Fuzzy Multi-objective Programming 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.

Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems

The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

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.

Multi-Objective Non-Linear Programming Problems in Linear Diophantine Fuzzy Environment

Due to various unpredictable factors, a decision maker frequently experiences uncertainty and hesitation when dealing with real-world practical optimization problems. At times, it’s necessary to simultaneously optimize a number of non-linear and competing objectives. Linear Diophantine fuzzy numbers are used to address the uncertain parameters that arise in these circumstances. The objective of this manuscript is to present a method for solving a linear Diophantine fuzzy multi-objective nonlinear programming problem (LDFMONLPP). All the coefficients of the nonlinear multi-objective functions and the constraints are linear Diophantine fuzzy numbers (LDFNs). Here we find the solution of the nonlinear programming problem by using Karush-Kuhn-Tucker condition. A numerical example is presented.

A multi-period optimization model for medicine supply chains using modified interactive multi-objective fuzzy programming

The research on multi-period optimization using modified interactive multi-objective fuzzy programming for product complaints in pharmaceutical supply chains is new and evolving. This study proposes and develops an integrated multi-period, multi-objective medicine supply chain model in healthcare. The study considers an unknown number of drug manufacturer complaints. The business triad is a term used to describe the combination of the three objectives: time, quality, and cost. The process starts with developing a mathematical model for the business triad. A modified interactive multi-objective fuzzy programming is then proposed for the optimization of the business triad, has been proposed. The proposed method blends expert opinion and experience using fuzzy linguistic variables and a triangle membership function. A numerical example demonstrates the practical application of the proposed model. This study considers a model for fuzzy inventory pharmaceutical products with a two-tier supply chain. This supply chain model aids healthcare decision-makers in acquiring medications that meet the necessary time, quality, and cost standards.

Location–allocation problem for green efficient two-stage vehicle-based logistics system: A type-2 neutrosophic multi-objective modeling approach

In recent decades, global climate change has become one of the most critical environmental issues, leading to increased environmental and social concerns about the sustainability of logistics networks. This study proposes a novel multi-objective, multi-facility location–allocation model for a two-stage solid logistics network that supports green practices. To account for uncertainty in real-world problems, some parameters of the model are represented as triangular type-2 neutrosophic numbers to deal with hesitant situations. The fuzzy model is then converted into a deterministic one using a new ranking approach. Three conflicting objective functions – minimizing total financial costs, maximizing customers’ satisfaction levels, and ensuring sustainable and effective conveyances – are simultaneously optimized using the ϵ-constraint approach. The proposed model and solution approach are tested with two numerical examples. A comparative study is also presented, comparing the proposed approach with other Pareto-based multi-objective approaches, such as the global criterion approach, multi-objective fuzzy programming, and weighted Chebychev programming. Finally, the paper concludes with some remarks.

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.

Multi-skill resource-constrained project scheduling problem considering overlapping: fuzzy multi-objective programming approach to a case study

Resource-constrained project scheduling problem (RCPSP) is a broadly researched issue in the literature. The purpose of the classic form of the problem is scheduling a set of activities considering resource and precedence constraints for minimizing the project completion time. Companies mostly deal with the issue of properly assigning multi-skilled workforces and maintaining the needed skill levels while implementing projects. In this study, a novel MILP model with three objectives is presented to tackle multi-skill RCPSP (MS-RCPSP). This study concentrates on minimizing project makespan, minimizing resource costs as well as tardiness costs, and maximizing quality under uncertainty. However, the standard MS-RCPSP is not able to consider several practical engineering requirements owing to its narrow assumptions. Therefore, key assumptions including overlap between activities, tardiness penalties of activities and the rework duration concept for activities in this model are considered. Due to the complexity of the real world, interval valued fuzzy numbers are taken into account for some of the problem’s parameters. The efficiency of the proposed mathematical framework is represented using both a real case study to construct a railway bridge with 34 activities and large-size problem instances from MMLIB (MM50 and MM100). Since this model is multi-objective, a new extended IVF-ABS approach is presented in this study. Finally, the proposed approach is compared with two methods, namely SO and ABS, from the literature.

