A Multi-Criteria Model for the Techno-Economic Evaluation of Fat Removal Technologies From Dairy Waste

This paper presents a multi-criteria model to identify the best technology for separating fat from dairy waste and evaluates the economic feasibility of its implementation. Also, the model incorporates the analysis of the project specificities. The methodology was structured in four steps: (i) identification of criteria and technologies by systematic literature review; (ii) acquisition of qualitative information (linguistic variables) from Brazilian and international experts; (iii) application of the TOPSIS 2-tuple multi-criteria linguistic method to rank the technologies; and (iv) evaluation of the economic viability of the best technology identified using the EMIM (expanded multi-index methodology). Separation by centrifugal force, solvent, heating/decanting, acid hydrolysis, and combined methods were the separation technologies most used in the literature and, therefore the considered alternatives. The model was validated in a dairy industry that produces 3,000 m3/day of waste, with 3% fat. The performance of the technologies concerning five criteria was between medium poor and good for both groups of experts. Also, the experts indicate centrifugal force as the preferred technology. This technology is economically viable, as it presented a high degree of return and low levels of risks and sensitivities. It is estimated a potential profit of R$ 55 million (NPV) over the project’s entire life cycle, equivalent to an annual return of approximately R$ 14 million (ANPV). This represents an Additional Return on Investment—ROIA of 51.17% annually. The Payback discounted occurs in the first year of its implementation. Similar analyses may apply the model we propose for other contexts involving technologies selection.


