zadeh’s max-min criteria are used to transform the fuzzy capacity investment model into a model with a crisp objective and constraints. The applicability of methodology is illustrated by a case study on the Turkish electric market in which GenCo tries to find the optimal power generation investment portfolio that contains five various generation technologies alternatives, namely, hydropower, wind, conventional and advanced combined-cycle natural gas, and steam (lignite) turbines. The results show that wind turbines with low marginal costs and steam turbines with high energy conversion efficiency are preferable, compared with hydroelectric power plant investments when the fuzziness in hydroelectric output exists (i.e., the expectation of increasing drought conditions as a result of climate change). Furthermore, the results indicate that the gas turbine investments were found to be the least preferable due to high gas prices in all scenarios.

Intuitionistic fuzzy optimization approach in optimal irrigation planning of Ukai-Kakrapar irrigation project, India

ABSTRACT This article addresses the formulation of the Intuitionistic Multiobjective fuzzy linear programming (IFO MOFLP) model for optimal allocation of crops in the command area of the Ukai-Kakrapar Irrigation Project, India. Initially, the crisp linear programming (LP) model is applied to acquire the optimal results of three conflicting objectives, namely, maximization of net irrigation benefits (NIBs), minimization of cost of cultivation (CC) and maximization of revenue generation from industrial and municipal supplies (MI). Subsequently, the LP solutions were used to develop the IFO MOFLP, IFO MOFLP with a hesitation index and two-phase IFO MOFLP (TPIFO MOFLP) models for the complete command area. The performance of the aforesaid models is assessed in terms of irrigation intensity, degree of acceptance (α), rejection (β) and hesitation index (π) for inflows at 75% probability of exceedance. The irrigation intensity from the proposed TPIFO MOFLP model has been found to be 101.28%, while NIB, CC and MI from the proposed model are 10,575.38, 5438.42 and 2638.20 million Rs, respectively, with α = 0.64, β = 0.18 and π = 0.18, respectively. The proposed TPIFO MOFLP model has been compared better with MOFLP as the former gives additional uncertainty controlling parameters like α, β and π, which would help the planner to take better decisions for real-world problems.

Dynamic programming approach for fuzzy linear programming problems FLPs and its application to optimal resource allocation problems in education system

This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the established dynamic programming model for solving linear programming problems in a crisp environment. The mentioned approach is upgraded to address the problem in an uncertain environment. Dynamic programming model can either be passing forward or backward. In the proposed approach backward dynamic programming approach is adopted to address the problem. It is then followed by implementing the proposed method on the education system of Pakistan. The education system of Pakistan comprises of the Primary, Middle, Secondary, and Tertiary education stages. The problem is to maximize the efficiency of the education system while achieving the targets with minimum usage of the constrained resources. Likewise the model tries to maximize the enrollment in the Primary, Middle, Secondary and Tertiary educational categories, subject to the total available resources in a fuzzy uncertain environment. The solution proposes that the enrollment can be increased by an amount 9997130, by increasing the enrollment in the Middle and Tertiary educational categories. Thus the proposed method contributes to increase the objective function value by 30%. Moreover, the proposed solutions violate none of the constraints. In other words, the problem of resources allocation in education system is efficiently managed to increase efficiency while remaining in the available constrained resources. The motivation behind using the dynamic programming methodology is that it always possesses a numerical solution, unlike the other approaches having no solution at certain times. The proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.

Application of fuzzy random-based multi-objective linear fractional programming to inventory management problem

This research article aims to study a multi-objective linear fractional programming (FMOLFP) problem having fuzzy random coefficients as well as fuzzy pseudorandom decision variables. Initially, the FMOLFP model is converted to a single objective fuzzy linear programming (FLP) model. Secondly, we show that a fuzzy random optimal solution of an FLP problem is resolved into a class of random optimal solution of relative pseudorandom linear programming (LP) model. As a result, some of theorems show that a fuzzy random optimal solution of a fuzzy pseudorandom LP problem is combined with a series of random optimal solutions of relative pseudorandom LP problems. As an application, the developed approach is implemented to an inventory management problem by taking the parameters as trapezoidal fuzzy numbers, ultimately resulting in a new initiative for modelling real-world problems for optimization. In the last, some numerical examples are introduced to clarify the obtained results and their applicability.