МЕТОДЫ НЕЧЕТКОГО МНОГОКРИТЕРИАЛЬНОГО ГРУППОВОГО ПРИНЯТИЯ РЕШЕНИЙ ДЛЯ ЗАДАЧ ЭВАКУАЦИИ ПРИ ЧРЕЗВЫЧАЙНЫХ СИТУАЦИЯХ

The purpose of this article is to analyze the current state of research in the field of fuzzymulticriteria optimization methods, as well as the development of aggregation operators and algorithmsusing fuzzy multicriteria group decision-making using an intuitionistic attitude of linguisticpreferences. The most well-known fuzzy methods of multicriteria optimization are presented:ELECTRE, PROMETHEE, VIKOR, TOPSIS, AHP, ANP, MACBETH, DEMATEL, Shoke integraland DEA, their features, applications and the most cited articles are considered. Most real optimizationproblems may have conflicting goals. The method of fuzzy multi-purpose decision-makingFMODM is also presented for situations where there are inaccuracies and uncertainty in somegoals and variables on which they depend; methods of fuzzy multi-purpose linear programmingFMOLP, fuzzy multi-objective target programming FMOGP and fuzzy heuristic decision-makingmethods. The problem of fuzzy multicriteria group decision-making during evacuation with anintuitive relation of linguistic preferences is considered. It is noted that fuzzy logic methods areparticularly suitable for making evacuation decisions when there is little data, knowledge ofcause-and-effect relationships is inaccurate, and observations and criteria can be expressed inlinguistic qualitative terms. The main stages of group making the best decision among alternativesin a fuzzy environment are presented: combining expert assessments; obtaining a final assessmentfor each alternative represented by a linguistic variable; ranking alternatives; group making themost preferred decision. An approach to group decision-making with an intuitive preference relationshipbased on aggregation procedures is proposed. The group model of decision-making andthe concept of fuzzy group decision and linguistic variables used in predicting an emergency situationand planning evacuation are considered. It is noted that the well-known operators of orderedweighted averaging OWA, LOWA do not take into account the weights of experts. The Low operatoris defined, which allows taking into account the weight values of experts, as well as an approachto determining a fuzzy group solution of aFCS as a type 2 set. Algorithms for determininga fuzzy group multicriteria solution based on aFCS are presented

G-resilient multi-tier supplier selection and order allocation in food industry: a hybrid methodology

In the post epidemic era, food industry associations need to build a green and resilient (G-resilient) supply chains network through supplier selection and order allocation (SS/OA) decisions to avoid unexpected disruption risks and meet uncertain demand and cost for green food. This paper proposes a hybrid methodology using fuzzy multi-objective mixed integer linear programming model (FMOMILPM) to solve G-resilient multi-tier SS/OA problem within the uncertain demand and cost environment in food industry. We first proposed a G-resilient multi-criteria framework that consists of traditional, green and resilience pillars as well as their criteria for evaluating multi-tier suppliers. Second, FMOMILPM is developed based on the fuzzy evaluation of group decision makers and the uncertain demand and cost to handle the G-resilient multi-tier SS/OA problem towards minimizing cost and transportation time of orders and maximizing purchasing value of G-resilient. The LP-metrics and ϵ-constraint methods are employed to obtain a set of Pareto solutions out of the FMOMILPM, and then the final Pareto solution is determined by TOPSIS. The applicability of the proposed methodology is validated by a real case study in the UK halal food industry.

Designing a portfolio-based closed-loop supply chain network for dairy products with a financial approach: Accelerated Benders decomposition algorithm

Product portfolio design is one of the important and effective factors in the financial and physical flows of various supply chains, especially dairy products. Accordingly, the financial and physical flows of the portfolio should be taken into consideration during the supply chain design. In this study, a closed-loop supply chain (CLSC) network is designed for dairy products aiming at maximizing the net cash flow from assets and maximizing the amounts paid to shareholders simultaneously. To find the optimal policy, an accelerated Benders decomposition (ABD) algorithm is implemented to tackle the complexity of the model. Moreover, three multi-objective optimization solution approaches of the weighted sum method (WSM), augmented ε-constraint (AEC), and fuzzy multi-objective programming (FMOP) are implemented to tackle the bi-objectiveness of the model. Next, a real case study in Iran is investigated to reveal the applicability of the developed methodology. Numerical results reveal that the ABD method reduces CPU time by about 10.8%. Moreover, the results of the case study demonstrate that by integrating financial and physical flows, an improvement of 4.8478% in the net cash flow from assets and a 2.3% improvement in the amounts paid to shareholders compared to the current situation.

