Exploring the optimal crop planting structure to balance water saving, food security and incomes under the spatiotemporal heterogeneity of the agricultural climate.

Crop planting provided foods, generated incomes, and consumed water resources to different extents under different spatiotemporal agroclimatic conditions. For balancing three aspects, targeting the rice, maize, wheat, and sorghum planted in Liaoning during the recent two decades, we established an integrated research framework consisting of water footprint (WF) accounting, clustering analysis, and fuzzy optimization programming to quantify the temporal trends and spatial distribution of water footprints, and optimized the planting structure under the different spatiotemporal agroclimatic conditions. Results showed that the maximum water footprint differences were 4166.73 m3/t and 4790.71 m3/t in spatial distribution and temporal series, respectively. Based on precipitation, we established 12 agroclimatic scenarios according to K-Means clustering. The fuzzy optimization result indicated that the planting area percent ranges of maize, wheat, rice, and sorghum in Liaoning province were 4.96%-98.62%, 0.00%-8.55%, 0.00%-18.18%, and 0.00%-95.04%, respectively under the different spatiotemporal conditions. This study's methods and results help make targeted decisions related to grain planting structure while considering the complex spatial-temporal conditions.

Fuzzy multi-objective optimization case study based on an anaerobic co-digestion process of food waste leachate and piggery wastewater.

This paper presents the development and evaluation of fuzzy multi-objective optimization for decision-making that includes the process optimization of anaerobic digestion (AD) process. The operating cost criteria which is a fundamental research gap in previous AD analysis was integrated for the case study in this research. In this study, the mixing ratio of food waste leachate (FWL) and piggery wastewater (PWW), calcium carbonate (CaCO3) and sodium chloride (NaCl) concentrations were optimized to enhance methane production while minimizing operating cost. The results indicated a maximum of 63.3% satisfaction for both methane production and operating cost under the following optimal conditions: mixing ratio (FWL: PWW) - 1.4, CaCO3 - 2970.5 mg/L and NaCl - 2.7 g/L. In multi-objective optimization, the specific methane yield (SMY) was 239.0 mL CH4/g VSadded, while 41.2% volatile solids reduction (VSR) was obtained at an operating cost of 56.9 US$/ton. In comparison with the previous optimization study that utilized the response surface methodology, the SMY, VSR and operating cost of the AD process were 310 mL/g, 54% and 83.2 US$/ton, respectively. The results from multi-objective fuzzy optimization proves to show the potential application of this technique for practical decision-making in the process optimization of AD process.

FACNN: fuzzy-based adaptive convolution neural network for classifying COVID-19 in noisy CXR images.

COVID-19 detection using chest X-rays (CXR) has evolved as a significant method for early diagnosis of the pandemic disease. Clinical trials and methods utilize X-ray images with computer and intelligent algorithms to improve detection and classification precision. This article thus proposes a fuzzy-based adaptive convolution neural network (FACNN) model to improve the detection precision by confining the false rates. The feature extraction process between the successive regions is validated using a fuzzy process that classifies labeled and unknown pixels. The membership functions are derived based on high precision features for detection and false rate suppression process. The convolution neural network process is responsible for increasing detection precision through recurrent training based on feature availability. This availability analysis is verified using fuzzy derivatives under local variances. Based on variance-reduced features, the appropriate regions with labeled and unknown features are used for normal or infected classification. Thus, the proposed FACNN improves accuracy, precision, and feature extraction by 14.36%, 8.74%, and 12.35%, respectively. This model reduces the false rate and extraction time by 10.35% and 10.66%, respectively.

Path planning algorithm for percutaneous puncture lung mass biopsy procedure based on the multi-objective constraints and fuzzy optimization.

