Fuzzy Robust Optimization Research Articles

Designing a sustainable–resilient disaster waste management system under hybrid uncertainty: A case study

Due to the increase in the number of natural disasters and the significant amounts of waste generated in these events, having a comprehensive framework for its management in the recovery and response phases of disaster is necessary. Hence, this research investigates the disaster waste management problem by simultaneous consideration of sustainability and resiliency. In this regard, a multi-objective mathematical model is presented to minimize total costs, environmental impacts, and transportation risks while maximizing social impacts and resilience of the logistics system. Since uncertainty is an integral part of disaster conditions, the research problem formulates the fuzzy robust stochastic optimization model under the hybrid uncertainty. Then, a real-world case study is studied in Golestan province, Iran. Afterward, transportation risks are calculated by adopting the fuzzy failure mode and effects analysis (FMEA) method, and then the proposed model is solved by a hybrid algorithm based on the multi-choice goal programming method and particle swarm optimization algorithm (PSO). Eventually, sensitivity analyses on some important model parameters are conducted, and practical managerial/theoretical implications are presented. The obtained results show the efficiency and performance of the model and the developed hybrid algorithm.

Designing an eco-efficient supply chain network considering carbon trade and trade-credit: A robust fuzzy optimization approach

Classical supply chain networks primarily focus on economic optimization by determining the optimal supply chain configuration in a chaotic business environment. Owing to rapidly increasing greenhouse gas emissions, there has been immense pressure from society to design eco-efficient supply chain networks to reduce the carbon emissions generated from supply chain activities at a reasonable cost. This study addresses the eco-efficient supply chain network design problem considering carbon trading and trade credit from suppliers to maximize the total supply chain profit in both the physical and carbon markets. The problem determines the optimal number, location, and capacity of facilities (e.g., production and distribution centers), optimal product flow among entities in the network, optimal product-selling price, and optimal economic order quantity for suppliers under different trade credit schemes. A robust fuzzy optimization model based on the integration of robust optimization and fuzzy programming was applied to address the uncertainties in demand and relevant costs. A case study of a Taiwanese steel firm was conducted to demonstrate the efficacy and efficiency of the proposed model. The results show that the proposed model improves the total supply chain profit, including the profits from physical and carbon markets, by around 3%, and reduces the computation time by approximately 72.44 %, compared to scenario-based robust stochastic programming. Our findings also show that the optimal configuration of the supply chain network is sensitive to different scenarios of carbon trade, and the selection of suppliers is affected by the trade credit policy.

COVID-19: Government subsidy models for sustainable energy supply with disruption risks

The outbreak of the COVID-19 pandemic poses great challenges to the current government subsidy models in the renewable energy sector for recovering in the post-pandemic economy. Although, many subsidy models have been applied to accelerate renewable energy investment decisions. However, it is important to develop a new model to ensure the sustainability of the renewable energy supply network under disruptions on both the supply and demand sides due to hazardous events. This study investigates different subsidy models (renewable credit, supplier subsidy, and retailer subsidy) to find a win-win subsidy model for sustainable energy supply under disruption risks. The objective is to determine the optimal capacity of renewable energy added to the grid, the optimal wholesale price of the power plant, and the optimal retail price of the aggregator under different subsidy models to maximize the economic, social, and environmental benefits of the whole network. A novel scenario-based robust fuzzy optimization approach is proposed to capture the uncertainties of business-as-usual operations (e.g., some relevant costs and demand) and hazardous events (e.g., COVID-19 pandemic). The proposed model is tested in a case study of the Vietnamese energy market. The results show that for a high negative impact level of hazardous events on the supply side, the renewable credit and supplier subsidy models should be considered to recovery the renewable energy market. Further, the proposed approach has a better performance in improving the power plant's robust profit for most of the hazard scenarios than the robust optimization model.

