Fuzzy Multi-objective Linear Programming Research Articles

Ride-Hailing Matching with Uncertain Travel Time: A Novel Interval-Valued Fuzzy Multi-Objective Linear Programming Approach

This study introduces an innovative approach to tackle multi-objective linear programming (MOLP) problems amidst uncertainty, employing interval-valued fuzzy numbers. The method is tailored to resolve ride-hailing matching challenges encompassing uncertain travel times. Findings reveal that managing uncertainty parameters within interval-valued fuzzy MOLP is achieved through strategic reformulations, focusing on constraint coefficients, resulting in streamlined linear programming formulations conducive to solution simplicity. The efficacy of the proposed model in efficiently handling ride-hailing matching quandaries is demonstrated. Moreover, this study delves into the prospective applications of the developed method, including its potential for generalization to address non-linear programming (NLP) issues pertinent to the ride-hailing domain. This research advances decision-making processes under uncertainty and paves the way for broader applications beyond ride-hailing.

Synergizing economic growth and carbon emission reduction in China: A path to coupling the MFLP and PLUS models for optimizing the territorial spatial functional pattern

Carbon emissions caused by economic growth are the main cause of global warming, but controlling economic growth to reduce carbon emissions does not meet China's conditions. Therefore, how to synergize economic growth and carbon emission reduction is not only a sustainable development issue for China, but also significant for mitigating global warming. The territorial spatial functional pattern (TSFP) is the spatial carrier for coordinating economic development and carbon emissions, but how to establish the TSFP of synergizing economic growth and carbon emission reduction remains unresolved. We propose a decision framework for optimizing TSFP coupled with the multi-objective fuzzy linear programming and the patch-generating land use simulation model, to provide a new path to synergize economic growth and carbon emission reduction in China. To confirm the reliability, we took Qionglai City as the demonstration. The results found a significant spatiotemporal coupling between TSFP and the synergistic states between economic growth and carbon emission reduction (q ≥ 0.8220), which resolves the theoretical uncertainty about synergizing economic growth and carbon emission reduction through the path of TSFP optimization. The urban space of Qionglai City in 2025 and 2030 obtained by the decision framework was 6497.57 hm2 and 6628.72 hm2 respectively, distributed in the central and eastern regions; the rural space was 60,132.92 hm2 and 56,084.97 hm2, concentrated in the east, with a few located in the west; and the ecological space was 71,072.52 hm2 and 74,998.31 hm2, mainly located in the western and southeastern areas. Compared with the TSFP in 2020, the carbon emission intensity of the TSFP obtained by the decision framework was reduced by 0.7 and 4.7 tons/million yuan, respectively, and realized the synergy between economic growth and carbon emission reduction (decoupling index was 0.25 and 0.21). Further confirming that TSFP optimization is an effective way to synergize economic growth and carbon emission reduction, which can provide policy implications for coordinating economic growth and carbon emissions for China and even similar developing countries.

A novel approach for multi-objective linear programming model under spherical fuzzy environment and its application

Every decision-making process particularly those involving real-life issues is disproportionately plagued by uncertainty. It is also unavoidable and obvious. Since its conception are several ways for representing uncertainty have been proposed by numerous academics to cope with uncertainty. Fuzzy sets and hierarchical such as picture fuzzy sets stand out among them as excellent representation techniques for modeling uncertainty. However, there are several significant drawbacks to the current uncertainty modeling techniques. Due to its vast versatility and benefits we here embrace the idea of the spherical fuzzy set, an extension of the picture fuzzy set. On the other hand amid uncertainty in real life the multi-objective plays a critical role. In this research paper determining a Multi-Objective Linear Programming Problem of Spherical fuzzy sets serves to stimulate nous. The score function corresponding to the degree positive, negative and neutral is the foundation upon which the suggested approach is developed. Additionally we apply the suggested strategy to the solution of the multi-objective linear programming problem to demonstrate its superiority through certain numerical examples. Maximization or Minimizing of the cost is the primary goal of the multi-objective linear programming problem. Using an explicitly defined score function the suggested solution transformed the Spherical Fuzzy Multi-Objective Linear Programming Problem into a Crisp Multi-Objective Linear Programming Problem (CMOLPP). We establish some theorems to show that the efficient solution of CMOLPP is likewise an efficient solution of SFMOLPP. The CMOLPP is then further simplified into a single-objective Linear Programming Problem (LPP) thus we revamp the modified Zimmermann’s approach in the environment of a nonlinear membership function with the aid of the suggested technique. It is possible to simply solve this single-objective LPP using any software or standard LPP algorithm. The suggested approach achieves the fuzzy optimum result without altering the nature of the issue. An application of the suggested approach has been used to illustrate it and its results have been distinguished from those of other preexisting methods found in the literature. To determine the importance of the suggested technique which adjudicate thorough theorem and result analysis is conducted.