Objective. The percutaneous puncture lung mass biopsy procedure, which relies on preoperative CT (Computed Tomography) images, is considered the gold standard for determining the benign or malignant nature of lung masses. However, the traditional lung puncture procedure has several issues, including long operation times, a high probability of complications, and high exposure to CT radiation for the patient, as it relies heavily on the surgeon's clinical experience.Approach.To address these problems, a multi-constrained objective optimization model based on clinical criteria for the percutaneous puncture lung mass biopsy procedure has been proposed. Additionally, based on fuzzy optimization, a multidimensional spatial Pareto front algorithm has been developed for optimal path selection. The algorithm finds optimal paths, which are displayed on 3D images, and provides reference points for clinicians' surgical path planning.Main results.To evaluate the algorithm's performance, 25 data sets collected from the Second People's Hospital of Zigong were used for prospective and retrospective experiments. The results demonstrate that 92% of the optimal paths generated by the algorithm meet the clinicians' surgical needs.Significance.The algorithm proposed in this paper is innovative in the selection of mass target point, the integration of constraints based on clinical standards, and the utilization of multi-objective optimization algorithm. Comparison experiments have validated the better performance of the proposed algorithm. From a clinical standpoint, the algorithm proposed in this paper has a higher clinical feasibility of the proposed pathway than related studies, which reduces the dependency of the physician's expertise and clinical experience on pathway planning during the percutaneous puncture lung mass biopsy procedure.

Adaptive fuzzy iterative learning control based neurostimulation system and in-silico evaluation.

Closed-loop neural stimulation has been an effective treatment for epilepsy patients. Currently, most closed-loop neural stimulation strategies are designed based on accurate neural models. However, the uncertainty and complexity of the neural system make it difficult to build an accurate neural model, which poses a significant challenge to the design of the controller. This paper proposes an Adaptive Fuzzy Iterative Learning Control (AFILC) framework for closed-loop neural stimulation, which can realize neuromodulation with no model or model uncertainty. Recognizing the periodic characteristics of neural stimulation and neuronal firing, Iterative Learning Control (ILC) is employed as the primary controller. Furthermore, a fuzzy optimization module is established to update the internal parameters of the ILC controller in real-time. This module enhances the anti-interference ability of the control system and reduces the influence of initial controller parameters on the control process. The efficacy of this strategy is evaluated using a neural computational model. The simulation results validate the capability of the AFILC strategy to suppress epileptic states. Compared with ILC-based closed-loop neurostimulation schemes, the AFILC-based neurostimulation strategy has faster convergence speed and stronger anti-interference ability. Moreover, the control algorithm is implemented based on a digital signal processor, and the hardware-in-the-loop experimental platform is implemented. The experimental results show that the control method has good control performance and computational efficiency, which provides the possibility for future application in clinical research.

Arsenate removal using chitosan-coated bentonite via fixed-bed system: a process integration by fuzzy optimization.

Groundwater contamination is a global concern that has detrimental effect on public health and the environment. Sustainable groundwater treatment technologies such as adsorption require attaining a high removal efficiency at a minimal cost. This study investigated the adsorption of arsenate from groundwater utilizing chitosan-coated bentonite (CCB) under a fixed-bed column setup. Fuzzy multi-objective optimization was applied to identify the most favorable conditions for process variables, including volumetric flow rate, initial arsenate concentration, and CCB dosage. Empirical models were employed to examine how initial concentration, flow rate, and adsorbent dosage affect adsorption capacity at breakthrough, energy consumption, and total operational cost during optimization. The ε-constraint process was used in identifying the Pareto frontier, effectively illustrating the trade-off between adsorption capacity at breakthrough and the cost of the fixed-bed system. The integration of fuzzy optimization for adsorption capacity and its total operating cost utilized the global solver function in LINGO 20 software. A crucial equation derived from the Box-Behnken design and a cost equation based on energy and material usage in the fixed-bed system was employed. The results from identifying the Pareto front determined boundary limits for adsorption capacity at breakthrough (ranging from 12.96 ± 0.19 to 12.34 ± 0.42 µg/g) and total operating cost (ranging from 955.83 to 1106.32 USD/kg). An overall satisfaction level of 35.46% was achieved in the fuzzy optimization process. This results in a compromise solution of 12.90 µg/g for adsorption capacity at breakthrough and 1052.96 USD/kg for total operating cost. Henceforth, this can allow a suitable strategic decision-making approach for key stakeholders in future applications of the adsorption fixed-bed system.

Advancing gasoline desulfurization: Multi-objective fuzzy optimization in systems technology.