A Regional Water Resource Allocation Model Based on the Human–Water Harmony Theory in the Yellow River Basin

Considering the issues of water scarcity, water environment deterioration, and unreasonable allocation of water resources in the urban area of the Yellow River Basin, this paper introduces the human–water harmony theory to the allocation of regional water resources. Based on an analysis of the structural characteristics of the regional water resource system, the harmonious water resource allocation (HWRA) model—which includes three sub-systems (i.e., the water service system, ecological environmental system, and economic and social system)—is established. In addition, considering the uncertain factors in the HWRA model, the inexact fuzzy multi-objective programming (IFMOP) method is used to solve the model, aiming at achieving the minimum amount of regional water scarcity, the minimum amount of sewage discharge, and the maximum total economic benefit. A case study of water resource allocation of Binzhou, a city located in the Yellow River Basin, is conducted to validate the model. The model solution results show that the water resource system in Binzhou in 2025 and 2035 could be optimized after harmonious allocation, especially in terms of the water service and ecological environmental systems. Compared with the optimal water resource allocation (OWRA) model, the HWRA model has a more scientific water supply structure, and a smaller amount of sewage discharge. The HWRA model solves the variables using an interval number, so it can flexibly and scientifically reflect the decision-making process.

A Smart Decision Support Framework for Sustainable and Resilient Supplier Selection and Order Allocation in the Pharmaceutical Industry

Supplier selection and order allocation (SS-OA) are two of the most important strategic decisions for supply chain network design and operation. If sustainability and resilience criteria are taken into consideration together and a holistic sustainable and resilient SS-OA is carried out, it may enable the supply chain network to perform better when subjected to disruption scenarios. In this research paper, a novel comprehensive multi-phase, multi-period sustainable, and resilient SS-OA decision support framework has been proposed. This framework integrates fuzzy multi-criteria decision-making (MCDM) techniques with a fuzzy multi-objective mixed integer nonlinear programming (MOMINLP) mathematical model to optimize triple bottom line (TBL) sustainability and resilience criteria simultaneously for a multi-modal, multi-echelon supply chain network. The proposed framework has been implemented using real-time data collected from the pharmaceutical industry. The results show that among the TBL sustainability criteria, product price, past business, innovative capability, and information disclosure rank as the most significant sub-criteria for the DMs in the pharmaceutical industry, while robustness and flexibility are considered the most valued attributes for potential suppliers as far as the resilience criterion is concerned. An assessment of the results has revealed that transfer cost and custom clearance cost together comprise more than two-thirds of the overall cost of the supply chain network. It has also been noted that inland transportation of goods is dominated by rail as the most preferred mode of transport. Transportation by rail is particularly preferred by suppliers located in geographically contiguous countries.

Integrating Fuzzy Multiobjective Programming and System Dynamics to Develop an Approach for Talent Retention Policy Selection: Case on Health-Care Industry.

The demand for medical services has been increasing yearly in aging countries. Medical institutions must hire a large number of staff members to provide efficient and effective health-care services. Because of high workload and pressure, high turnover rates exist among health-care staff members, especially those in nonurban areas, which are characterized by limited resources and a predominance of elderly people. Turnover in health-care institutions is influenced by complex factors, and high turnover rates result in considerable direct and indirect costs for such institutions (Lo and Tseng 2019). Therefore, health-care institutions must adopt appropriate strategies for talent retention. Because institutions cannot determine the most effective talent retention strategy, many of them simply passively adopt a single human resource (HR) policy and make minor adjustments to the selected policy. In the present study, system dynamics modeling was combined with fuzzy multiobjective programming to develop a method for simulating HR planning systems and evaluating the suitability of different HR policies in an institution. We also considered the external insurance policy to be the parameter for the developed multiobjective decision-making model. The simulation results indicated that reducing the turnover rate of new employees in their trial period is the most effective policy for talent retention. The developed procedure is more efficient, effective, and cheaper than the traditional trial-and-error approaches for HR policy selection.