Fuzzy Mathematical Approach for Solving Multi-Objective Fuzzy Linear Fractional Programming Problem with Trapezoidal Fuzzy Numbers

Fuzzy Mathematical Approach for Solving Multi-Objective Fuzzy Linear Fractional Programming Problem with Trapezoidal Fuzzy Numbers

A New Method to Solve Fully Intuitionistic Fuzzy Multi-objective Linear Programming Problem Through Conflict and Non-conflict

A New Method to Solve Fully Intuitionistic Fuzzy Multi-objective Linear Programming Problem Through Conflict and Non-conflict

A fuzzy multiobjective linear programming approach for green multiechelon distribution network design

PurposeDistribution network design involves a set of strategic decisions in supply chains because of their long-term impacts on the total logistics cost and environment. To incorporate a trade-off between financial and environmental aspects of these decisions, this paper aims to determine an optimal location, among candidate locations, of a new logistics center, its capacity, as well as optimal network flows for an existing distribution network, while concurrently minimizing the total logistics cost and gas emission. In addition, uncertainty in transportation and warehousing costs are considered.Design/methodology/approachThe problem is formulated as a fuzzy multiobjective mathematical model. The effectiveness of this model is demonstrated using an industrial case study. The problem instance is a four-echelon distribution network with 22 products and a planning horizon of 20 periods. The model is solved by using the min–max and augmented ε-constraint methods with CPLEX as the solver. In addition to illustrating model’s applicability, the effect of choosing a new warehouse in the model is investigated through a scenario analysis.FindingsFor the applicability of the model, the results indicate that the augmented ε-constraint approach provides a set of Pareto solutions, which represents the ideal trade-off between the total logistics cost and gas emission. Through a case study problem instance, the augmented ε-constraint approach is recommended for similar network design problems. From a scenario analysis, when the operational cost of the new warehouse is within a specific fraction of the warehousing cost of third-party warehouses, the solution with the new warehouse outperforms that without the new warehouse with respective to financial and environmental objectives.Originality/valueThe proposed model is an effective decision support tool for management, who would like to assess the impact of network planning decisions on the performance of their supply chains with respect to both financial and environmental aspects under uncertainty.

Optimal maintenance planning for offshore wind farms under an uncertain environment

The operation and maintenance costs of wind power generation systems can be reduced through the implementation of maintenance policies at suitable procurement indenture and maintenance levels. Purchasing components involves uncertainties associated with cost and component reliability due to objectives which frequently lack precision. In order to solve fuzzy multi-objective lot-sizing decisions of spare parts for a long term predictive maintenance planning problem in offshore wind farms, this study develops a novel fuzzy multi-objective linear programming model with piecewise linear membership function and S-curve membership function to simultaneously evaluate maintenance cost and system reliability. This model integrates multi-OWT (offshore wind turbines), multi-component, multi-supplier, and component reliability functions for offshore wind systems under an uncertain environment. The analytical results can help operation and maintenance managers to systematically analyze the cost-effectiveness and system reliability of predictive maintenance planning in practical applications.

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.

Target-Oriented Compromised Sales and Profit Approach for Production and Distribution Planning in a Supply Chain

This paper aims to determine optimal aggregate production and distribution plans in a supply chain system that simultaneously achieve two business targets of total profit and total sales, with uncertain parameters, e.g., production rate during regular time and overtime, inventory holding costs for a manufacturer and distribution centers, and transportation cost. A fuzzy multi-objective linear programming (FMOLP) model is developed to represent the planning problem. The proposed method that minimizes maximum deviation from satisfaction targets of fuzzy profits and sales is more effective, compared with the method that maximizes minimum satisfaction of fuzzy profits and sale, to determine various compromised solutions, which are Pareto-optimal, and to allow a planner to select the most desirable solution based on his/her opinion. This paper has made a significant contribution since it is the first one that proposes the FMOLP approach to determine compromised solutions with two target-based objectives of simultaneously achieving total fuzzy profit targets and total sales target.