Introduction
Every year, worldwide, it is estimated that between 4 and 11 million tons of dairy waste are released into the environment (Ahmad et al., 2019).This procedure poses a risk to biodiversity (Damert et al., 2017;Rosa et al., 2009).If discarded without treatment, this waste can alter the soil's physical and chemical properties, resulting in reduced productivity of crops and the availability of oxygen in the water (De Jesus et al., 2015;Gabisa & Gheewala, 2018;Maccarini et al., 2020).Dairy waste may contain dissolved and suspended solids, lactose, and fats resulting in high chemical oxygen demand (COD) and biological oxygen demand (BOD) (Slavov, 2017).The presence of fat, oil, and grease in the dairy waste may form a film on the water's surface, precluding the oxygen transfer and leading to lower survival of aquatic plants and animals (Ahmad et al., 2019).
The recovery of compounds of interest from dairy waste can generate environmental and economic gains (Cao et al., 2020;Gopinatha Kurup et al., 2019;Kavacik & Topaloglu, 2010;Osset-a´lvarez et al., 2019).Previous studies have reported different technologies for fat separation, such as centrifugal force (Khatri & Shao, 2017), use of solvents (Phan et al., 2016), heating and decanting (Shahryar Jafarinejad, 2019), acid/aqueous hydrolysis (Daaou & Bendedouch, 2012), or combined methodologies (El-Naas et al., 2014).Centrifugation has been reported to be a simple, reliable, and economical method of fat separation (Khatri & Shao, 2017).It requires low space, short operation times, and low operation costs (Phan et al., 2016).The utilization of solvents may destabilize emulsions and separate the fat from wastes, being efficiency dependent, mainly on the type of solvent used (Shahryar Jafarinejad, 2019).This technology also has low cost and allows the reutilization of the solvent for posterior use (Yang et al., 2006).The use of heating and decanting has been proposed as a suitable methodology and allows the utilization of the removed fat for food applications (Shahryar Jafarinejad, 2019).However, it is vulnerable to fire hazards (Putatunda et al., 2019).The utilization of acid hydrolysis has a low cost, but it is non-continuous process (Daaou & Bendedouch, 2012).In combination methods, a bed bioreactor and polyvinyl alcohol may be used.From the industry point of view, a suitable technology must have high yield and be energy-efficient and economically viable (El-Naas et al., 2014).Industries aim to achieve the highest fat removal separation as possible (Anderson et al., 2016;Dada et al., 2018).
The effective waste management strategy must consider the complex interdependencies and interactions between waste handling processes and their effects on competing management objectives (e.g., minimizing costs, maximizing net energy production, increasing waste diversion landfills, and minimize greenhouse gas emissions), a complex choice as it involves several conflicting criteria to be assessed (Tan et al., 2014).
Decision-making based on multiple criteria methods (multi-criteria decision-making-MCDM) focuses on solving multiple criteria decision problems, that is, complex decision situations in which several, often contradictory, points of view must be considered (Vincke, 1992).The usual approach is to select the best alternative from the set of possibilities relates to the predefined attributes (Anojkumar et al., 2014).The application of the MCDM serves to represent different approaches in a multi-criteria context, including decision-making, decision support, and decision analysis (de Almeida et al., 2017;Vincke, 1992).
To analyze the economic viability (EV) of an investment project (IP), there are traditional methodologies that were proposed by (Lima et al., 2015;Souza & Clemente, 2012).These authors named them the multiindex methodology (MIM) and the expanded multi-index methodology (EMIM).The approaches for analyzing EV of an IP can be divided into three groups, namely: deterministic EMIM, and stochastic with the use of Monte Carlo simulation (MCS), and real options analysis-ROA (Copeland & Antikarov, 2002;Dranka et al., 2020;Lima et al., 2015Lima et al., , 2017;;Souza & Clemente, 2012).
In concern to ROA (Real Options Analysis) we emphasize that this methodology can be applied in investment projects appraisal that present relevant managerial uncertainties and flexibilities (Copeland & Antikarov, 2002;Dixit & Pindyck, 1994;Dranka et al., 2020).
Some companies deal with this issue by developing strategies and activities aimed at sustainability (Penz et al., 2019).According to (Ikhu-Omoregbe & Masiiwa, 2002;Na˘da˘ban et al., 2016), linguistic variables are used so that it is possible, in the decision-making process, to consider human cognitive ability, that is, when it is not possible to apply precision in judgment.Linguistic variables are words or sentences in natural language that help express the decision maker's feeling or intention (Zimmermann, 2001).In the context of assisting the decision-making process, Fuzzy numbers were introduced (Mardani et al., 2015).
Previous studies that evaluated the fat separation technologies were experimental approaches and aimed to identify an adequate, efficient, and low-cost technology (Daaou & Bendedouch, 2012;El-Naas et al., 2014;Khatri & Shao, 2017).However, they were not supported by a model to help select the ideal technology.Therefore, it is necessary a systematic strategy to assist in the choice of the most suitable technology for fat separation from dairy wastes.
Furthermore, an economic assessment of the technology should be performed to highlight the possible gains for the dairy industry.To the best of our knowledge, this is the first study to construct a multi-criteria model to assist dairy companies in making decisions about their generated effluents.
The fuzzy linguistic approach has been employed successfully to various contexts.Nevertheless, this method has a limitation, the loss of information caused by the need to express the results in the initial expression domain that is discrete by an approximate process.This loss of information indicates a lack of precision in the results from the fusion of linguistic information.2-tuple linguistic model overcomes this limitation.The main advantage of this representation is to be continuous in its domain.Therefore, it may express any counting of information in the universe of the discourse (Herrera & Martı´nez, 2000).
Therefore, the objective of this study is to present an MCDM approach to select the best separation technology for fat removal from dairy wastes and evaluate the economic viability of its application in a real dairy processor.
The methodology was structured in four steps: (i) identification of criteria and technologies by systematic literature review; (ii) acquisition of qualitative information (linguistic variables) from Brazilian and international experts; (iii) application of the TOPSIS 2-tuple multi-criteria linguistic method to rank the technologies; and (iv) evaluation of the economic viability of the best technology identified using the EMIM (expanded multiindex methodology).