A capacity planning approach for sustainable-resilient supply chain network design under uncertainty: A case study of vaccine supply chain

This paper introduces a multi-objective mathematical model to design a sustainable-resilient supply chain based on strategic and tactical decision levels. The resolution is to proactively plan for an optimal configuration to satisfy customer demands when the firm is highly vulnerable to operational and disruption risks. Compared to previous studies, we take the application of capacity planning in terms of redundancy to design a supply chain network that is resilient toward the demand-side by an optimization framework. A real-world influenza vaccine supply chain is studied to validate the proposed model and examine the tradeoff between resilience and sustainability. A robust fuzzy optimization approach is employed to cope with uncertainties. Then, the multi-objective model is solved by applying multi-choice goal programming with a utility function approach. Accordingly, managerial insights are suggested by analyzing the effects of structural parameters on the quantitative results. It is revealed that having redundancies in the supply chain does not always increase the total costs.

A multi-objective fuzzy robust stochastic model for designing a sustainable-resilient-responsive supply chain network

This study proposes a multi-objective mixed-integer programming model to configure a sustainable supply chain network while considering resilience and responsiveness measures. The model aims at minimizing the total costs and environmental damages while maximizing the social impacts, as well as the responsiveness and resilience levels of the supply chain network. An improved version of the fuzzy robust stochastic optimization approach is proposed to tackle the uncertain data arising in the dynamic business environment. Furthermore, a new version of meta-goal programming named the multi-choice meta-goal programming associated with a utility function is developed to solve the resulting multi-objective model. A case study in the water heater industry is investigated to illustrate the application of the proposed model and its solution approach. The numerical results validate the proposed model and the developed solution method. Finally, interactions between the sustainability, responsiveness, and resilience dimensions are investigated and several sensitivity analyses are performed on critical parameters by which useful managerial insights are provided.

A robust fuzzy optimization approach for reverse logistics network design with buyback offers

PurposeIn this paper, the authors aim to investigate the relationship between buyback policy and the potential number of used products that could be collected by developing a robust fuzzy reverse logistics network.Design/methodology/approachIn this approach, the authors seek to determine the amount of buyback based on the condition of used products at the time of return. In this process, the authors also take into account that apart from the condition of used products, other factors exist that the actual return rate could be dependent on them. This matter propelled us to make a novel distinction between the probability of return estimated from appropriate buybacks offered to consumers, and the actual return rate of used products using fuzzy mathematical methods. Besides that, a compatible robust fuzzy optimization method has been implemented on the model to deal with uncertain properties of it and simultaneously fortifying its responses against any possible effect of return rate fluctuation.FindingsTo analyze and evaluate the model performance, the authors decided to apply a series of exhaustive randomly generated experiments onto it. Also, the authors introduced a Lagrangian relaxation solution methodology to facilitate and improve the solving process of the model. Then, the evaluation of the results enabled us to demonstrate the model validity, and underscore its utility to deal with problems with more sophisticated used product collection process that practitioners tend to encounter in the real-world circumstances.Originality/valueThis study suggests a novel way to design the return rate of used products in a reverse logistics network with buyback offers through a complete set of factors affecting it. Furthermore, the procedure of developing the model encompasses several important aspects that significantly decrease its complexity and improve its applicability.

A heuristic-based multi-choice goal programming for the stochastic sustainable-resilient routing-allocation problem in relief logistics

Natural or man-made disasters impose destructive effects like human injuries and urban infrastructure damages, which lead to disruptions that affect the entire distribution system. This research addresses the routing-allocation problem in the response phase of disaster management. The related literature shows that the researchers had less attention to some features like sustainability and resiliency in the mentioned problem. Hence, to cover these gaps, this study proposes a scenario-based multi-objective programming model to examine the resilient-sustainable routing-allocation problem considering the concept of fairness. The proposed model aims at minimizing total traveling time, total environmental impacts and total demand loss. The fuzzy robust stochastic optimization approach is utilized to cope with uncertain data arisen in disaster conditions. Then, due to the complexity of the research problem, a hybrid approach based on the multi-choice goal programming method and a heuristic algorithm is developed to solve the problem in a reasonable time. A case study is then selected to demonstrate the efficiency of the proposed model and the developed method. Finally, sensitivity analyses have been conducted in some parameters of the model and also the robustness of the solution has been investigated.

