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Research Article

Inputs-Oriented VRS DEA in dairy farms

[version 1; peer review: 1 approved with reservations, 2 not approved]
PUBLISHED 28 Jul 2023
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This article is included in the Agriculture, Food and Nutrition gateway.

Abstract

Background: This paper aims to examine the efficiency of Mexico's dairy farms within its four regions of Tlaxcala Stated.
Methods: The Envelope Data Analysis (DEA) applied to the variable returns to a scale model (VRS) for the year 2020. Also, the results reveal that Tlaxcala's dairy farm efficiency, on the other hand, was adversely influenced by three inputs (costs): cost of investment in livestock, the total annual cost for feeding, reproduction, diseases and treatments, preventive medicine, sanitation, milking, fuel, and total labor.
Results:  The main findings are as follows, first, the mean efficiency for CRS, VRS, and efficiency scale was poor, below 50%. Second, 11 dairy farms were found that acted as relative pairs or reference points in the efficiency frontier. Third, excesses (slack) are estimated by identifying the farms that needed to reduce their costs to maintain the optimal level of milk production. Fourth, it observed that there were farms with very high slack; therefore, in the cost reduction projections they exceeded 50% of the original costs.
Conclusions: Finally, It concluded that based on the DEA estimates of the efficiencies indicators, discovered that the mean efficiencies of the constant and variable returns to scale, and efficiencies scale is relatively poor but significant in this production process.   As part of the study, provided The Policy suggestions.

Keywords

Slack, Technical Efficiency, Scale Efficiency, Peers, Lambda

Introduction

Cattle farming is generally regarded as one of the most significant activities in Latin America due to its pronounced economic impact.13 For this reason, the animal husbandry sector is the central axis of various performance evaluation studies and is where the analysis of technical efficiencies in this type of study becomes important.4,5 The need for efficiency is not a new debate, but rather a concern that has its antecedents in Farrell.6 The scientific community, producers, and policymakers are concerned about improving the efficiency and productivity of production, which is why they have decided to focus on rural development programs that seek to convert large-scale livestock production systems to intensive ones. Some plans to incorporate different strategies into their plans where efficiency and productivity variables are inherent.7 Perez,1 has measured that in America cattle practices positioned seventh in the world making and tenth in milk manufacture in 2001, which added about 7% to the world’s total meat production and 0.17% to milk. The problem is that it has not been possible to satisfy the requirements of demand,8 meaning an imminent study of the efficiency of dual-purpose production systems in Latin America, where the tropics have great potential. Morrillo and Urdaneta9 suggested that a farm that has cows will make 80% of their income from the milk and the last 20% from meat/grass/other products.10 In any case, it’s influenced by the agroecological characteristics of the farm and the techniques used mainly depending on the grower’s goals, the stage of growth at which the males are sold, and the type of breed.11 According to The Ministry of Agriculture and Rural Development of Mexico, in the State of Tlaxcala, the total economically active population employed 88.3% in agriculture and 11.7% in the livestock industry. Figure 1 depicts the increasing trend of Mexico’s Cheese, Whole cow milk, and Milk, skimmed cow production during 2015-2019.7

41e21775-1859-4477-bd23-579b634ad35e_figure1.gif

Figure 1. The Cheese, Whole cow milk and Milk, skimmed cow production, 2015–2019 (FAOSTAT).

