Fuzzy Robust Programming Research Articles

Sustainable-resilient-responsive supply chain with demand prediction: An interval type-2 robust programming approach

This study configures a novus multi-objective three-stage supply chain network that aims at optimizing sustainability, resilient and responsive measures, simultaneously. At first, a novel prediction model based on Markov chain, Dempster-Safer evidence theory and Shapely value is developed under trapezoidal interval type-2 fuzzy ambience to predict the demand of future scenarios. The prediction model prevents undesired loss occurred due to illogical demand consideration. To encounter interval type-2 fuzziness as well as risk in decision making, an unprecedented trapezoidal interval type-2 fuzzy robust possibilistic programming approach is introduced. The DEcision MAking Trial and Evaluation Laboratory method is suggested in the framework of trapezoidal interval type-2 fuzzy to prioritize the objective function by scrutinizing the interrelationship among different objective function components. As a result, the subjectiveness in the decision making framework is reduced. The generated configuration is then analysed using a blended approach that merges multi-choice reference goal programming with utility functions and particle swarm optimization. The integrated approach produces high-quality solution in lesser computational time. The insightful explorations are delivered based on a case study of hydrogen fuel supply chain in India. The outcomes show how resilient tactics are quite effective and can significantly enhance social, environmental, and economic aspects. It is determined that the best results for supply chain are obtained when the suggested sustainable, resilience and responsiveness tactics are used jointly. Moreover, the sensitivity analysis results suggest that the objective functions are substantially affected by the responsive level; therefore, managers ought to envisage the trade-off between responsiveness and other objective functions.

Fuzzy robust flexible programming with [formula omitted] measure for electric sustainable supply chain

Electricity as a source of energy, is one of the most essential part in our life. In recent time, it is noted that the temperature of earth increases in compare to the previous years. It is caused due to burning of the conventional energy sources such as gas, oil, and coal from thermal power plant and other sources, which brings about global warming. Bases on this fact, we propose a multi-objective mixed-integer programming model to design an electric sustainable supply chain network by considering resiliency and responsiveness. In order to formulate the environmental issues, a power-to-gas (P2G) technology is considered as an environment-friendly system. The presence of P2G can reduce the carbon level and it has some major advantages, i.e., it collects carbon dioxide (CO2) from thermal power plant and then converts CO2 to hydrogen (H2) with the help of water (H2O) and methane (CH4) gas. The drawbacks in addressing the uncertainty of the parameters are overcome by proposing a novel fuzzy robust flexible programming approach based on Me measure. Thereafter, a new approach namely, multi-choice conic goal programming with utility function is introduced to solve the proposed multi-objective model. Damodar Valley Corporation (DVC) in India is considered as a case study about electric network that envisages the sustainable issues of an electric supply chain. Finally, experimental results show that one bio-fuel plant, one photovoltaic plant, one air turbine plant, and two mixed-cycle power plants are build at the end of the scheduled period.

A Fuzzy Robust Programming Model for Sustainable Closed-Loop Supply Chain Network Design with Efficiency-Oriented Multi-Objective Optimization

Sustainable closed-loop supply chain (SCLSC) network design and decision-making is a critical problem for enterprises and organizations’ operations because of its excellent economic, environmental, and social performance. This article proposes a multi-objective mixed-integer programming model with targets for minimum total cost, reduction in environmental damage, and maximum social responsibility. In order to deal with the uncertainty caused by the dynamic business environment, a fuzzy robust programming (FRP) approach is applied. Furthermore, an efficiency-oriented optimization methodology, hybridizing meta-heuristics and efficiency evaluation, is proposed to solve the developed multi-objective model and functions as auxiliary decision-making. Data envelopment analysis is applied to evaluate the sustainability performance of feasible solutions and calculate their efficiency. The efficiency can comprehensively reflect the sustainability performance and guide the evolution process of meta-heuristic algorithms. A numerical case validates the proposed FRP model and efficiency-oriented optimization methodology. The results demonstrate that with the proposed methodology, decision-makers not only can obtain a set of efficient schemes but also can determine the optimal scheme with the best sustainability performance.