A fuzzy robust multi-objective optimization model for building energy retrofit considering utility function: A university building case study

The majority of energy sources are limited and non-renewable and will soon be depleted if overused. One of the world's significant energy consumers is the building sector, which also is accounted for a considerable amount of GHG emissions. This study uses mathematical modelling to find the best strategy for building energy retrofit. The multi-objective optimization model takes into account economic criteria such as profit, initial cost, and payback period, as well as environmental objectives such as energy-saving and the use of clean and renewable energy. On the other hand, unlike many previous studies in which the mathematical models consider specific parts of the building, the generalized mathematical model of this study can examine any desired parts of the building for the decision-maker and add new items to enhance energy efficiency. Besides, the problem is investigated and solved with certain and uncertain parameters to determine the impact of uncertainty on the results, which is closer to reality. In this study, an actual university building is simulated to evaluate the model's validity by implementing the obtained energy retrofit strategy on the simulated building, which led to a 40% decrease in energy consumption. The results indicate that the presented model can find the best possible strategy to improve energy efficiency and significantly affect buildings' energy saving.

Stackelberg Game Approach for Robust Optimization With Fuzzy Variables

In this article, a new robust optimization method is proposed to simultaneously optimize the expectation and variability of system performance with parametric uncertainties and fuzzy variables. The expectation-entropy model is presented to characterize the fuzzy robust optimization problem as an equivalent biobjective optimization problem. An approximate mapping method is developed to calculate the response of fuzzy variables, which improves the computational efficiency of objective functions. Then, according to the decision makers’ preference for objectives, the optimization framework based on Stackelberg game is established. A leader–follower state transition algorithm is designed to search for the equilibrium solutions. Two practical case studies are provided to show the effectiveness of the new optimization approach in both subjective judgment and objective assessment.

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.

Multi-objective fuzzy robust optimization approach to sustainable closed-loop supply chain network design

Nowadays, the importance of sustainable development has persuaded the supply chain managers to shift their network to sustainable supply. This research develops a multi-objective mathematical model to configure a Sustainable Closed-Loop Supply Chain (SCLSC) network for a water tank considering sustainability measures. The goals of the proposed model are optimizing financial, environmental and social impacts of the SCLSC. Generally, the uncertainty exists in configuring the SCLSC network problem according to the changes in the business environment (like transportation costs and demand). As a result, a Fuzzy Robust Optimization (FRO) is applied to cope with uncertainty in this study. Then, the proposed model is solved using the goal programming approach. The numerical results showed some insightful observations regarding planning and strategic decisions for the SCLSC network design. Finally, several sensitivity analyses are carried out on some important parameters, the changes in objective functions are investigated and the robustness of the proposed model is examined.

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 Robust Fuzzy Optimization Model for Closed-Loop Supply Chain Networks Considering Sustainability

Supply chain network design (SCND) is an important strategic decision determining the structure of each entity in the supply chain, which has an important impact on the long-term development of a company. An efficient and effective supply chain network is of vital importance for improving customer satisfaction, optimizing the allocation of resources, and increasing profitability. The environmental concerns and social responsibility awareness of the whole society have spurred researchers and managers to design sustainable supply chains (SSCs) integrating the economic, environmental, and social factors. In addition, the innate uncertainty of the SCND problem requires an integrated method to cope. In this regard, this study develops a multi-echelon multi-objective robust fuzzy closed-loop supply chain network (CLSCN) design model under uncertainty including all three dimensions of sustainability. This model considers the total cost minimization, carbon caps, and social impact maximization concurrently to realize supply chain sustainability, and is able to make a balance between the conflicting multiple objectives. Meanwhile, the uncertainty of the parameters is divided into two categories and addressed with two approaches: the first category is missed working days related to social impact, which is solved by the fuzzy membership theory; the second category is the demand and remanufacturing rate, which is settled by a robust optimization method. To validate the ability and applicability of the model and solution approach, a numerical example is conducted and solved using ILOG CPLEX. The result shows that the supply chain network structure and the value of the optimization objectives will change when considering sustainability and different degrees of uncertainty. This will enable supply chain managers to reduce the environmental impact and enhance the social benefits of their supply chain activities, and design a more stable supply chain to better cope with the influence of uncertainty.

