Fuzzy Multi-objective Programming Model Research Articles

A novel and dynamic land use/cover change research framework based on an improved PLUS model and a fuzzy multiobjective programming model

Spatial reconstruction and scenario simulation of historical processes and future trends of land use/cover change (LUCC) can help to reveal the historical background of land conversion and the spatial distribution of future land. Moreover, there is a close relationship between the spatiotemporal dynamics of land use/cover and changes in different ecosystem services (ESs). Using this relationship to simulate future land use scenarios is important. In this study, an LUCC dynamic analysis framework (LSTM-PLUS-FMOP) was constructed based on a deep learning time series forecasting model (LSTM), a parallelized urban land use simulation (PLUS) model and a fuzzy multiobjective programming (FMOP) model. The PLUS model was used to analyze the driving mechanism of land expansion and explore the land conversion pattern. In addition, three land conversion scenarios were established: natural land expansion (NLE), economic development priority (EDP) and regional sustainable development (RSD). The FMOP model and the relationship between LUCC and ES were used to perform a spatial simulation of land conversion. The uncertainty parameters in the model were treated by intuitionistic fuzzy numbers (IFSs). This study applied the constructed framework to the Yellow River Basin of Shaanxi Province (YRB-SX). The results showed that (1) from 2000 to 2020, the cropland area of the YRB-SX continuously decreased by 12.67 × 104 ha, while the built-up area continuously increased by 28.25 × 104 ha. The net reduction in woodland and grassland area was 13.90 × 104 ha. (2) The relative error range of land prediction using the LSTM model was 0.0003– 0.0042. This model had better accuracy than the Markov chain prediction model. (3) The cropland area decreased by 0.26% (NLE), 0.85% (EDP) and 1.68% (RSD) under the three scenarios. The built-up area increased by 25.01%, 32.76% and 14.72%, respectively. The RSD scenario followed the principles of ecological protection and spatial constraints, which mitigated the degradation of the ecosystem to some extent. This coupled simulation framework will help to obtain land allocation schemes that meet the requirements of ecological protection and provide solutions for rational land management.

Aiming at low nitrogen leaching diets based on nitrogen fertilizer regulatory policy: A regional bio-economic assessment of the Zayandeh-Rud river basin-Iran

Negative environmental impacts of nitrogen (N) intensive diets have triggered global debates on sustainable nitrogen management. Solutions such as dietary transitions, cropland reallocation and N Regulatory Policy (NRP) have been proposed to mitigate the adverse environmental impacts of N use in food production. However, there is still insufficient understanding of how NRPs could be designed to minimize negative environmental impact across diverse agro-ecological zones without sacrificing human dietary requirements. To increase this understanding, we evaluated the consequences of three NRP scenarios (low, moderate, and high N fertilizer rates) on the amount of livestock and non-livestock diet components as well as the associated N leaching and farmers' Gross Margin (GM) by optimizing the allocation of cropland between food and feed crops. We developed a bio-economic Interval Fuzzy Multi-Objective Programming (bio-economic IFMOP) model for the Zayandeh-Rud river basin, Iran, and a procedure that accounts for annual average availability of calories per capita, calorie sources from livestock and non-livestock components of three dietary preferences, and inequality in calorie distribution. The interaction among soil, climate and weather variability and NRPs across nine sub-regions of the case study region was handled by crop yield simulation using the DSSAT software. The solution of farmers' GM, derived from the optimization problem across possibilities of water fluctuations, was assessed to determine the uncertainty in GM. We also introduced an N leaching per Block of Distributed Calories (BDC) criterion based on solutions of supplied calories and associated N leaching. The upper bound of the moderate NRP scenario resulted in the smallest N leaching per BDC. This corresponded to ∼0.34, ∼0.34, ∼3.77 and 19.00 million BDC of meat, dairy, wheat and potato, respectively. Also, the upper bound of this scenario satisfied the lowest instability in farmers’ GM against water fluctuation compared with low and high NRP scenarios. The affordable volume of N leaching per BDC varied across sub-regions between [1.53,3.49], [1.52,3.33], [0.76,0.99] and [0.05,0.08] kg for meat, dairy, wheat and potato, respectively. Our results highlighted both optimistic and pessimistic prospects of producing low N leaching diets. The approach of this study could also be applied to other regions and countries.