Ultrasonic-assisted oxidative desulfurization (UAOD) is utilized to lessen environmental problems due to sulfur emissions. The process uses immiscible polar solvents and ultrasonic waves to enhance desulfurization efficiency. Prior research focused on comparing the effectiveness of UAOD for gasoline using response surface methodology. This study evaluates the desulfurization efficiency and operating costs, including ultrasonic power, irradiation time, and oxidant amount to determine optimal conditions. The study used a multi-objective fuzzy optimization (MOFO) approach to evaluate the economic viability of UAOD for gasoline. It identified upper and lower boundaries and then optimized the desulfurization efficiency and operating costs while considering uncertainty errors. The fuzzy model employed max-min aggregation to optimize the degree of satisfaction on a scale from 0 (unsatisfied) to 1 (satisfied). Optimal conditions for gasoline UAOD were found at 445.43 W ultrasonic power, 4.74 min irradiation time, and 6.73 mL oxidant, resulting in a 66.79 % satisfaction level. This yielded a 78.64 % desulfurization efficiency (YA) at an operating cost of 13.49 USD/L. Compared to existing literature, gasoline desulfurization was less efficient and less costly. The solutions provided by MOFO demonstrate not only economic viability through decreased overall operating costs and simplified process conditions, but also offer valuable insights for optimizing prospective future industrial-scale UAOD processes.

Manufacturing system reconfiguration towards sustainable production: a novel hybrid optimization methodology.

Developing a sustainable manufacturing system is a progressively challenging issue as governments across the world have been enforcing increasingly severe regulations by promoting the reduction of environmental waste for manufacturing and energy-saving production activities. Thus, there is a need for developing a sustainable manufacturing system that can be fully examined by incorporating ecological aspects (e.g., consumed energy) for related operations of a manufacturing system using computer-based discrete event simulation tools. In this study, a combined framework of a novel hybrid fuzzy multi-objective optimization and discrete event simulation approach is presented. We combine ecological and economic data and optimization techniques that are aimed at minimizing economic and ecological objectives in a manufacturing system at an early design phase. Hence, the fuzzy multi-objective optimization model is formulated by incorporating economic and ecological parameters. Again, the discrete event simulation model is established based on a comprehensive performance evaluation of the production system. This study also supports design decisions in determining optimum machine numbers, lighting, and cooling equipment required for the production processes within the sustainable manufacturing in conjunction with the most effective level of material flows. In addition, an integrated Decision-Making Trial and Evaluation Laboratory (DEMATEL)-epsilon constraint approach is applied to handle the multiple-objective optimization problem towards a set of trade-offs among the optimization objectives. A real-life application is carried out for investigating the applicability of the created hybrid framework. The findings of this study demonstrate that this framework is useful as a decision-making tool since it can develop a sustainable manufacturing system design considering an optimal solution associated with amounts of energy usage and CO2 emissions under economic constraints.

Cell-specific genome-scale metabolic modeling of SARS-CoV-2-infected lung to identify antiviral enzymes.

Computational systems biology plays a key role in the discovery of suitable antiviral targets. We designed a cell-specific, constraint-based modeling technique for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-infected lungs. We used the gene sequence of the alpha variant of SARS-CoV-2 to build a viral biomass reaction (VBR). We also used the mass proportion of lipids between the viral biomass and its host cell to estimate the stoichiometric coefficients of viral lipids in the reaction. We then integrated the VBR, the gene expression of the alpha variant of SARS-CoV-2, and the generic human metabolic network Recon3D to reconstruct a cell-specific genome-scale metabolic model. An antiviral target discovery (AVTD) platform was introduced using this model to identify therapeutic drug targets for combating COVID-19. The AVTD platform not only identified antiviral genes for eliminating viral replication but also predicted side effects of treatments. Our computational results revealed that knocking out dihydroorotate dehydrogenase (DHODH) might reduce the synthesis rate of cytidine-5'-triphosphate and uridine-5'-triphosphate, which terminate the viral building blocks of DNA and RNA for SARS-CoV-2 replication. Our results also indicated that DHODH is a promising antiviral target that causes minor side effects, which is consistent with the results of recent reports. Moreover, we discovered that the genes that participate in the de novo biosynthesis of glycerophospholipids and ceramides become unidentifiable if the VBR does not involve the stoichiometry of lipids.

A global satisfaction degree method for fuzzy capacitated vehicle routing problems.

There are several uncertain capacitated vehicle routing problems whose delivery costs and demands cannot be estimated using deterministic/statistical methods due to a lack of available and/or reliable data. To overcome this lack of data, third-party information coming from experts can be used to represent those uncertain costs/demands as fuzzy numbers which combined to an iterative-integer programming method and a global satisfaction degree is able to find a global optimal solution. The proposed method uses two auxiliary variables α , λ and the cumulative membership function of a fuzzy set to obtain real-valued costs and demands prior to find a deterministic solution and then iteratively find an equilibrium between fuzzy costs/demands via α and λ. The performed experiments allow us to verify the convergence of the proposed algorithm no matter the initial selection of parameters and the size of the problem/instance.