Designing a sustainable-remanufacturing closed-loop supply chain under hybrid uncertainty: Cross-efficiency sorting multi-objective optimization

Government legislations, resource scarcity, the recycling of end-of-life products and process development have spurred researchers to design the sustainable closed-loop supply chain as well as consider improved remanufacturing process. In this article, a multi-objective mixed-integer programming model is developed to configure and optimize a sustainable-remanufacturing closed-loop supply chain (SRCLSC) network. The model aims to reduce net costs, environmental degradation, and lost working days resulting from occupational accidents. Furthermore, a scenario-based fuzzy robust programming approach, which combines fuzzy robust programming and robust optimization, is developed to address the high hybrid uncertainty in the SRCLSC network. To solve the resulting model, a cross-efficiency sorting multi-objective optimization methodology that combines network optimization and performance evaluation is proposed. Data envelopment analysis is applied to evaluate the performance and cross-efficiency of feasible solutions. Performance evaluation results can guide the optimization process of multi-objective optimization algorithms. On the other hand, supply chain managers can determine the optimal solution based on the cross-efficiency values of solutions. The numerical case result verifies the effectiveness and applicability of the proposed model. In addition, it demonstrates that the proposed optimization method achieves the optimal solution based on the cross-efficiency of feasible solutions and has better solution performance than the conventional algorithm. Finally, sensitivity analyses and managerial insights are conducted.

Improving footprint-based water use efficiency through planting structure optimization

Unreasonable utilization of water resources cause serious water shortage and associated pollution problems. Improving water use efficiency (WUE) is helpful for alleviating water scarcity and mitigating water pollution. However, due to the conflict between water saving and economic development as well as uncertain parameter information, it is challenging to improve WUE. To address these problems, a water-footprint-based interval fuzzy robust fractional programming (WF-IFRFP) model was developed through integrating water footprint (WF), interval parameter programming (IPP) and fuzzy robust optimization (FRP) into a fractional programming (FP) framework. The developed WF-IFRFP model improved upon traditional methods by being able to tackle interval numbers and fuzzy sets under different system-violation risks. The developed model was applied to a water management case in the northwest of Inner Mongolia, China. The results of WF assessment showed that the water consumption of crop growth increased, water, whereas that used for reducing total nitrogen concentration decreased from 2012 to 2016. Then, specific benefit- and risk-explicit plans for cropping pattern adjustments were generated. The results showed that the water supply-demand ratio from WF-IFRFP would be [5.1, 10.7] % higher than that in the benchmark year of 2016. To assess its performance and merits, the optimal results from the WF-IFRFP model were compared to four alternative models. These comparisons reveal that the WF-IFRFP model is beneficial for improving irrigation WUE.

Robust decision support for seawater desalination system management under consideration of environmental pollution control.

Seawater desalination is one of the most popular options to alleviate the water crisis worldwide. Effective management of a seawater desalination system is thus critical. In this study, a fuzzy robust optimization programming model, named FROP, has been proposed to provide robust decision support for seawater desalination management under consideration of environmental pollution control and uncertainty. The major contributions of the proposed FROP model include the following: (1) it is designed for effectively addressing the interactions among seawater desalination development, desalted water distribution, water requirement, and control of environmental pollutant emission within an integrated seawater desalination system; (2) it is an effective decision support tool for decision-makers to provide robust planning strategies through simultaneously considering the optimality robustness and feasibility robustness; (3) it can quantify imprecise and vague uncertainties related to the various aspects of the integrated seawater desalination system expressed as fuzzy parameters; and (4) it can address the tradeoffs among meeting the economic objective and environmental protection requirements and guaranteeing the stability of the system (i.e., risk of violating system constraints) under uncertainty. In order to demonstrate its applicability, the FROP model is applied in a hypothetical seawater desalination management system which is consistent with management schemes in practices. The results indicate that despite a higher total system cost, the management objective and environmental requirements are met, whereas a lower total system cost results in a higher risk of violating the constraints and the possibility of destabilizing the system. The FROP model is helpful for decision-makers to develop robust and cost-effective management schemes for seawater desalination systems under different economic and environmental constraints and complex uncertain conditions.