Sustainable microgrid design with peer-to-peer energy trading involving government subsidies and uncertainties

Sustainable microgrid is a feasible approach to handle environmental impacts and satisfy customer demand due to its economic, environmental, and social benefits. Due to the high initial investment cost, the installation rate of microgrids has been limited. Various studies investigated the influence of government subsidies on sustainable microgrid design to increase the installation rate. However, the effect of government subsidies, financial factors, and elasticity coefficient of demand under peer-to-peer energy trading has not been explored in the current sustainable microgrids design literature. To overcome this limitation, this paper investigates the sustainable microgrid design problem to simultaneously consider the effect of government subsidies, peer-to-peer energy trading, time value of money, elasticity coefficient of demand, and uncertainties. The objectives are to maximize total profit and minimize the total environmental cost to satisfy electric energy demand. Fuzzy multi-objective programming is applied to determine the optimal decisions on the number, location, type of renewable energy, the capacity of renewable distributed generation sources, electricity flows, price for selling electricity to demand areas and P2P energy trading, and government subsidy rates. A genetic algorithm and its hybrid versions to include tabu search and simulated annealing are then used to solve the proposed model. Numerical experiments used to evaluate the performance of the proposed model and algorithms show that the proposed genetic algorithm is most effective in maximizing total profit and minimizing environmental cost. Computational results demonstrate that on average, the inclusion of the peer-to-peer trading and government subsidies in the proposed model increases total profit by 13.23% and reduces total environmental cost by 6.29%.

Application of Fuzzy Multi-Objective Programming to Regional Sewer System Planning

Planning of sewer systems typically involves limitations and problems, regardless of whether traditional planning methods or optimization models are used. Such problems include non-quantifiability, fuzzy objectives, and uncertainties in decision-making variables which are commonly applied in the planning of any process. Particularly, uncertainties have prevented the inclusion of these variables in models. Consequently, the theoretical optional solution of the mathematical models is not the true optimum solution to practical problems. In this study, to solve the above problems for regional sewer system planning, multi-objective programming (MOP), nonlinear programming, mixed-integer programming, and compromise fuzzy programming were used. The objectives of this study were two-fold: (1) determination of the necessary decision-making variables or parameters, such as the optimum number of plants, piping layout, size of the plant, and extent of treatment; (2) establishment of a framework and methodology for optimal planning for designing a regional sewer system, matching demanded targets with the lowest cost, which would achieve the aim of lower space and energy requirements as well as consumption and high treatment efficiency for the purpose of meeting effluent standards. The findings of this study revealed that individual regional sewage treatment plants could be merged to form a centralized system. Land acquisition was difficult; thus, reducing the number of plants was required. Therefore, the compromise-fuzzy-based MOP method could effectively be used to build a regional sewer system plan, and the amount of in-plant establishment reached its maximized value with a minimized cost.

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

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

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%.

Selecting the Optimal LoA to Prevent the Expansion of COVID-19 in the Chemical Industry considering Sustainability Factors: A Fuzzy Mathematical Optimization Approach

Automation has attracted interest from the industry sector for its potential to improve energy efficiency, cost efficiency, and environmental performance. By elevating the LoA to the highest degree, associated costs will grow accordingly and its implementation will be far more complicated. This will also result in losing workers and decreasing environmental pollutants. On the other hand, increasing power consumption at high levels of automation leads to the production of greenhouse gases. This paper aims to increase the level of automation (LoA) considering the concept of sustainability. This study presents fuzzy multi-objective programming to determine the optimal LoA considering sustainability factors to achieve competitive advantages. To solve the model, the Zimmermann max-min approach was adopted and a cosmetics factory in Iran was chosen to optimize LoA according to this model. The results showed that it is possible to improve the LoA and also consider sustainability factors with the available resources without using the highest LoA. This study can help managers optimize the LoA in their organizations considering the current resources and sustainability issues, and control the company's return on investment and cost of overhead. They can run the model with every definition of LoA proposed till now. This research can benefit the environment and the workers' health in the production line by reducing environmental pollutants and prevent the dismissal of all personnel due to its negative social effects. It also reduces the risk of COVID-19 by minimizing the number of workers. So far, a mathematical model for selecting optimal LoA in the chemical industry considering sustainability has not been presented.