Preliminary: Linguistic 2-tuple Model
The 2-tuple linguistic computational model (Herrera & Martı´nez, 2000) is a symbolic model that extends the use of indexes modifying the fuzzy linguistic approach representation.It includes a parameter to the basic linguistic representation in order to improve the accuracy of the linguistic computations after the retranslation step, keeping the computing with words scheme showed in and the interpretability of the results (Herrera & Martı´nez, 2000;Herrera & Martinez, 2001).The computing with words scheme can be summarized in the following steps: (i) linguistic input; (ii) translation; (iii) manipulation; (iv) retranslation; and (v) linguistic input (Yager, 1999).(Herrera & Martı´nez, 2000;Herrera & Martinez, 2001) developed the 2-tuple linguistic representation model based on the concept of symbolic translation.It is used for representing the linguistic assessment information by means of a 2-tuple (s i , a i ), where s i is a linguistic label from the predefined linguistic term set S and a i is the value of symbolic translation, with a i 2 [20.5, 0.5).
Definition 1 (Herrera & Martı´nez, 2000;Herrera & Martinez, 2001).Let b be the result of an aggregation of the indexes of a set of labels assessed in a linguistic term set S, that is, the result of a symbolic aggregation operation.b 2 [0, g], being g the cardinality of S. Let i = round (b) and a = b2i be two values such that i 2 [0, g] and a 2 [20.5, 0.5), then a is called a Symbolic Translation.Definition 2 (Herrera & Martı´nez, 2000;Herrera & Martinez, 2001).Let S = {s 0 , s 1 , . . ., s g } be a linguistic term set and b 2 [0, g] be a value representing the result of a symbolic aggregation operation, then the 2-tuple that expresses the equivalent information to b is obtained with the following function: where round (Á) is the usual round operation, s i has the closest index label to b and a i is the value of the symbolic translation.
Definition 3 (Herrera & Martı´nez, 2000;Herrera & Martinez, 2001).Let S = {s 0 , s 1 , . . ., s g } be a linguistic term set and (s i , a i ) be a 2-tuple.There is always a function D 21 can be defined, such that, from a 2-tuple (s i , a i ) it returns its equivalent numerical value b2 [0, g], which is: From Definitions 1 and 2, we can conclude that the conversion of a linguistic term into a linguistic 2-tuple consists of adding a value 0 as symbolic translation: D(s i ) = (s i , 0).Definition 4 (Herrera & Martı´nez, 2000;Herrera & Martinez, 2001).Let a = (s k , a k ) and b = (s l , a l ) be two 2-tuples, they should have the following properties: (3) There is exists a negative operator: Neg(s i , a) =D(g2 (D 21 (s i , a))), where (s i , a i ) is an arbitrary 2-tuple, g + 1 is the cardinality of S, S = {s 0 , s 1 , . . ., s g }.