FUZZY MULTI-OBJECTIVE NONLINEAR PROGRAMMING PROBLEMS UNDER VARİOUS MEMBERSHIP FUNCTIONS: A COMPARATİVE ANALYSIS

Fuzzy sets have been applied to various decision-making problems when there is uncertainty in real-life problems. In decision-making problems, objective functions and constraints sometimes cannot be expressed linearly. In such cases, the problems discussed are expressed by nonlinear programming models. Fuzzy multi-objective programming models are problems containing multiple objective functions, where objective functions and/or constraints include fuzzy parameters. Membership functions are crucial to obtain optimal solution of fuzzy multi-objective programming model. In this study, a green supply chain network model with fuzzy parameters is proposed. Proposed model with nonlinear constraints is a fuzzy multi-objective nonlinear programming model that minimizes both transportation costs and emissions generated by two vehicle types during transportation. The model is used in Zimmermann's Min-Max approach by considering triangular, hyperbolic and exponential membership functions and optimal solutions are obtained. When optimal solutions are compared, it is seen that optimal solution obtained using the hyperbolic membership function is better than the optimal solutions obtained from triangular and exponential ones. Maximum common satisfaction level calculated using hyperbolic membership function for proposed model is λ=0.97. Sensitivity analysis is also carried out by taking into account distances between suppliers, manufacturers, distribution centers and customers, as well as customer demands.

A New Decision Framework of Online Multi-Attribute Reverse Auctions for Green Supplier Selection under Mixed Uncertainty

In order to realize the “dual carbon” goal proposed for the world and to seek the low-carbon and sustainable development of the economy and society, the green supply chain management problem faced by Chinese enterprises and governments is particularly important. At the same time, how to quickly and efficiently select the suitable green supplier is the most basic and critical link in green supply chain management, as well as an important issue that Chinese government and enterprises must face in the process of green material procurement. In addition, there are various uncertainties emerging in the current market environment that hinder the green suppliers and the buyer to make the efficient decisions. Therefore, in order to find a more suitable and efficient method for green supplier selection, from the standpoint of the buyer, a new decision framework of online multi-sourcing, multi-attribute reverse auction (OMSMARA), which effectively improves the procurement efficiency and reduces procurement costs and risks, is proposed under the mixed uncertainty. Specifically, the main innovation work includes three aspects: Firstly, the trapezoidal fuzzy numbers are applied to describe the uncertain bidding attribute values by the green suppliers. Secondly, the hesitant fuzzy sets theory is introduced to characterize the buyer’s satisfaction degrees of the bidding evaluation attribute information, and the attribute weights are determined by using the hesitant fuzzy maximizing deviation method. Thirdly, a fuzzy multi-objective mixed integer programming model is proposed to solve the green supplier selection and quantity allocation question in OMSMARA. A numerical example is given to demonstrate the feasibility and effectiveness of the proposed decision framework, and the sensitivity analysis and comparison analysis further show the robustness and reliability of the proposed solution method.

Robust possibilistic programming to design a closed-loop blood supply chain network considering service-level maximization and lateral resupply.

Reconfiguring the structure of the supply chain network is one of the most strategic and vital decisions in designing a supply chain network. In this study, a Closed-Loop Blood Supply Chain Network (CLBSCN) considering blood group compatibility, ABO-Rh(D), and blood product shelf life has been studied to determine the best strategic and tactical decisions simultaneously considering lateral resupply/transshipment and service-level maximization. Several vital parameters, including supply and demand, are considered fuzzy numbers to approximate reality due to the nature of the world. Furthermore, two crucial factors include ABO-Rh(D) and blood product shelf life considered, while the concept of lateral resupply governs the interconnections of hospitals’ excess blood units. We propose a fuzzy multi-objective Mixed-Integer Non-Linear Programming (MINLP) model to consider two critical objective functions: minimizing the total costs of the network and maximizing the minimum service level to the patients at each Hospital. The fuzzy multi-objective MINLP model is converted to a deterministic multi-objective model using the equivalent auxiliary crisp model to deal with uncertainty. Then, by utilizing two interactive fuzzy solution approaches, the results have been compared based on a real case study to suggest the best solution for the proposed model. Also, we conduct sensitivity analysis on essential parameters such as demand, supply, and capacity to understand how these parameter variations impact two proposed objective functions. Then, the proposed model is tested on a real case study for model validation. The results confirmed that considering the lateral resupply could significantly save the costs of the designed network by a total of $343,000. Interestingly, maximizing the minimum service level at hospitals increased the service level from 58% to 68%.