A Robust Multi-objective Fuzzy Model for a Green Closed-loop Supply Chain Network under Uncertain Demand and Reliability (A Case Study in Engine Oil Industry)

Given the importance of supply chain and environmental issues, this paper presents a new mathematical model for a green closed-loop supply chain (GCLSC) network with the objectives of maximizing profits, maximizing the number of jobs created, and maximizing reliability. Due to the uncertainty on some parameters such as demand and transportation costs, the new method of robust fuzzy programming model was utilized. Multi-objective Grey Wolf Optimizer (MOGWO) and Non-dominated Sorting Genetic Algorithm II (NSGA II) were used to tackle the problems for larger sizes. A number of instances of the problem in larger sizes were solved. The results from comparing the algorithms considering some criteria including means of objective functions, spacing index, distance index from ideal point, maximum amplitude index, Pareto response number index and computational time showed the fast convergence and high efficiency of MOGWO algorithm for this problem. Finally, the implementation of the model for a real case study in Iranian engine oil industry, showed the efficiency of the obtained solutions for this network.

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.

Integrated voltage control and maintenance insurance planning for distribution networks considering uncertainties

Distributed generation (DG) is a promising solution to climate change problems related to rapidly increasing electric power consumption. However, the increasing penetration of DG units poses challenges in enhancing the distribution network reliability owing to their intermittent nature. This paper proposes an integrated voltage control and maintenance insurance planning model for power system reliability under uncertainties in demand loads and active power output of DG units. Voltage control is executed to solve the power quality issue by optimally coordinating the reactive power outputs of the DG units and the active power outputs of storage batteries (SBs). A maintenance insurance scheme is applied to ensure the operating conditions of DG units and SBs in a continuous manner without unexpected interruptions. The reliability indices represented by the voltage deviation cost and expected interruption cost are employed in the proposed planning model to minimize the total power system cost. The decisions include the number and location of DG units and SBs, the reactive and active power of DG units and SBs, respectively, as well as the preventive maintenance cycle and insurance coverage level. A robust fuzzy programming model based on type-2 fuzzy numbers is proposed to obtain the optimal solution in the planning horizon. The application of the proposed model is examined using an empirical case study. The results indicated that the voltage control and maintenance insurance can aid in enhancing the distribution network reliability by reducing the related cost by approximately 26.09%.

Sustainable design modifications municipal solid waste management network and better optimization for risk reduction analyses

The staggering rate of waste generation due to industrialization, urbanization and population growth has raised a pressing problem regarding environmental damages and human health hazards, especially in developing nations. Severe environmental and social risks such as surface and groundwater pollution, soil and air contamination, serious human health hazards and damage to aesthetic aspects are some inappropriate waste management results. To overcome these burdens and move toward sustainable municipal solid waste management, effective and efficient practices are required. This study deals with a sustainable municipal solid waste network design problem under uncertainty. For this purpose, a multi-objective fuzzy robust programming model with the aim of minimizing the total costs of the network and environmental damages and optimizing social impacts is proposed. Different practical waste treatment practices are considered in the proposed network, including incineration, recycling, composting and sanitary landfilling. Also, a risk that is related to the population of facilities’ potential location is introduced and the Fuzzy Failure Mode and Effects Analysis is applied to determine the value of the mentioned risk. In order to tackle uncertain parameters of the proposed model, the Fuzzy Robust Optimization approach is applied. The proposed multi-objective model solves as a single-objective model using the Fuzzy Goal Programming approach with Different Importance and Priorities. The applicability of the model is demonstrated through a real case study of Minudasht’s municipal solid waste management system. The optimal location with the least risk and environmental impacts for each treatment facility with related technology and method is introduced. Furthermore, sensitivity analysis has done on some parameters to determine the effect of parameters’ changes on objective functions. The results showed the effectiveness and efficiency of the proposed model.

Integrated forward/reverse logistics thin-film photovoltaic power plant supply chain network design with uncertain data

Unique features of solar energy, such as the low cost of operation and low pollution, make photovoltaic power plants attractive. Despite the advantages of these power plants, such as low cost of operation and operating without pollution, their high establishment cost compared to that of the conventional fossil fuel-fired power plants prevents their rapid growth. Therefore, designing and optimizing an efficient supply chain network will help to develop the photovoltaic industry. This study proposes a bi-objective model to design and optimize a thin-film photovoltaic power plant supply chain network integrating reverse logistics. The first objective minimizes the costs of supply chain network design, which optimizes decisions from suppliers to disposal centers. The second objective maximizes the efficiency of the data envelopment analysis model to find suitable locations of facilities. As there is uncertainty in electricity demand prediction and perfect foresight is not possible, a fuzzy-robust programming approach is devised to cope with the uncertain parameters. The validity and practicality of the proposed approach are investigated by a case study based on real-world data. Finally, K-Means clustering is incorporated into the model to analyze the installed photovoltaic capacity of different cities in each period. The results show that using an optimistic approach to deal with uncertainty reduces the total cost by 20% in comparison with using a pessimistic approach. The results also provide helpful insights for decision-makers and policymakers in allocating and optimizing the operation of facilities by considering the real-world characteristics of the candidate locations.