An application of interactive fuzzy optimization model for redesigning supply chain for resilience.

Supply chain disruptions compel professionals all over the world to consider alternate strategies for addressing these issues and remaining profitable in the future. In this study, we considered a four-stage global supply chain and designed the network with the objectives of maximizing profit and minimizing disruption risk. We quantified and modeled disruption risk as a function of the geographic diversification of facilities called supply density (evaluated based on the interstage distance between nodes) to mitigate the risk caused by disruptions. Furthermore, we developed a bi-criteria mixed-integer linear programming model for designing the supply chain in order to maximize profit and supply density. We propose an interactive fuzzy optimization algorithm that generates efficient frontiers by systematically taking decision-maker inputs and solves the bi-criteria model problem in the context of a realistic example. We also conducted disruption analysis using a discrete set of disruption scenarios to determine the advantages of the network design from the bi-criteria model over the traditional profit maximization model. Our study demonstrates that the network design from the bi-criteria model has a 2% higher expected profit and a 2.2% lower profit variance under disruption than the traditional profit maximization solution. We envisage that this model will help firms evaluate the trade-offs between mitigation benefits and mitigation costs.

Dynamic Performance Assessment of Hospitals by Applying Credibility-Based Fuzzy Window Data Envelopment Analysis.

The goal of the current research is to propose the credibility-based fuzzy window data envelopment analysis (CFWDEA) approach as a novel method for the dynamic performance evaluation of hospitals during different periods under data ambiguity and linguistic variables. To reach this goal, a data envelopment analysis (DEA) method, a window analysis technique, a possibilistic programming approach, credibility theory, and chance-constrained programming (CCP) are employed. In addition, the applicability and efficacy of the proposed CFWDEA approach are illustrated utilizing a real data set to evaluate the performance of hospitals in the USA. It should be explained that three inputs including the number of beds, labor-related expenses, patient care supplies, and other expenses as well as three outputs including the number of outpatient department visits, the number of inpatient department admissions, and overall patient satisfaction level, are considered for the dynamic performance appraisal of hospitals. The experimental results show the usefulness of the CFWDEA method for the evaluation and ranking of hospitals in the presence of fuzzy data, linguistic variables, and epistemic uncertainty.

Dynamic collaborative optimization for disaster relief supply chains under information ambiguity.

Large-scale disasters occur worldwide, with a continuing surge in the frequency and severity of disruptive events. Researchers have developed several optimization models to address the critical challenges of disaster relief supply chains (e.g., emergency material reserving and scheduling inefficiencies). However, most developed algorithms are proven to have low fault tolerance, which makes it difficult for disaster relief supply chain managers to obtain optimal solutions and meet the emergency distribution requirements within a limited time frame. Considering the uncertainty and ambiguity of disaster relief information and using Interval Type-2 Fuzzy Set (IT2TFS), this paper presents a collaborative optimization model based on an integrative emergency material supplier evaluation framework. The optimal emergency material suppliers are first selected using a multi-attribute group decision-making ranking method. Multi-objective fuzzy optimization is then run in three emergency phases: early -, mid-, and late-disaster relief stages. Focusing on a massive flash flood disaster event in Yunnan Province as a case study, a comprehensive numerical analysis tests and validates the developed model. The results revealed that the proposed optimization method can optimize emergency material planning while ensuring that reserve material safety inventory is always maintained at a reasonable level. The presented method suggests a fuzzy interval to prevent emergency materials' safety inventory shortage and minimize continuous life/property losses in disaster-affected areas.

Human/SARS-CoV-2 genome-scale metabolic modeling to discover potential antiviral targets for COVID-19.