Neuro-Fuzzy Programming to Finding Fuzzy Multiple Objective Linear Programming Problems

Neuro-Fuzzy Programming to Finding Fuzzy Multiple Objective Linear Programming Problems

An ε-Constraint Method for Multiobjective Linear Programming in Intuitionistic Fuzzy Environment

Effective decision-making requires well-founded optimization models and algorithms tolerant of real-world uncertainties. In the mid-1980s, intuitionistic fuzzy set theory emerged as another mathematical framework to deal with the uncertainty of subjective judgments and made it possible to represent hesitancy in a decision-making problem. Nowadays, intuitionistic fuzzy multiobjective linear programming (IFMOLP) problems are a topic of extensive research, for which a considerable number of solution approaches are being developed. Among the available solution approaches, ranking function-based approaches stand out for their simplicity to transform these problems into conventional ones. However, these approaches do not always guarantee Pareto optimal solutions. In this study, the concepts of dominance and Pareto optimality are extended to the intuitionistic fuzzy case by using lexicographic criteria for ranking triangular intuitionistic fuzzy numbers (TIFNs). Furthermore, an intuitionistic fuzzy ε-constraint method is proposed to solve IFMOLP problems with TIFNs. The proposed method is illustrated by solving two intuitionistic fuzzy transportation problems addressed in two studies (S. Mahajan and S. K. Gupta’s, “On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions,” Ann Oper Res, vol. 296, no. 1, pp. 211–241, 2021, and Ghosh et al.’s, “Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem,” Complex Intell Syst, vol. 7, no. 2, pp. 1009–1023, 2021). Results show that, in contrast with Mahajan and Gupta’s and Ghosh et al.’s methods, the proposed method guarantees Pareto optimality and also makes it possible to obtain multiple solutions to the problems.

Simulating multiple scenarios of land use/cover change using a coupled model to capture ecological and economic effects

AbstractThe conflict between the demands of ecological protection and economic development is increasingly prominent. Land use change is sensitive to whether economic or ecological profits dominate, and prediction of future land use changes has become an important scientific issue. This article constructs a coupled model that comprises the grey model (GM), the fuzzy multiple objective linear programming model (FMOLP) and the future land use simulation model (FLUS). We used this model to calculate a macro‐scale quantitative forecast using the top‐down GM‐FMOLP model, and calculated micro‐scale spatial simulations of land use/cover change (LUCC) using the bottom‐up FLUS model under three dissimilar future scenarios, with different emphases on ecological and economic benefits. The scenarios were designed to meet different planning requirements in Chongqing: ecological benefits maximization, economic benefits maximization, and combined ecological and economic benefits maximization. The proposed model, FLUS, was applied to a LUCC simulation for Chongqing in 2015, beginning from verified historical land use data from 2010. The results show that the simulation agrees well with the actual land use in 2015. The overall accuracy and kappa coefficient are 85.92% and 0.76, respectively, which indicates the model performs well. The three land use types with the highest producer and user accuracies are forest, cropland and water areas. The GM‐FMOLP model was used to forecast future LUCC quantity demand, and the FLUS model was then used to calculate spatial predictions for the three scenarios for 2040. The prediction results for the six land use types were significantly different under the three different scenarios. The total areas of forest, urban land and water increased by different degrees under the three scenarios, and the unused land area dwindled. Cropland areas were largely converted into forest, urban land and water areas. The increases in forest and urban land areas generally represents internal gap‐filling between disparate areas and peripheral expansion of areas of the same land use type. The increase in water area results from increased surface runoff in mountainous valleys with severe terrain. Areas of unused land are fully transformed into other land use types. The outcomes from the designed scenarios demonstrate that the proposed models are reliable and effective for future LUCC simulation, and highlight key areas where land use changes differently according to the scenario. In summary, in the predictions for the scenario that combined ecological and economic benefits maximization, each land use type tried to maximize ecological and economic benefits under the constraints, taking into account ecological safety and economic growth, which is in line with the coordination, comprehensiveness and binding requirements in Chongqing's development plan. Therefore, this scenario becomes the optimal scenario for land use optimization in Chongqing in the future. This study provides an example of the application of simulation and forecast models in land use management, remediation and urban planning, and addresses the growing requirement for low‐cost and effective tools for prediction of dynamic land use succession patterns.

Solving Three Objectives Single-Machine Scheduling Problem Using Fuzzy Multi-Objective Linear Programming

In this paper, three criteria scheduling problem of n jobs on a single machine is considered. Each of these n jobs is to be processed without interruption and becomes available for processing at time zero. The problem is to minimize three objectives simultaneously, which are the completion time, maximum tardiness, and maximum earliness. Here, we develop a fuzzy multi-objective linear programming (FMOLP) model for solving multi-objective scheduling problem in a fuzzy environment by using piecewise linear membership function (PLMF). A numerical example demonstrates the feasibility of applying the proposed model to scheduling problem, and yields a compromised solution to help the decision maker’s overall levels of satisfaction. The algorithm is tested to show the ability of applying this model to three criteria.