RETRACTED: Selecting and balancing market portfolio using artificial intelligence and fuzzy multiobjective decision-making model

Most enterprises focus on product portfolio management (PPM) and exclude market portfolio management, and individual markets are selected solely based on financial performance which may not be appropriate because other factors may dictate the outcome of the market selection. This study proposes a market portfolio model that considers market share, market growth, market competition, market risk, and market cost to maximize overall profit. A three-stage approach is proposed to identify potential product markets using an AI algorithm. A set of the most promising market is then determined based on the results of Stage 1 using a fuzzy multi-objective mathematical programming model by concurrently maximizing the total market share and market growth, and minimizing the market competition and market risk. A single-objective mathematical programming model is then used to determine a market portfolio to maximize the total profit using the results for Stage 2. The single-objective model is tested using two sets of threshold constraints. The balance of the market portfolio is discussed and the results are compared. The novelty of the article: (1) the first study involves a product market portfolio, (2) the decision of market selection is scientific (using AI instead of personal judgment), holistic (factors include market share, growth, competition, risk, cost, and profit) and optimized (using mathematical optimization), and (3) the market portfolio maximizes total profit. (4) the proposed method produces a portfolio with a higher profit than the TOPSIS method.

A Fuzzy Approach for Generalized Project Selection and Scheduling Problem with Resource Management

In this study, the problem of project selection and scheduling with resource management is considered project setup times, dynamic project arrivals, priorities and relationship between projects. A fuzzy multi-objective mixed integer linear programming (MILP) model is proposed for the solution of the problem. The classic two-phase fuzzy goal programming (FGP) approach is modified to solve the proposed multi-objective MILP model. The addressed problem is defined over the project selection and scheduling problem of a construction company. The effect of resource management on the project selection and scheduling problem is demonstrated over the generated test problems. Modified two-phase FGP and classic two-phase FGP approaches are compared over test problems. With the use of the modified two-phase FGP approach, additional alternative solutions are found for the problem.

A hybrid fuzzy multi-objective model for carpet production planning with reverse logistics under uncertainty

With the presence of ever-rising customers' concerns about environmental impacts, companies are utilizing used products and recyclable materials in their supply chains to manage the products' end-of-life effectively. Effective utilization requires a proper logistical structure to flow used and recovered products throughout the supply chain. In the carpet industry, reverse logistics operations are complex and susceptible to high uncertainty affecting the collection rate, recovered items’ availability, and reverse channel capacity. Besides total cost efficiency, carpet manufacturers and other logistics actors are willing to plan the production and reverse logistics functional areas to optimize sustainability attributes. Armed with these insights, this paper addresses a multi-product, multi-site, and multi-period production planning problem integrated with reverse logistics under uncertainty. A novel fuzzy multi-objective programming model (combining possibility and flexibility) is proposed with chance constraints. Finally, new hybrid fuzzy goal programming is presented to solve the developed model. Numerical study in the carpet industry is included to show the model applicability and sensitivity.

A Fuzzy Multi-Objective Mixed Integer Linear Programming Model for End of Life Use

One of the main challenges of designing the effective reverse logistic network is to predict the amount of product which reach end of their useful life. Thus, in this study, we propose fuzzy multi-objective mixed integer linear programming (Fuzzy-MOMILP) model which the amount of returned product is considered as an uncertain parameter. In order to solve the proposed multi objective fuzzy mathematical programming model, a fuzzy solution approach is applied. The proposed Fuzzy-MOMILP model seeks to minimize the total reverse logistic network cost and minimize the total carbon emissions related to the transportation and processing of used products. To validate the model, a case study is examined. The results of this study indicate that the proposed model can be used to design a sustainable reverse logistic network for end-of-life (EOL) products.

Designing a sustainable closed-loop supply chain network considering lateral resupply and backup suppliers using fuzzy inference system.