Multicriteria Model for Fat Removal From Dairy Waste
This section discusses the method and strategy adopted, which is structured in two phases: (i) technical evaluation (multi-criteria method); and (ii) economic viability analysis (EVA).In phase 1, the following steps are executed:(i) selection of technologies for the separation of fat from dairy waste through a systematic literature review (SLR); (ii) selection of criteria by SLR; (iii) acquisition of qualitative information (linguistic variables) from Brazilian and international experts; and (iv) applying of the TOPSIS 2-tuple method to rank the technologies.Lastly, it is performed the economic viability analysis (EVA) of the selected technology by the TOPSIS 2-tuple method in the previous step (Cavalcante & Almeida, 2005;Molinos-Senante et al., 2012;Reck & Schultz, 2016).The proposed model is illustrated in Figure 1.
Step 1.1 and 1.2: Identification of Technologies and Criteria for the Separation of Fat From Dairy Wastes The Technologies employed to separate the fat from the waste were selected from previous studies that used these technologies.Technologies and criteria used in the selection with the respective authors are showed in Table 1.
The initial investment criterion (C1) seeks to portray the subjectivities related to the technologies under analysis to the sector and the business (Reck & Schultz, 2016).The initial investment criterion (C1) was chosen because a project of this importance must consider implementation costs.The operation and maintenance cost criterion (C2) is related to maintenance based on availability; thus, if the criterion contemplates replacing parts and components, a crucial factor in choosing a technology (Cavalcante & Almeida, 2005).The operation and maintenance cost criterion (C2) also considers that the selected technology does not have a high maintenance value.The productivity criterion (C4) evaluates the process demand and if it is productive (Wei, 2010).Afterward, the efficiency (C3) and productivity (C4) criteria assume that the most efficient and productive technology is chosen from those analyzed, meeting the desired demand.Reliability criteria (C5) considers that the technology performs a reliable separation (Reck & Schultz, 2016).
Step 1.3: Experts Evaluation The Brazilian experts are from chemistry and include professors, technicians, and engineers, all with specific knowledge about fatty dairy waste.In contrast, the international experts were researchers from four countries, with international publications on fatty dairy waste.According to (Wang & Xu, 2019) experts in a homogeneous group are from adjacent (or the same) disciplines, as in this paper, overcome the potential disadvantages of individuals.
The information from the experts was obtained through two research instruments applied remotely by Google Forms Ò .The first research instrument was used to determine the importance of the criteria (weights) using the linguistic variables presented in Table 1.The second instrument was used to construct the linguistic decision matrix.Each technology was evaluated against each criterion; the experts expressed their preferences with the linguistic variables (Table 1) based on their background and expertise.Step 1.4: Selection of Best Technology The method for selecting the technologies used to separate fat from dairy wastes was the TOPSIS 2-Tuple method adapted from (Wei, 2010).The steps for the development are presented below (Wei, 2010).
Initially, the set of linguistic terms used to process the information and convert the linguistic variables into their 2-tuple information equivalent must be established.For this, the linguistic scale was used, as shown in Table 1.The remaining information processing steps in the TOPSIS 2-tuple method are presented below: Step 1.4.1:Preferences of the decision-maker (criteria weights).Decision-makers determine each criterion's importance, that is, the weights of the criteria through a set of linguistic variables.The aggregate linguistic weight of the criteria is obtained by Equation ( 5), and the weight of the criteria in the form of real numbers is obtained by Equation ( 6) as proposed by (Setti et al., 2019).
Where w j , a j À Á = aggregate linguistic weight of criterion j in the form of a 2-tuple linguistic variable.
w j = weight of criterion j, in the form of a real number.
Step 1.4.2:Transform the linguistic decision matrix of each of the decision-makers single decision matrix in the form of a 2-tuple linguistic variable aggregated using the Equation ( 7). Where = the performance of alternative i concerning criterion j for decision-maker k in the form of a 2tuple linguistic variable r ij , a ij À Á = performance of alternative i concerning criterion j after aggregation in the form of a 2-tuple linguistic variable.
Step 1.4.3:Check the ideal positive solution (A*) and the Ideal negative solution (A-) and the distance between them.For this, we use Equations ( 8) and ( 9), which refer to the identification.
Where r + j , a + j = ideal positive solution for criterion j in the form of a 2-tuple linguistic variable.r À j , a À j = ideal negative solution for criterion j in the form of a 2-tuple linguistic variable.
Step 1.4.4:In this stage, the distances of alternative i are calculated concerning the ideal positive solution and the ideal negative solution of each of the criteria j, using Equations ( 10) and ( 11). Where = total distance of the alternative i concerning the ideal positive solution of each of the criteria j in the form of linguistic variable 2-tuple; = total distance of the alternative i concerning the ideal negative solution of each of the criteria j in the form of linguistic variable 2-tuple.
Step 1.4.5:Calculate the closeness index with the ideal solution of alternative i using the Equation ( 12).
with the ideal solution of alternative i in the form of a 2-tuple linguistic variable.
The higher the 2-tuple linguistic variable of the alternative i, the better the classification of that alternative.
Step 1.4.6:Calculate the closeness index with the ideal solution of alternative i using the Equation (13).
Where CC i = closeness index with the ideal solution of alternative i in the form of real number, can be compared with results from the TOPSIS or Fuzzy TOPSIS methods.