According to the analysis of the 2013-2018 Sectoral Program for Agrarian, Fisheries and Nutritional Progress of Mexico, in 2050 the population will be 9.3 billion people and the Food and Agriculture Organization of the United Nations (FAO) estimates that the world demand for food will increase by 60%, this means that there will be more people to feed, provide housing, transportation, etc. For this reason, it is very important to assess whether productivity and efficiency grow at the rate that the population grows.12 In Mexico between 1960 and 2021, the population has increased from 37.77 million to 126.71 million.1 This represents an increase of 235.4% in 61 years. In relation to the problem of population growth and the capacity of governments to meet that demand, it is estimated that the population of the population of Mexico is predicted grow by three million during the year 2023, reaching 151 million.1 The continued progress in some developing countries such as China, India and Brazil positions tasks and opportunities for the growth of the agri-food sector in order to meet the growing demand. Likewise, the International Monetary Fund projects that the world economy will grow at a compound annual rate of 3.8% over the next six years, with wide variations between groups of countries, of which 5.2% are in emerging markets and 2.2% in developed countries increasing global food consumption and trade.13,14 This trend represents a huge opportunity for Mexico, which could play a leading role in gathering global food demand. However, the cultivable parcel is incomplete both in the world and in Mexico. We need to tackle climate change leading to extreme weather events affecting food production. In this context, increasing food making through increased efficiency is a major global challenge. In Mexico, climate change has emerged as an unexpected and unprecedented extreme. Regarding the rainfall regime, 2009 saw the greatest deficiency in 60 years and 2010 was the rainiest year on record.1,9 In September 2013, heavy rains devastated agriculture and unfortunately claimed lives. In just a few days, several parts of the country received as much rain as in 2012. These regular sensations resulted in the loss of some production, the occurrence of disease, and the loss of earnings and prosperity of the people. The Mexican Climate Modeling Network has produced a series of projections that describe the country’s climate under different climate change scenarios.1,9 There is consensus that overall temperature increases in Mexico over the next few decades will be 6% above the historical average and will exceed global temperature increases over the same period.1,9

Therefore, an increased risk of climate events associated with rising temperatures or reduced agricultural production is expected in historically unrecorded locations. Most models do this for precipitation not taking into account the effects of tropical cyclones, northerly winds and hurricanes meaning the precipitation forecast is more uncertain. It is in this situation that learning about the effects of efficiency in livestock production systems is valuable as part of the livestock bioeconomy of the productive route of eco intensification.1518

Some works with a data envelope analysis (DEA) approach have been carried out in Latin America, such as the case of Arcos et al.19 on milk production in the Ecuadorian mountain range, which represents 74% of the country. In the second phase of his research, he used the DEA model, which determined the efficiency of scale (EE) and the elasticities from 2014 to 2017 in each province.

In the same way, Sperat et al.20 used DEA used on the grounds of data provided by the interviews carried out on each farm. Cluster analysis and discriminant analysis were completed in this study. The results show an efficiency level of 59.5% for the area and apparently, there are no indications to assume that certain production styles are a limiting factor for the productive potential of each farm.

The contribution of this article focused on the DEA study for efficiencies of Tlaxcala’s dairy farms, the mean efficiency for constant returns scale (CRS), variable returns scale (VRS), and the efficiency scale estimated. The DEA slack variable was directly related to problem-solving. The most productive and efficient dairy farms were identified, allowing the establishment of the efficiency frontier. This allowed estimating the slack of each dairy farm and then projecting the costs required to decrease in comparison with the benchmark or efficient pair. This was important for decision makers in the study region because it allowed identifying the causes of the low yields of efficiency and productivity in the area with the highest dairy production in Mexico.

This work is divided into a section related to a literature review of technical efficiency models, a third section devoted to the methodology (VRS) and scale efficiencies, a fourth sections to the empirical results, a fifth to a discussion (efficiencies measure VRS DEA model, slack measurements), and finally conclusions presented later.

Literature review

The purpose of this section is to emphasize the importance of measuring efficiency and discuss how relative technological efficiency, often expressed as a frontier function, using several methods. The two methods that are the most commonly used: a) DEA,21 which uses mathematical programming; and b) Stochastic frontier analysis (SFA), which uses econometric methods.7 DEAP 2.1 software (RRID:SCR_023002).22 For this study DEA methods were used.

Modern performance measurement Färe23 started with Farrell6 who improved on the work of Debreu24 and Koopmans25 to identify two components of efficiency in a decision-making unit (DMU). Technical efficiency, which represents a DMU’s ability to maximize its revenues through a range of inputs, and allocation efficiency, which is a DMU’s ability to optimize the ratio of inputs to changes in market prices.6,24,25 Farrell’s initial idea was to identify the input space, so he derived an input reduction approach and an input-oriented measure.

Slack

The DEA slack variable (λ) directly was related to problem-solving (see equation 3). For example, if the model finds that the optimal solution to the problem given by the model has an efficiency of one (perfect efficiency or Frontier), this means that the DMU being evaluated is efficient compared to other DMUs. Otherwise, the closer it gets to zero, the more inefficient it is. So, it can be said that efficiency is measured from 0 to 1. Summarizing, when closer to one (Efficiency Frontier [ϕ]) the DMU will be efficient and when closer to zero the DMU will be inefficient.