BACKGROUND: Coronavirus disease 2019 (COVID-19) has caused a substantial increase in mortality and economic and social disruption. The absence of US Food and Drug Administration-approved drugs for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) highlights the need for new therapeutic drugs to combat COVID-19. METHODS: The present study proposed a fuzzy hierarchical optimization framework for identifying potential antiviral targets for COVID-19. The objectives in the decision-making problem were not only to evaluate the elimination of the virus growth, but also to minimize side effects causing treatment. The identified candidate targets could promote processes of drug discovery and development. SIGNIFICANT FINDINGS: Our gene-centric method revealed that dihydroorotate dehydrogenase (DHODH) inhibition could reduce viral biomass growth and metabolic deviation by 99.4% and 65.6%, respectively, and increase cell viability by 70.4%. We also identified two-target combinations that could completely block viral biomass growth and more effectively prevent metabolic deviation. We also discovered that the inhibition of two antiviral metabolites, cytidine triphosphate (CTP) and uridine-5'-triphosphate (UTP), exhibits effects similar to those of molnupiravir, which is undergoing phase III clinical trials. Our predictions also indicate that CTP and UTP inhibition blocks viral RNA replication through a similar mechanism to that of molnupiravir.

Computer-Aided Design for Identifying Anticancer Targets in Genome-Scale Metabolic Models of Colon Cancer.

The efficient discovery of anticancer targets with minimal side effects is a major challenge in drug discovery and development. Early prediction of side effects is key for reducing development costs, increasing drug efficacy, and increasing drug safety. This study developed a fuzzy optimization framework for Identifying AntiCancer Targets (IACT) using constraint-based models. Four objectives were established to evaluate the mortality of treated cancer cells and to minimize side effects causing toxicity-induced tumorigenesis on normal cells and smaller metabolic perturbations. Fuzzy set theory was applied to evaluate potential side effects and investigate the magnitude of metabolic deviations in perturbed cells compared with their normal counterparts. The framework was applied to identify not only gene regulator targets but also metabolite- and reaction-centric targets. A nested hybrid differential evolution algorithm with a hierarchical fitness function was applied to solve multilevel IACT problems. The results show that the combination of a carbon metabolism target and any one-target gene that participates in the sphingolipid, glycerophospholipid, nucleotide, cholesterol biosynthesis, or pentose phosphate pathways is more effective for treatment than one-target inhibition is. A clinical antimetabolite drug 5-fluorouracil (5-FU) has been used to inhibit synthesis of deoxythymidine-5'-triphosphate for treatment of colorectal cancer. The computational results reveal that a two-target combination of 5-FU and a folate supplement can improve cell viability, reduce metabolic deviation, and reduce side effects of normal cells.

Fuzzy Optimization for the Remediation of Ammonia: A Case Study Based on Electrochemical Oxidation.

This case study covers the application of the fuzzy optimization in simultaneously satisfying various constraints that include the compliance of ammonia and nitrate concentrations with stringent environmental standards. Essential components in the multi-criteria decision-making analysis is in the utilization of the Box-Behnken design (BBD) response equations, cost equations and the cumulative uncertainty of response towards the sodium chloride dosage, current density and electrolysis time parameters. The energy consumption in the electrochemical oxidation of ammonia plays an essential role in influencing the total operating cost analysis. The determination of boundary limits based on the global optimum resulted in the complete ammonia removal and USD 64.0 operating cost as its maximum boundary limits and the 40.6% ammonia removal and USD 17.1 as its minimum boundary limits. Based on the fuzzy optimal results, the overall satisfaction level incurred a decrease in adhering with a lower ammonia standard concentration (10 mg/L at 80.3% vs. 1.9 mg/L at 76.1%) due to a higher energy consumption requirement. Global optimal fuzzy results showed to be highly cost efficient (232.5% lower) as compared to using BBD alone. This demonstrates the practicality of fuzzy optimization applications in the electrochemical reactions.

Fuzzy Optimization on the Synthesis of Chitosan-Graft-Polyacrylic Acid with Montmorillonite as Filler Material: A Case Study.

In this paper, the synthesis of a chitosan-montmorillonite nanocomposite material grafted with acrylic acid is presented based on its function in a case study analysis. Fuzzy optimization is used for a multi-criteria decision analysis to determine the best desirable swelling capacity (YQ) of the material synthesis at its lowest possible variable cost. For YQ, the integrating the result's cumulative uncertainty is an essential element to investigate the feasibility of the developed model equation. The Pareto set analysis is able to set the appropriate boundary limits for YQ and the variable cost. Two case studies are presented in determining the lowest possible cost: Case 1 for maximum YQ, and Case 2 for minimum YQ. These boundary limits were used in the fuzzy optimization to determine its global optimum results that achieved the overall satisfaction ratings of 67.2% (Case 1) and 52.3% (Case 2). The synthesis of the polyacrylic acid/chitosan material for Case 1 resulted in 305 g/g YQ and 10.8 USD/kg, while Case 2 resulted in 97 g/g YQ and 12.3 USD/kg. Thus, the fuzzy optimization approach proves to be a practical method for examining the best possible compromise solution based on the desired function to adequately synthesize a material.