A multi-objective pharmaceutical supply chain network based on a robust fuzzy model: A comparison of meta-heuristics

The pharmaceutical supply chain has features that distinguish it from other supply chains. Medicine is considered a strategic commodity, and the smallest disruption in its supply chain may cause severe crises. This is why the distribution of pharmaceutical products needs to combine the minimization of costs with strong compliance with service standards while taking into account risks due to uncertainty. In this study, we present a new multi-objective multi-echelon multi-product multi-period pharmaceutical supply chain network (PSCN) along with the production–distribution–purchasing–ordering–inventory holding-allocation-routing problem under uncertainty. We formulate the problem as a Mixed-Integer Non-Linear Programming model and develop a novel robust fuzzy programming method to cope with uncertainty parameters. To find optimal solutions, several multi-objective metaheuristic algorithms, namely, MOSEO, MOSAM MOKA, and MOFFA considering different criteria and multi-objective assessment metrics are suggested. Since there are no benchmarks existing in the literature, 10 numerical instances in large and small sizes are generated and also the trapezoidal fuzzy numbers of the uncertain parameters were randomly generated based on a uniform distribution. The required parameters were set and also the simulated data were examined in an exact method and by metaheuristic algorithms. The results confirm the efficiency of the MOFFA algorithm to detect a near-optimal solution within a logical CPU time. The solution methods are complemented with several sensitivity analyses on the input parameters of the proposed model.

A multi-objective fuzzy robust optimization approach for designing sustainable and reliable power systems under uncertainty

A sustainable and reliable power system is extremely important to ensure the prosperity of a country and its society. Traditional power systems are facing serious environmental and social issues while renewable energy systems possess low reliability due to the intermittent nature of energy sources. This paper addresses the sustainable and reliable power system design problem in an uncertain environment by using an approach called multi-objective fuzzy robust programming. The proposed approach, which is an integration of robust programming and two main branches of fuzzy programming (possibilistic and flexible programming), solves the presented multi-objective problem by simultaneously improving both sustainability and reliability, as well as by capturing uncertain factors. The objective is to determine the optimal number, location, capacity, and technology of the generation units as well as the electricity generated and transmitted through the network while minimizing the sustainability and reliability costs of the system. The proposed model considers uncertainties in the demand, the intermittent nature of renewable energy resources, and cost parameters. A case study in Vietnam was conducted to demonstrate the efficacy and efficiency of the proposed model. Results show that the proposed model improves the total cost of the power system, including sustainability and reliability costs, by approximately 4.2% and reduces the computational time by 20% compared to the scenario-based stochastic programming approach. Our findings also show that due to risk disruption, the reliability cost of the power system increases to 56.72% when more electric power is generated.

A novel hybrid approach for synchronized development of sustainability and resiliency in the wheat network

In addition to the great importance of minimizing total cost, resiliency and social indicators have a special place in the agricultural food supply chain. In this respect, a novel multi-objective model is developed that addresses the design/redesign wheat supply chain network, which comprises several suppliers, existing silos, candidate locations for establishing silos, flour factories, and demand zones in an uncertain environment. To develop the mathematical model, two additional and essential dimensions of the supply chain including social impact and resiliency are simultaneously considered. This model is the integration of several proper indicators of resiliency, social responsibility dimensions through considering three objective functions to minimize the cost, non-resiliency, and negative impacts of social responsibility. Due to the fact that input parameters taint with inherent uncertainty, a hybrid stochastic fuzzy-robust programming is introduced, and four different hybrid approaches are developed. Finally, to demonstrate the superiority of the proposed model as well as solution methodology, a real case study is provided. The obtained results show that simultaneously considering cost, resiliency, and social impacts can significantly assist to improve the performance of the wheat supply chain. Moreover, making trade-off between mentioned measures can help the decision-makers to have the principled preference.