Phase 2: Economic Viability Analysis of the Implementation of the Selected Technology
After identifying the best separation technology for the fat from dairy waste, we evaluated the technology's economic viability to support the company in adding value by implementing the project.In this step, we applied the deterministic approach through an expanded multi-index methodology (EMIM) or the stochastic approach via Monte Carlo simulation (MCS) or real options analysis (ROA), both supported by the open-access web application $AVEPI Ò (Donizetti de Lima et al., 2017).If there are managerial flexibilities, we use ROA for economic evaluation.On the other hand, with variability in the data, MCS was used.Finally, in the absence of managerial flexibility and uncertainty expressive, we applied EMIM (Lima et al., 2015(Lima et al., , 2017)).
The mathematical models of the EMIM, MCS, and ROA can be found in (Guares et al., 2021).On the other hand, the procedure to support selecting the most appropriate methodology considering the singularities of the project can be found in (Dranka et al., 2020).(Guares et al., 2021) presents in Appendix A indicators for the economic viability analysis (EVA) of each methodology.

Application of the Proposed Method
The criteria described in Table 1 cover several aspects related to the disciplines of Mechanical Engineering, Materials Engineering, and Economic Engineering.Thus, according to each of the integrated areas, eight experts were interviewed to verify each criterion's importance.Four of the professionals were Brazilian experts with extensive experience in the use and reuse of the waste understudy, experts in developing new products and projects, managers of the dairy processing unit, and a researcher.The other four experts are international researchers with extensive experience in the project areas, being researchers from the academic environment.In real applications, groups decision-making (GDM) is usually taken into account instead of individual decision-making.A group takes advantage of the diverse strengths and expertise of its members and reaches superior solutions than the individuals.
Table 2 show the results obtained (linguistic variables) by applying the survey instrument to identify the importance of each criterion, according to the experts' opinion, the weights of the criteria using Equations ( 5) and ( 6), respectively.The criteria weights are shown as 2-tuple linguistic variables and in real numbers.
The criteria weights indicate their relevance in the context of the experts involved in evaluating the technologies.The comparison between each group of experts' weights has only the informative character of the differences in preferences existing between these groups.
Using Equation ( 7), Table 3 present the aggregated 2tuple linguistic matrices.The 2-tuple decision matrix with the aggregated results of the four Brazilian experts varied between (S 3 , 20.50) and (S 5 , 0.00), while the 2-tuple decision matrix for the international experts varied between (S 2 , 20.25) and (S 5 , 0.00).Thus, the performance of the technologies concerning the criteria was between medium poor (MP) and good (G) for both groups of experts.