Sustainability is key factor for transforming traditional supply chain networks into modern ones. This study, for the first time, considers the impacts of the backup suppliers and lateral transshipment/resupply simultaneously on designing a Sustainable Closed-Loop Supply Chain Network (SCLSCN) to decrease the shortage that may occur during the transmission of produced goods in the network. In this manner, the fuzzy multi-objective mixed-integer linear programming model is proposed to design an efficient SCLSCN resiliently. Moreover, the concept of circular economy has been studied in this paper to reduce environmental effects. This study aims to optimize total and environmental costs, including energy consumption and pollution emissions, while increasing job opportunities. A demand uncertainty component is considered to represent reality more closely. Due to the importance of demand, this parameter is estimated using the Fuzzy Inference System (FIS) as an input into the proposed mathematical model. Then, the fuzzy robust optimization approach is applied in a fuzzy set’s environment. The model is tackled by a Multi-Choice Goal Programming Approach with Utility Function (MCGP-UF) to be solved in a timely manner, and the equivalent auxiliary crisp model is employed to convert the multi-objective function to a single objective. The proposed model is tested on the case study of the tire industry in terms of costs, environmental impacts, and social effects. The result confirmed that considering the concept of lateral resupply and backup supplier could considerably decrease the total costs and reduce shortages on the designed SCLSCN. Finally, sensitivity analysis on some crucial parameters is conducted, and future research directions are discussed.

Sustainable microgrid design with multiple demand areas and peer-to-peer energy trading involving seasonal factors and uncertainties

The intermittent nature of renewable sources, uncertain demand load, and the location of microgrids cause challenges for the proper energy balance between supply and demand. To overcome the issues caused by such challenges and to be economically efficient while minimizing environmental impacts, microgrid design with renewable energy sources has recently attracted the attention of researchers. However, the sustainable microgrid design involving multiple types of demand areas (residential and industrial areas) and seasonal factors has not been explored by researchers. Therefore, this paper investigates the sustainable microgrid design problem with multiple types of demand areas and peer-to-peer energy trading involving seasonal factors and uncertainties to maximize total profit and to minimize environmental costs while satisfying demand. The problem is to determine optimal decisions on the number, location, and capacity of renewable distributed generation sources, energy flows, and seasonal electricity sales prices for the system that includes peer-to-peer trading. A fuzzy multi-objective programming model is developed to handle the uncertainties of demand load and capacity of renewable distributed generation sources. A genetic algorithm is applied to solve the proposed model. Results of computational experiments to assess its effectiveness and efficiency show that the proposed model increases total profit by over 12% and reduces environmental costs by almost 30% compared to the cases of no peer-to-peer energy trading and seasonal factors.

Adapted Fuzzy Multi-Objective Programming Algorithm for Vehicle Routing

The vehicle routing problem (VRP) is a well-known problem in the logistics sector. In this study, two objectives, minimizing the total distance and maximizing the saving value, were considered in VRP with a fuzzy environment. The game theory approach is proposed for determining the weights of objectives when decision-makers have insufficient knowledge of assigning the weights. Thus, a fuzzy pay-off matrix is proposed for determining the weights of objectives by combining the fuzzy two-person zero-sum game with mixed strategies (FTZG with MS) and membership functions. Therefore, the fuzzy multi-objective programming (FMOP) model is adapted to the VRP model, which is named Adapted FMOP algorithm for VRP. Proposed algorithm clusters customers according to two objectives and by using four fuzzy operators, and routes customers with the traveling salesman problem (TSP) model in order to avoid the non-deterministic polynomial-time hardness (NP-hard) structure of VRP. In the end, the results are improved using local search methods. The main contribution of the Adapted FMOP algorithm for VRP is that it provides a solution that considers more than one objective without the need for decision makers’ view on the weights of objectives in all decision models in the fuzzy environment. Also, the proposed algorithm can find the solution with the help of a mathematical model without requiring any heuristics or metaheuristics, since it primarily performs clustering. Firstly, the efficiency of this algorithm was tested on problems in the literature. The Adapted FMOP algorithm for VRP achieved the best-known solutions by some small margins and exceeded the best-known solution for one problem in the literature. After seeing that the performance of the algorithm was sufficient, a data set of a firm in the construction sector was implemented to see how the algorithm works in real life and the obtained results were discussed. The solutions demonstrate that the Adapted FMOP algorithm for VRP also works well for real-world problems.