Duality in nonlinear programming problems under fuzzy environment with exponential membership functions.

In this paper, we have established appropriate duality relations for a general nonlinear optimization problem under fuzzy environment, taking exponential membership functions and using the aspiration level approach. A numerical example has also been shown to justify the results presented in the paper.

Allocation of marine environmental carrying capacity in the Xiamen Bay.

Three optimization methods are employed to allocate Marine Environmental Carrying Capacity (MECC) in the Xiamen Bay. The hydrodynamic and pollutant fields are first simulated by the Princeton Ocean Model. Taking phosphorus as an index of the water quality, the response fields are then calculated. These response fields represent the relationship between the concentration of the sea zone and the pollution sources. Finally, MECC is optimized and distributed in the Xiamen Bay by three optimization methods. The results show classical linear optimization can only maximize the satisfaction level for one of the stake holders', e.g., dischargers or environmental protection bureau, satisfaction level. However, the fuzzy and grey fuzzy optimizations can provide a compromise, and therefore a fairer result, by incorporating the conflicting goals of all of the different stakeholders. Compared with fuzzy optimization, the grey fuzzy optimization provides a more flexible choice for the decision-makers.

Contribuição para análise dos custos no tratamento da água utilizando programação linear fuzzy: um modelo para o gerenciamento do abastecimento do município de Campos (RJ) / Contribution to cost analysis in water treatment using fuzzy linear programming: a model for the supply management in the city of Campos, Rio de Janeiro, Brazil

RESUMO A água é um dos recursos naturais essenciais à sobrevivência humana, porém tem sofrido com problemas como sobrecarga de utilização, em âmbito global; distribuição desigual; e escassez, o que contribui negativamente com a disponibilidade do recurso, evidenciando, assim, a crise da água. ­Nesse cenário, surge então a necessidade de se gerenciar de maneira eficaz esse recurso que é tão importante e que apresenta fortes componentes de incertezas. Um importante objeto do gerenciamento é o tratamento químico pelo qual a água bruta passa para se tornar tratada e, então, adequada para o consumo - este processo corresponde ao segundo maior custo nas estações de tratamento de água, atrás apenas de despesas envolvendo recursos humanos, materiais e serviços. Sendo assim, o presente trabalho propõe um modelo de programação linear que incorpora a lógica fuzzy, uma ferramenta eficiente em modelos com incertezas, para auxiliar no gerenciamento de abastecimento de água, considerando os custos com produtos químicos usados no tratamento desse recurso no município de Campos dos Goytacazes. Este modelo foi resolvido utilizando o ambiente Rstudio e apresentou uma redução dos custos em 9,8% em relação ao modelo de programação linear padrão preparado para o sistema. Conclui-se, então, que o trabalho desenvolvido serve de ponto de partida para uma análise mais minuciosa sobre o impacto dos custos de alocação de água tratada no município e contribui positivamente para a racionalização da água bruta.

ABSTRACT Water is one of the essential natural resources for human survival, but it has undergone problems such as: use overload at global level; unequally distribution; and scarcity that contributes negatively to the availability of the resource, thus evidencing a water crisis. Thus, there is a need to effectively manage this important resource, which presents strong components of uncertainties. An important management object is the chemical treatment through which raw water passes in order to be treated and then appropriate for consumption, because it corresponds to the second largest cost in water treatment plants, only after expenses involving human resources, materials, and services. Thus, the present work proposes a linear programming model that incorporates the fuzzy logic, which is an efficient tool in models with uncertainties to assist in any water supply management, considering costs with chemicals used in the treatment of this resource in the city of Campos dos Goytacazes, Brazil. This model was solved using the Rstudio environment and presented a 9.8% cost reduction compared with the standard linear programming model prepared for the system. In conclusion, the developed work serves as a starting point for a more detailed analysis of the impact of the costs of treated water allocation in the municipality and contributes positively to the raw water rationalization.