Results of the Application of the TOPSIS 2-Tuple Method
Table 4 shows the ranking of technologies using the TOPSIS 2-tuple method with information from Brazilian and international experts.The analysis of the results of the TOPSIS 2-tuple method showed in first, Table 4, that Separation by centrifugal force (T1) performance concerning the two groups of experts shaded slight differences (S 5 , 0.314) and (S 5 , 0.496) for Brazilian and international experts.The combined methods (T5) technology were ranked second in both groups, with a more significant difference between Brazilian (S 4 , 20.179) and international (S 1 , 0.313) experts.For the Brazilian experts, solvent separation (T2) and heating/decantation (T3) technologies were ranked third and fourth.For the international experts, these technologies were placed in reverse order.The acid/aqueous hydrolysis technology (T4) came in last for both groups of experts.
A sensitivity analysis was performed to illustrate the effectiveness and robustness of the TOPSIS 2-tuple method for selecting and ranking the most suitable technologies for separating fat from dairy waste.The results derived by the TOPSIS 2-tuple method with those deduced by VIKOR 2tuple (Wu et al., 2015) and TARGET 2-tuple (Setti et al., 2019) are shown in Table 4.
The VIKOR 2-tuple method ranks the alternatives from the linguistic decision matrix and the criteria weights.This method provides a compromise solution, the closest achievable solution to the ideal solution.The VIKOR 2-tuple method was developed with the data from Tables 2 and 3 and the parameter v = 0.7, that is, a decision strategy that prioritizes the benefits of the alternatives (technologies) in the decision-making process.
The TARGET 2-tuple method ranks the alternatives with the linguistic decision matrix and criteria weights as input data.This method provides the aggregate distance of each alternative from the desired target for each criterion.The TARGET 2-tuple method was derived with the data from Tables 2 and 3 and the following targets for the criteria: low initial investment-C1 = (S 1 , 0), low maintenance cost-C2 = (S 1 , 0), high efficiency-C3 = (S 5 , 0), high productivity -C4 = (S 5 , 0) and high reliability -C5 = (S 5 , 0).
The centrifugal force separation (T1) was ranked as the best technology in the VIKOR and TARGET 2-tuple methods in the same way as the TOPSIS 2-tuple method employed in this paper.From these results, it can be determined that this technology can be evaluated in the next step of the method, that is, the economic viability analysis.Table 4 shows that the other ranking positions were not similar for all methods, the experts' opinions may differ slightly even in a homogeneous group, however this did not affect the final result where the centrifugal force separation technology (T1) was unanimously chosen by all multicriteria methods.
As highlighted in Table 4, the centrifugal force separation technology (T1) was the best classified in both groups of experts.However, before managers carry out   an investment project (IP), it is necessary to evaluate the economic viability, incorporating specificities of the enterprise in the analysis (Lima et al., 2015(Lima et al., , 2017)).