A fuzzy robust stochastic mathematical programming approach for multi-objective scheduling of the surgical cases

In this paper, the problem of elective surgery scheduling is studied, and resources like surgeons, nurses and operating rooms (ORs) are considered. The problem is to assign surgeries to operating rooms in order to meet three goals: (1) maximizing the number of surgeries that can be done using given fixed resources, (2) minimizing the total fixed costs and overtime costs of the ORs, and (3) minimizing the maximum of completion time of operating rooms. We take into account the uncertainty with the stochastic parameter for the regular operating time of OR in model and fuzzy constraint for resources and overtime. A multi-objective model is proposed to choose the operations to be scheduled on the selected day, and to assign the elective surgeries to OR sessions. In the first phase, we formulated a fuzzy robust optimization model and in the second phase, the sensitivity of the model to different values for penalties in the objective function, is analyzed. The efficiency of the proposed solution is validated by numerical results of applying the model to the case of a public hospital in Iran.

Modelling single-period inventory problem by distributionally robust fuzzy optimization method

Modelling single-period inventory problem by distributionally robust fuzzy optimization method

Fuzzy robust optimization for handling feed stream and model parameter uncertainties during comminution process

Uncertainty analysis of an industrial grinding optimization process involving various sources of uncertainties and multiple numbers of objective functions has been studied in this work. Two primary sources of uncertainties, e.g. (1) operational parameters such as feed size distributions that are subjected to uncertainty due to varied range of feed sources that the industrial grinding process handles, and (2) model parameters that are obtained by the regression analysis of experimental data and subjected to regression and experimental errors, have been considered. Moreover, obtaining statistical distributions for these uncertain parameters are practically challenging. Hence, these parameters are considered as fuzzy numbers and the embedded uncertain multi-objective optimization problem has been analyzed using credibility based fuzzy robust optimization (FRO) technique. This technique helps in converting the uncertain fuzzy optimization formulation into a deterministic equivalent form, which can be further utilized to obtain the Pareto solutions by well-developed evolutionary algorithms. Initially, PO solutions are obtained by considering the uncertainty in different sets of uncertain parameters separately. This is followed by the study of amalgamated effect of uncertain parameters on PO solutions. Along with this, different fuzzy measures e.g. credibility, possibility, necessity etc. are utilized to observe their effects on final solutions. PO solutions obtained from possibility and necessity based FRO show the optimistic and pessimistic attitudes of risk, respectively. This provides a key to a decision maker to select any point based on the existing risk appetite. As compared to the deterministic results, the robust Pareto solutions show potential improvements of 26% and 16% in throughput and mid-size fractions, respectively. This generic approach not only provides the solution for robust range of operation based on the risk appetite of the enterprise, but also helps a decision maker to decide which parameters, amidst the set of uncertain parameters, are more sensitive to the results utilizing various fuzzy measures such as credibility, possibility and necessity. Along with this, the PO solutions obtained with robust optimization are compared with the solutions obtained by Expected Value Model (EVM).

TH‐CD‐209‐04: Fuzzy Robust Optimization in Intensity‐Modulated Proton Therapy Planning to Account for Range and Patient Setup Uncertainties