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.

A fuzzy based solution to multiple objective LPP

<abstract><p>This study presents a Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) method to solve the Linear Programming Problem (LPP). Initially Multiple Objective Linear Programming Problem (MOLPP) is solved using Chandra Sen's approach along with various types of mean approaches. Furthermore, FMOLPP is solved using Chandra Sen's approach and various categories of fuzzy mean techniques. The simplex form is used to solve the LPP, where the three-tuple symmetric triangular fuzzy number with the constraints of the fuzzy objective function is considered. We have presented a comparative study of optimum values of MOLPP with optimum values of FMOLPP, to show the significance of our proposed method.</p></abstract>

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.

Solving Tea Blending Problems Using Interactive Fuzzy Multi-Objective Linear Programming

Blending is a classical and well-known optimization problem that has been applied in the food, steel, and composite material industries. However, tea blending is more complicated than general problems due to the variety of products, processes, and sources of raw materials and semi-products. So, in this research, a fuzzy multi-objective model for the tea blending problem was proposed to minimize the total production cost and the deviation of quality target score; it provides a more robust and flexible method than existing models for complex real-world problems. Existing research works of a blending problem consider only raw material cost, but semi-product cost and processing cost are included in the proposed model that matches the actual case. Losses that occur during production are also incorporated. The selection of appropriate raw materials and semi-product sources can be obtained with the preferred levels of cost and quality by the proposed algorithm. The interactive fuzzy multi-objective programming to solve the problem has advantages over existing interactive programming methods. It is easy to manipulate interactively to obtain more efficient solutions than existing methods and both balanced and unbalanced solutions can be selected. The comparison of the results of an existing approach and the interactive fuzzy multi-objective programming algorithm for the tea industry is illustrated.

Optimal cropping pattern based on short-term streamflow forecasts to improve agricultural economic benefits and crop productivity under uncertainty conditions

ABSTRACT Accelerated urbanization has led to diminished land for agricultural activities. Riverine ecosystems play an important role in allocating fertile lands to support agricultural activities. A substantial component of the uncertainty in agricultural productivity comes from seasonal variations linked to inter-annual climate fluctuations. Therefore, understanding the complicated phenomena of streamflow in a riverine environment is important for agricultural and water resources decision making. The present work focuses on forecasting monthly to seasonal streamflow using persistence flow, historical analogues, and artificial neural network approaches. Based on these forecasts, decisions on cropping patterns were made by developing an optimization framework using the constrained linear programming and inexact multiobjective fuzzy linear programming approaches. The proposed fuzzy programming approach was found to be beneficial in producing fair and stable solutions under uncertainty. The findings reveal that integrating forecasting and optimization knowledge could aid in precisely evaluating ecosystem services and meeting rising food demand.

A new interactive fuzzy programming with priority control for multi-objective decision-making problems

Fuzzy multiple objective linear programming (FMOLP) approaches have been used to be solved many applications of multi-objective decision-making (MODM) problems. Several methods have been proposed including max-min approaches, preemptive approaches, and weighted approaches. However, they have some limitations in use; some may not be able to obtain efficient solutions or can give only a few solutions. Some methods need to be solved in two steps or specify the target level, which may be difficult for decision-makers (DMs). In this research, a new single-phase interactive fuzzy programming approach with priority control that can find several efficient solutions is proposed. It is not necessary to specify the target value for each objective and it can solve with only one step for each solution. The DM can easily select the appropriate solutions from a set of efficient solutions. This method is different from existing single-phase approaches by controlling the satisfaction level of the last priority instead of using weight additive. Simple examples and a practical example of a perishable product supply chain network were tested to show the effectiveness of the proposed model. The performance of the proposed method was also compared with existing methods to verify and validate the model.

On generating fuzzy Pareto solutions in fully fuzzy multiobjective linear programmingviaa compromise method

In the present paper, it is unified and extended recent contributions on fully fuzzy multiobjective linear programming, and it is proposed a new method for obtaining fuzzy Pareto solutions of a fully fuzzy multiobjective linear programming problem. For its formulation, triangular fuzzy numbers and variables are combined with fuzzy partial orders and fuzzy arithmetic, and no ranking functions are required. By means of solving related crisp multiobjective linear problems, it is provided algorithms to generate fuzzy Pareto solutions; in particular, to generate compromise fuzzy Pareto solutions, what is a novelty in this field.