Economic Viability of the Selected Technology
This section describes the economic viability analysis (EVA) for the centrifugal force separation technology (T1).The investment project (IP) was designed to meet the organization's current demand regarding its generated effluent.Dairy waste can have various commercial purposes for the studied company, such as: selling it to other companies to produce biodiesel, biofertilizers, fermentative hydrogen, or biomethane (Chandra et al., 2018;Damert et al., 2017;Hamawand et al., 2016;H. Lu et al., 2016).Currently, the company donates the waste to the cooperative members to use it in the ground cover.
It is necessary to purchase two centrifuges to process the current amount of dairy waste, budgeted around R$ 4,125,000.00.Besides, the purchase of three tanks, with a cost estimated at R$ 2,750,000.00,which have a total storage capacity of 150 m 3 of this by-product.All currency values shown below are in Brazilian Real (1 USD = R$ 5.60 on 10/21/2020).
At this stage, a training cost was also estimated at R$ 46,750.00.Also, the transportation of this by-product requires the purchase of two trucks, totaling R$ 1,100,000.00.The company chose to consider a 5-year service life for these vehicles.Table 5 presents these data.
Thus, initial investment or cash flow zero (CF 0 ) was budgeted at R$ 8,021,750.00(Table 5).This investment covers the entire process of separation and storage of the by-product: the feed pump, the pipes, the valves, the necessary connections, and the equipment control panel.The mode of project execution was using its own resources.
Manufacturers have estimated equipment life to be 10 years.However, the managers considered the horizon planning (N) of this IP in 5 years, given that this is a new enterprise.The resale value (RV), after 5 years, was not considered because the equipment is customized, making resale difficult.
The fat content in the waste is about 3%.Currently, the company generates 3,000 m 3 /day of waste.Thus, it was estimated at 90 m 3 /day of fat.The company considered selling the residue for 0.67 R$/L for an impurity index of 8%.If this index were below 3%, then the market value would be 1.45 R$/L.To determine the real degree of impurities, the managers should evaluate several samples at various periods of the year, which is outside of the scope of this paper.Therefore, the increase in revenue was estimated at approximately 21,708,000.00 R$/year.
The current employees who work at the effluent treatment station (ETS) are not available to carry out these new operations.The additional human resources required for the new process demands 315,000.00R$/ year.Besides, the company estimates an annual cost of R$ 121,704.00 for hiring employees to transport the byproduct.This cost includes all labor charges, considering a baseline salary of 3,300.00R$/month, which is the current amount paid by the organization for the truck drivers.Therefore, the total labor force was estimated at R$ 436,704.00.
The delivery of this by-product to the manufacturing industry requires 114 km/day for each truck.On average, a truck does 2.5 km/L.With the average price of diesel at 3.29 R$/L, the company estimated to spend 108,017.28R$/year on transportation.
The electricity consumption in the project is estimated at 65 kWh.With the implementation of this IP, an increase of 263,952.00R$/year was expected.For the Pletsch et al.
region analyzed (Santa Catarina state-Brazil), the price of energy was 0.470 R$/kWh.The evaluation considered 30 days of operation per month.The cost of maintaining the equipment was estimated at 115,000.00 R$/year.It is worth mentioning that this value tends to be slightly lower in the first years, and over the years it increases, due to the need to replace parts.Therefore, the company considered an average of the total maintenance cost for 5 years.The cost of maintaining the transport fleet was estimated, based on its history, at 25,000.00R$/year.Thus, the organization estimates an operation and maintenance Cost (OM&C) for the project of approximately R$ 840,656.00/year.On the other hand, as detailed, the expected annual revenue (R) is R$ 21,708,000.00.Therefore, the projected annual Cash Flow (CF) is R$ 20,867,344.00 (Table 5).
A minimum rate of attractiveness (MRA) of 8% per year was used as the reference for the EVA of this IP, defined by the company's internal policy, which cannot be detailed due to the organization's restrictions.The tax rate used was 24%, 15% for income tax (IT), and 9% for social contribution on net income (SCNI) on the taxable base, as provided in the current legislation.Besides, the straight-line depreciation method was considered as recommended by the Brazilian federal revenue service, respecting the recommended rates and terms RFB.Receita Federal do Brasil.Depreciac xa˜o, 2020).
This IP does not present significant managerial flexibility that justifies applying the real analysis options-ROA (Dornelas, 2018;Dranka et al., 2020).Thus, it was used the expanded multi-index methodology-EMIM and assessed the use of Monte Carlo simulation-MCS.The company used the open-access computational tool $AVEPI Ò for EVA of this IP (Dornelas, 2018).
Figure 2 presents the main screen of the $AVEPI Ò web application.Table 6 shows the deterministic EMIM results (Dranka et al., 2020;Guares et al., 2021;Maccarini et al., 2020).The company may recover the investment in the first year.Also, Table 6 shows the associated risks and the main parameters' sensitivities that affect this project's economic performance.
If the company invests in this IP, it is estimated a profit of R$ 55,299,362.92(NPV) over the project's entire life cycle, equivalent to an annual return of R$ 13,850,082.38 (ANPV).It is worth mentioning that the estimated gain is in addition to that required by the company (8% per year).With this investment, each currency unit invested will return 7.8937.This represents an ROIA of 51.17% per year, in addition to the MRA.According to (Souza & Clemente, 2012), to measure IP performance, it is necessary to analyze the ROIA/MRA index, which in this project is 639.58%.According to the scale proposed by, the ROIA/MRA index signals that the investor expects a high degree of return, as shown in Table 6.
The IP understudy shows a return on investment (Payback) in the first year of implementation.Thus, the Payback/N index is 20.00% of the estimated life.Furthermore, there is a significant gap between IRR (196.84%) and MRA (8%).These results point to a low level of IP risk (Penz & Polsa, 2018) .
The sensitivities dimension analyzes the uncertainty related to the IP parameters.This enterprise remains economically viable as long as the annual MRA is less than or equal to 196.84%.On the other hand, initial investment (CF 0 ) supports an increase of almost 700%, as long as the MRA and cash flows (CF) estimates are maintained.Finally, the CF allows a maximum reduction of 87.33%, that is, it must be above R$ 2 million.These results enable the project to be classified as having low sensitivity (Lima et al., 2015), that is, minor variations in the estimates do not prevent the implementation of the technology.
The most sensitive variable is the CF, which managers must monitor to maintain economic viability.However, this variable has a percentage variation greater than 33.33%, that is, there is no need to apply the MCS (Dranka et al., 2020;Lima et al., 2015).Furthermore, the organization's critical point is the control of the residue impurity index.This factor strongly impacts the return of the enterprise, as the price is based on this index.
Based on the analyses, this technology's implementation is economically viable, as it presents a high degree of return and low levels of risks and sensitivities, according to the EMIM scale proposed by (Lima et al., 2015).Considering the results, the company's managers should consider the implementation of the centrifugal force separation technology.