Determining the optimal strategy for aggregate production planning (APP) during the Covid-19 crisis using an algorithm Harmony Search Algorithm

Determining the optimal strategy for aggregate production planning (APP) during the Covid-19 crisis using an algorithm Harmony Search Algorithm

A robust fuzzy multi-objective programming model to design a sustainable hospital waste management network considering resiliency and uncertainty: A case study.

With the increase in the number of patients and activity of hospitals, the issue of hospital waste management (HWM) is becoming more and more challenging and worrying. In addition to financial losses, there will be irreparable damage to the ecosystem and environment which will create many problems for people (because the job of some people in the area is livestock and agriculture and they have a lot to do with their surroundings). It also doubles the need to pay attention to the issue of sustainable development (simultaneous attention to social, economic and environmental dimensions) in waste management. Moreover, the climatic and geographical conditions and lack of proper waste management in this area lead to major problems. Therefore, in this research, by developing a novel multi-objective mixed integer linear programming model, HWM is addressed in the hospitals of Sari, Iran. The aim is to design an HWM network considering sustainability, resiliency and uncertainty. In order to deal with uncertainty, a robust fuzzy programming approach is employed, and then an improved goal programming technique and Lp-metric method is proposed to solve the model. It was revealed that goal programming outperforms the Lp-metric method in terms of all objectives. Furthermore, the obtained results demonstrate the applicability and efficiency of the proposed methodology to design an efficient sustainable HWM network.

Resilience cloud-based global supply chain network design under uncertainty: Resource-based approach

This study presents a fuzzy multi-objective mathematical programming model to design an efficient and resilience global supply chain network structure based on the service-oriented approach. Service composition and transportation within globally scattered resources are considered under the cloud manufacturing paradigm. The proposed comprehensive model is adapted to a global electrical medical device manufacturing system. Key performance measures include robustness, agility, leanness, and flexibility as resiliency pillars are considered in designing the network under uncertainty. To efficiently deal with the computational tractability of this non-linear and multi-objective optimization problem, a new hybrid solution algorithm is developed that incorporates fuzzy multi-criteria decision-making methods and augmented ε-constraint method. Obtained computational results of a real case study present that the proposed service-oriented global supply chain network design can respond to its global customers’ demands in a resilient as well as efficient manner.

Developing a two-stage model for a sustainable closed-loop supply chain with pricing and advertising decisions

Closed-Loop Supply Chain (CLSC) has become a critical problem due to its effects on various factors including economic motivations, environmental concerns, and social impacts. Moreover, there are coordination tools, such as pricing and advertising, which impact its performance. In this paper, we offer a two-stage approach to model and solve a sustainable CLSC, taking into account pricing, green quality, and advertising. In the first stage, optimal decisions on pricing, greening, and advertising are made, while in the second stage, a fuzzy multi-objective Mixed Integer Linear Programming (MILP) model is used to maximize the total profit, reduce CO2 emissions, and improve social impacts. Suitable solution methods are introduced according to the scale of the problem. For small-scale instances, an augmented ϵ-constraint method is used to solve the problem. For large-scale instances, approximations are required, and a Lagrangian relaxation algorithm solves the problem in polynomial time. The performance of the proposed model is evaluated through various numerical examples. The results illustrate the applicability and efficiency of the model, while confirming significant improvements in sustainable objectives under optimal pricing, green quality, and advertising. Besides, the proposed Lagrangian relaxation method significantly reduces the computational time for large-scale instances, with only a 2.308% deviation from the optimal results.

Closed-Loop Supply Chain Network Design under Uncertainties Using Fuzzy Decision Making

The importance of considering forward and backward flows simultaneously in supply chain networks spurs an interest to develop closed-loop supply chain networks (CLSCN). Due to the expanded scope in the supply chain, designing CLSCN often faces significant uncertainties. This paper proposes a fuzzy multi-objective mixed-integer linear programming model to deal with uncertain parameters in CLSCN. The two objective functions are minimization of overall system costs and minimization of negative environmental impact. Negative environmental impacts are measured and quantified through CO2 equivalent emission. Uncertainties include demand, return, scrap rate, manufacturing cost and negative environmental factors. The original formulation with uncertain parameters is firstly converted into a crisp model and then an aggregation function is applied to combine the objective functions. Numerical experiments have been carried out to demonstrate the effectiveness of the proposed model formulation and solution approach. Sensitivity analyses on degree of feasibility, the weighing of objective functions and coefficient of compensation have been conducted. This model can be applied to a variety of real-world situations, such as in the manufacturing production processes.