Purpose:We propose to apply a robust optimization model based on fuzzy‐logic constraints in the intensity‐modulated proton therapy (IMPT) planning subject to range and patient setup uncertainties. The purpose is to ensure the plan robustness under uncertainty and obtain the best trade‐off between tumor dose coverage and organ‐at‐risk(OAR) sparing.Methods:Two IMPT plans were generated for 3 head‐and‐neck cancer patients: one used the planning target volume(PTV) method; the other used the fuzzy robust optimization method. In the latter method, nine dose distributions were computed ‐ the nominal one and one each for ±3mm setup uncertainties along three cardinal axes and for ±3.5% range uncertainty. For tumors, these nine dose distributions were explicitly controlled by adding hard constraints with adjustable parameters. For OARs, fuzzy constraints that allow the dose to vary within a certain range were used so that the tumor dose distribution was guaranteed by minimum compromise of that of OARs. We rendered this model tractable by converting the fuzzy constraints to linear constraints. The plan quality was evaluated using dose‐volume histogram(DVH) indices such as tumor dose coverage(D95%), homogeneity(D5%‐D95%), plan robustness(DVH band at D95%), and OAR sparing like D1% of brain and D1% of brainstem.Results:Our model could yield clinically acceptable plans. The fuzzy‐logic robust optimization method produced IMPT plans with comparable target dose coverage and homogeneity compared to the PTV method(unit: Gy[RBE]; average[min, max])(CTV D95%: 59 [52.7, 63.5] vs 53.5[46.4, 60.1], CTV D5% ‐ D95%: 11.1[5.3, 18.6] vs 14.4[9.2, 21.5]). It also generated more robust plans(CTV DVH band at D95%: 3.8[1.2, 5.6] vs 11.5[6.2, 16.7]). The parameters of tumor constraints could be adjusted to control the tradeoff between tumor coverage and OAR sparing.Conclusion:The fuzzy‐logic robust optimization generates superior IMPT with minimum compromise of OAR sparing.This research was supported by the National Cancer Institute Career Developmental Award K25CA168984, by the Fraternal Order of Eagles Cancer Research Fund Career Development Award, by The Lawrence W. and Marilyn W. Matteson Fund for Cancer Research, by Mayo Arizona State University Seed Grant, and by The Kemper Marley Foundation. eRA Person ID(s) for the Principal Investigator: 11017970 (Research Supported by National Institutes of Health)

An enhanced fuzzy robust optimization model for regional solid waste management under uncertainty

In this study, an enhanced fuzzy robust optimization (EFRO) model is proposed for supporting regional solid waste management under uncertainty. This model is an extended version of robust optimization from a stochastic to a fuzzy environment, and novel in the following two aspects: (1) it uses multiple algorithms to tackle fuzzy constraints according to their characteristics; and (2) it incorporates fuzzy violation variables into the model, which could effectively reflect the trade-off between system economy and reliability. The regional waste management of the City of Dalian, China, was used as a case study for demonstration. A variety of solutions was obtained under various weight coefficients and confidence levels. From the case study, it was found that EFRO could help decision makers to design desired waste management alternatives under complex uncertainties. The successful application of EFRO in the studied real case is expected to be a good example for solid waste management in many other cities.

A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in electronics industry

Environmentalism has become an important global issue in the present century. During the recent years, the closed-loop green supply chain management has been increasingly a center of attention as a result of governmental laws and legislations (regarding the environmental effects of any activity) and the soaring consumers' expectations. In this study, effort has been made to investigate a facility location/allocation model for a multi-product closed-loop green supply chain network consisting of manufacturing/remanufacturing and collection/inspection centers as well as disposal center and markets. To design the network, we have proposed a mixed-integer linear programming model capable of reducing the network total costs. The model has been so developed as to consider such environmental objectives as reducing the rate of carbon dioxide emission in the environment throughout the network in question. Moreover, the model has been developed using a robust fuzzy programming approach to investigate the effects of uncertainties of the variable costs, as well as the demand rate, on the network design. To solve the bi-objective programming model, use has been made of the ε-constraint approach and a numerical illustration of Copiers Industry is used to show the applicability of the proposed optimization model. Results have revealed that the model is capable of controlling the network uncertainties as a result of which a robustness price will be imposed on the system.

Development of an Improved Fuzzy Robust Chance-Constrained Programming Model for Air Quality Management

A new uncertain optimization technology, called as improved fuzzy robust chance-constrained programming (IFRCCP) model, was applied for a case study involving air quality management. IFRCCP model was an integration of fuzzy robust optimization and fuzzy chance-constrained programming (FCCP), which was originated from robust possibilistic programming (RPP) model and was an extended version of robust optimization (RO) from stochastic to fuzzy environment. It improved RPP model through incorporating predefined fuzzy violation variables into model and overcoming the limitations in adopting FCCP approach to tackle all fuzzy constraints without consideration of their differences. The existence of violation variables was useful in maintaining the characteristics of RO model and evaluating the trade-off between system economy and reliability. The case study considers a real air quality management system in Fengrun district of Tangshan city, China. The applied results indicated that IFRCCP was capable of providing a sketch of proposed management system and generating a variety of control alternatives as the decision-making base. The successful application of IFRCCP provided good demonstration for air quality management in other cities or other management fields.