Novel robust fuzzy programming for closed-loop supply chain network design under hybrid uncertainty

Novel robust fuzzy programming for closed-loop supply chain network design under hybrid uncertainty

A robust possibilistic programming model for water allocation problem

Over the past few years, water allocation problem has increasingly spotlighted by governments, researchers and practitioners. As water plays an important role in people’s life and business environment, the problem of water allocation should be considered carefully to properly satisfy demand of water consumers. In the real world applications, problems like water allocation are uncertain owing to long-term planning horizon of such problems. Therefore, employing efficient methods for tackling uncertainty of parameters should be regarded by field researchers. In this regard, this paper proposes a bi-objective mathematical programming model for water distribution network design. The extended model maximizes total profit of water distribution as well as maximizing priority of water transferring among water customer zones. Then, to cope effectively with uncertainty of parameters, a novel robust possibilistic programming method is applied. Then, fuzzy and robust fuzzy programming models are compared against each other and output results confirm superiority and effective performance of the robust fuzzy model in the water allocation problem. Also, output results of the extended model show its accurate performance that results in applicability of the model as a strong planning tool in real world cases.

A robust fuzzy mathematical programming model for the closed-loop supply chain network design and a whale optimization solution algorithm

The closed-loop supply chain (CLSC) management as one of the most significant management issues has been increasingly spotlighted by the government, companies and customers, over the past years. The primary reasons for this growing attention mainly down to the governments-driven and environmental-related regulations which has caused the overall supply cost to reduce while enhancing the customer satisfaction. Thereby, in the present study, efforts have been made to propose a facility location/allocation model for a multi-echelon multi-product multi-period CLSC network under shortage, uncertainty, and discount on the purchase of raw materials. To design the network, a mixed-integer nonlinear programming (MINLP) model capable of reducing total costs of network is proposed. Moreover, the model is developed using a robust fuzzy programming (RFP) to investigate the effects of uncertainty parameters including customer demand, fraction of returned products, transportation costs, the price of raw materials, and shortage costs. As the developed model was NP-hard, a novel whale optimization algorithm (WOA) aimed at minimizing the network total costs with application of a modified priority-based encoding procedure is proposed. To validate the model and effectiveness of the proposed algorithm, some quantitative experiments were designed and solved by an optimization solver package and the proposed algorithm. Comparison of the outcomes provided by the proposed algorithm and exact solution is indicative of high quality performance of the applied algorithm to find a near-optimal solution within the reasonable computational time.

A fuzzy robust programming approach to multi-objective portfolio optimisation problem under uncertainty

A fuzzy robust programming approach to multi-objective portfolio optimisation problem under uncertainty

A fuzzy robust programming approach to multi-objective portfolio optimisation problem under uncertainty

Portfolio selection is one of the most important problems in financial markets. This paper proposes a novel robust flexible portfolio optimisation model based on possibilistic mean and variance and flexible constraints, to cope with inherent uncertainty of such problem. The proposed model is extended by introducing a modified robust flexible approach. The developed models are evaluated and validated by using the real data of Tehran stock exchange. The obtained results show that in higher violation penalties, the proposed models outperform the deterministic model. In addition, experimental analyses are provided to compare the performance of the robust flexible portfolio optimisation model to the modified version.

Optimal Use of Agricultural Water and Land Resources through Reconfiguring Crop Planting Structure under Socioeconomic and Ecological Objectives

Many economic, social and ecological problems can be attributed to the scarcity and mismanagement of water and land resources. In this study, a multi-objective fuzzy–robust programming (MOFRP) method was developed for supporting the optimal use of land and water resources in agriculture. MOFRP improved existing methods through taking ecological services of crop cultivation into account. It was also capable of reflecting fuzziness in preferences, priorities and parameters that were largely neglected in previous agricultural decision making. This method was applied to address a case in arid northwestern China. Optimal plans of crop cultivation reconfiguration were generated for sustaining local development under economic, ecological and social objectives as well as physical restraints in water and land resources. Compared to the status quo, the optimized plan would increase economic and ecological benefits by 12.2% and 18.8%, respectively. The efficiency of irrigation water could also be enhanced with the economic and ecological benefits per unit water being raised and the water consumption per unit land being reduced. The comparisons of the MOFRP model to four alternatives validated that it was capable of achieving satisfactory benefits and reducing system-violation risks without neglecting valuable uncertain information and ecological services of crops. The proposed method was also applicable to other multi-objective management problems under uncertainty without loss of generality.