Application of linier fuzzy multi-objective programming model in travelling salesman problem

Traveling salesman problem is a problem where a salesman must visit a number of cities, each of which is visited exactly once only, and has to start from and return to the origin city. The objective of this traveling salesman is to determine an optimal travel route by minimizing travel cost or travel distance. If a decision maker wants to determine an optimal route by minimizing travel cost and distance simultaneously, they need more than one destination function, and therefore traveling salesman problem can be formulated as a multi-objective problem. In a traveling salesman problem, salesman make decisions by choosing an optimal route based on an expected measurement. In fact, a number of real problems cannot be expressed as a constraint function and resources in a definite form, so it is necessary to use fuzzy logic which allows us for making decisions based on bias or incorrect data. This paper will discuss a solution to the traveling salesman problem by using a fuzzy multi-objective model, which aims to determine an optimal route of the salesman. Results obtained from data processing of five places to visit by using a Maple 18 software included minimum cost, distance, and time with satisfaction level α = 0.89.

Optimal irrigation water allocation in Hetao Irrigation District considering decision makers’ preference under uncertainties

In this study, a fuzzy multi-objective mλ-measure dependent-chance programming model was proposed to optimize limited irrigation water among three crops and five subareas in Hetao Irrigation District (HID) under uncertainties, with the objectives of ensuring food security and maximizing economic benefits. Three levels of droughts (100%, 85%, and 70% of annual average water diversion) that may happen in HID were set as future possible droughts scenarios. The optimization model considered the detailed physical process of soil water balance, which is necessary for irrigation districts where groundwater recharge plays a major role when available water limited. Moreover, sensitivities of crop yield to water deficit during crop growth periods were involved in model formulation to reflect the difference of crop water demand in different subareas. In optimization model, mλ-measure was introduced into the first objective to quantify optimistic and pessimistic decision attitudes of decision makers, and a series of alternatives were obtained. The obtained results indicate that: (1) the irrigation water of wheat, maize, and sunflower at rapid growth stage and middle growth stage should be preferentially guaranteed due to their high water-deficit sensitivities. The water demand at initial growth stage and late growth stage can be satisfied by soil water and groundwater recharge. (2) maize has the priority of irrigation in almost all subareas while sunflower has to face water deficit when drought occurs. (3) allocating more irrigation water to Yongji and Jiefangzha subareas can help increase food production. (4) the irrigation water allocated to grain crops increases along with the decrease of λ, representing decision makers’ more conservative preference. The optimization model and results in this study provide decision makers abundant water-allocation schemes under drought conditions.

Toward sustainable microgrids with blockchain technology-based peer-to-peer energy trading mechanism: A fuzzy meta-heuristic approach

Microgrids with renewable distributed generation units are a promising solution for reducing investment cost and greenhouse gas emissions in the face of rapidly rising energy demand and recent organizational concerns regarding social and environmental issues. However, microgrids closely located to demand areas cannot easily balance power supply and demand owing to the intermittency of renewable energy generation and the barriers to connecting with the main electricity grid. To overcome this problem, this study addresses a sustainable microgrid design problem, where blockchain technology is used for peer-to-peer energy trading in the microgrid. The adoption of the blockchain technology in peer-to-peer energy trading ensures the security and sustainability for participants in the microgrid. It enables the participants to take control of the energy system without the need for a central regulatory authority. The problem entails decisions regarding not only the power flow among entities in the grid and the number, location, and capacity of renewable distributed generation units but also the price mechanism for peer-to-peer trading. A sustainable network microgrid is modeled by considering economic and environmental objectives with social constraints related to maximizing demand satisfaction of consumers. A fuzzy multi-objective programming model is proposed to tackle the variability in the capacity of renewable distributed generation units and demand load. The proposed model is solved by a genetic algorithm. Numerical experiments are conducted to evaluate the feasibility of the proposed model in decision-making regarding microgrid design, the impact of peer-to-peer trading on the total profit of the microgrid, and the applicability of the developed solution approach.