On the other hand, to measure slack, or the value necessary to reach the frontier, the relative efficiency value of the DMU is subtracted from 1 (value between 0-1), indicating the distance or level of costs that the DMU must reach to have optimum efficiency (Frontier).26 Therefore, each DMU with an efficiency of one has a slip value equal to zero and a DMU with a Slack score means massive inefficiencies. Therefore, the higher the Slack score, the less efficient the evaluated DMU will be.27

Researchers have experienced rapid growth in the use and theoretical scope of DEA28,29 since its appearance in 1978 through the work of Farrell,6 and Charnes.30 The objective of the present study was to provide the measurement of the costs of inputs used in the production process (input) and the income (output) of the different DMUs. Each relative efficiency is assigned a quantification or measurement value. The output in terms of highest income achieves the lowest possible input in terms of costs and in this sense the efficiency frontier is determined.

Two strategies were used to estimate the above efficiencies, depending on whether they were input or output oriented.31 The first CRS/VRS model,31,32 input-oriented, is concerned with achieving the maximum proportional reduction of the input vector given the level of the output while keeping the limit or level of the output constant. Output-oriented models, on the other hand, consider a given input and aim for the maximum proportional increase in output while staying within possible limits.

Methods

The variable returns to scale model (VRS) and scale efficiencies

This study used an input-oriented multilevel DEA VRS model to process input slack variables and run a series of radial linear programming (LPs) to identify predicted efficiency points.32 The inputs-oriented technical efficiency measure addresses the question: “By how much can input values be proportionally reduced without changing the output values produced”. In the study this means measuring and identifying the farms that manage to reduce their costs while maintaining the same level of milk production.

The sample consisted of 102 observations for one output (y) and three inputs (x1, x2, x3). They were taken from six region of the Tlaxcala stated. The regions were selected by statistical criteria of conglomerates in such a way that the sample was homogeneous and statistically significant. For the data, a questionnaire with 42 variables was elaborated with the purpose of carrying out a socio-economic diagnosis and measuring the efficiency and productivity of the production units. For the measure on the efficiency and productivity, only three were selected (input-output), which are required for the purpose of the investigation.33

DEA is a nonparametric mathematical programming estimation focused on the computation of limits y. A research unit is a decision unit of the DMU.2,22,3437 Since DEA is best presented by percentage or ratio, it need to get the percentage of all outputs to all inputs so that u’ yi /v’ xi can be plotted, where u is an M-by-1 vector of output weights, v is a K-by-1 vector of input weights or proportions.7 Then the u’ yi/v’ xi represents the efficiency (ϕ) measured as a percentage. The following Banker Charnes Cooper (BCC) mathematical programming model32 is specified to select the optimal weights or proportions (Equation 1):

(1)
maxu,vuyi/vxi,s.tuyivxi1,J=1,2,.,Nu,v0

The resulting values of u and v represent the efficiency measure for each maximized DMU, subject to the constraint that all measures must be greater than or equal to one problem with this estimate is that there are infinitely many solutions. To avoid this, a restriction is proposed considering v’ xi=1, J represents the number of each farm dairy selected (Equation 2):32

(2)
maxu,vuyivxi,s.tuyivxi=1,uyivxi0,J=1,2,.,Nu,v0

Note that the expressions for u and v have changed. Were expanded to the shape is unknown in the way the multipliers in the linear programming problem posed. Therefore, using duality in linear programming, we can derive the equivalent form (Equation 3). This is the case when the CRS linear programming problem can be easily modified to account for VRS by adding the convexity constraint32: N1λ=1. Where θ is the Efficiency coefficients. yi represents the output and xi the inputs. Finally, λ represents the Slack in percentage, so it is the necessary value for reach the frontier.

(3)
min,θ,λθ,s.tyi+0,θxi0,N1λ=1λ0.