Conclusion
This paper presents a new model, using multi-criteria methods, to assist the dairy industry in choosing the Note that a reverse risk scale is considered for the ''sensitivities'' indexes compared to the ''return and risks'' dimensions.Thus, the lower the value for the indexes of the sensitivity dimension, the more easily the economic unfeasibility can occur (Dranka et al., 2020;Guares et al., 2021;Maccarini et al., 2020).
most appropriate technology for fat separation from its waste.Besides, a proposal for economic viability analysis (EVA) is presented through an approach proper to the enterprise's specificities.Academics and practitioners, through similar analyses may apply the model we propose for other contexts involving the selection among several technologies to implement it in other productive processes.This is particularly useful when there is a set of criteria to be pondered by the organizations.The centrifugal force separation technology was the most suitable technology, based on the TOPSIS 2-Tuple method, and with the support of two groups of experts.The implementation of this technology is economic viable.It presents a high degree of return and low levels of risks and sensitivities.With this IP's implementation, it is expected a total profit of R$ 55 million, equivalent to approximately R$ 14 million per year.In this context, the implementation of this technology is beneficial for the investigated organization.
The investment project (IP) required to implement the best technology (T1) was evaluated using the deterministic approach EMIM (expanded multi-index methodology).In addition, the need to use the MCS (Monte Carlo Simulation) was evaluated.However, as there was a low sensitivity in the critical parameters, the application of MCS was not necessary.Finally, as the IP did not present significant uncertainties and management flexibility, it was also not necessary to apply the ROA either.The economic analysis is important because it shows the EVA (economic value added) to the company with the implementation of the technology chosen by the MCDM method.
There is a scarce use of MCDM for this technology selection in the dairy industry.Therefore, future research is encouraged to extend the proposed approach, for example, by incorporating other MCDM such as VIKOR 2-tuple and TARGET 2-tuple.Besides, we recommend exploring different ways of aggregating and unifying linguistic opinions to apply other methodologies to capture the importance and influence.
Future research could focus on using different or complementary criteria to the one used in this paper and combining other multi-criteria methods so that selecting the most appropriate technology for separating fat from dairy waste can be improved.

Figure 1 .
Figure 1.A multi-criteria model for the techno-economic evaluation of fat removal from dairy waste.

Figure 2 .
Figure 2. Screen for entering enterprise data in the application $AVEPI Ò .

Table 1 .
Technologies for Separating Milk Fat and Criteria Used in the Selection of Technologies With the Respective Authors and Linguistic Variables.

Table 2 .
Linguistic Assessments of Criteria Weights, 2-tuple Linguistic Criteria Weights and Real Numbers Criteria Weights for Brazilian and International Experts.

Table 3 .
Aggregated 2-tuple Linguistic Decision Matrix for Brazilian and International Experts.

Table 4 .
Ranking of Separation Technologies Using the TOPSIS 2-tuple Method With Information From Brazilian and International Experts.

Table 5 .
Initial Investment and Annual Project Cash Flow.

Table 6 .
Dimensions and Indicators of EMIM. a