Equation 3 denotes the case of N1 that would be a vector N x1. It represents an enclosing or expansion form that minimizes the restrictions imposed by the multiplier form (KM < N 1) and is the preferred way of finding the solution according to Farrell.6 This equation allows us to convert from CRS to VRS. This is because cross-efficiency evaluation in DEA has been developed under the assumption of CRS, and no valid attempts have been made to apply the cross-efficiency concept to the VRS condition. This is due to the fact that negative VRS cross-efficiency arises for some DMUs. Since there exist many instances that require the use of the VRS DEA model, it is imperative to develop cross-efficiency measures under VRS. The value of θ represents an estimate of the efficiency measure for each DMU. This is true for θ ≤ 1 according to Farrel,6 Lanteri35 and Shephard.38 Here, a value of one indicates a cut-off point and therefore an efficiency measure for each DMU. This way, the efficiency (ϕ) and slack (λ) were estimated for each dairy farm. To run DEAP 2.1 software it is necessary to use three files. The first is the data file where the data of the variables built is located in the order Output, input 1, input 2 and input 3. The second file is the instructions file where it is specified that there are 102 observations (n), one output, and three inputs, the DEA orientation and the assumed scale that in the study is VRS.

Data source and location

The study was conducted in the state of Tlaxcala, located in the highlands of Mexico. The geographic coordinates are 98 degrees 3 inches west longitude, 19 degrees north latitude, 97 degrees 38 minutes north latitude, 19 degrees north latitude, and 06 degrees latitude. The state’s general climate is mild with some rain in the summer. The typical elevation of the revision area is 2,200 meters above sea level. The cluster technique was applied, carrying out the following steps to carry out a cluster sampling:

  • [a] Dairy farms were defined as the target population.

  • [b] The desired sample size to carry out the statistical study is determined

  • [c] The clusters were defined for this purpose, four types of farms were identified. The four type are defined by the size of each farm. Cesin-Vargas39 and Cuevas Reyes40 mention that in the study area there are four types of dairy farms, added through the use of principal components, cluster analysis and analysis of variance, four types of livestock farms were identified and characterized; small cattle farms (67%), medium cattle farms (24%), large cattle farms (7%), and large cattle farms with business potential (2%). For the purposes of this study, we worked with the typology of small livestock farms.

  • [d] The clusters that formed the sample of the statistical study were randomly selected.

The data collection procedure was as follows:

  • [a] The questionnaire was designed keeping in mind that it would be used for various purposes, such as socioeconomic diagnosis, efficiency and productivity analysis with the DEA approach, and efficiency analysis with the SFA approach. Consequently, of the 40 variables collected, only one output and three inputs were used. And of the 118 randomly visited dairy farms, only 102 met the statistical selection criteria.

  • [b] The collected data were entered into a database built with the IBM SPSS Statistics program (RRID: SCR_016479) v.22.

  • [c] The variables to be used in this study were selected. For this, the output variable was built by adding Total annual sale (USD) and Total annual sale of products obtained on the farm (USD).

  • [d] Input 1 was built from the variable Cost of investment in livestock (USD), input 2 was built by adding the variables Annual cost of fuel (USD), plus Annual cost of food (USD, plus Annual cost of concept of reproduction (USD, plus annual cost for animal health (USD). And input 3 was built by the variables Total annual cost of labor (USD), including hired labor and family labor.

  • [e] With the variables built (Output, and its three inputs) it was transferred to the database required by the DEAP 2.1 software (RRID:SCR_023002) transferring to the file data file format included in the software.

The processing of the data was similar in other studies, however the ordering and processing of the information is different. The software DEAP 2.1 consider tree file: datafile, instruction file and output or results. In this study, the data was organized using the DEA approach.33,41

Sample size and variables

In 2020, the study was performed. The sample number (n) was 102 dairy farms in six communities or regions across the Tlaxcala stated. The sample was estimated according to equation 4 where the population was 71,000 farms according to the Secretary of Agricultural and Livestock Information (SIAP),10 the Z is a parameter estimated of 1.93 (see Table 1) that was estimated with a probability (p) of 50% as well as (q) 50% and the margin of error of 9%. Of the 118 that were estimated according to the formula of equation 4, only 102 were worked on since the rest were not statistically significant for the objective of this investigation. The production units were selected randomly and distributed among the six regions of the stated of Tlaxcala that are important for milk production. The criteria for making the selection were: first, randomly selected, that is, that all the subjects of the population of dairy farms had the same possibility of being selected in this sample and therefore being included in the study; and secondly, that the number of selected dairy farms numerically represent the population that gave rise to it with respect to the distribution of the variable under study in the population, that is, the estimation or calculation of the sample size. For this, the following formula42 was used:

(4)
n=Nzα2pqe2N1+zα2pq

Where,

n Sample size

N Population size

Z Statistical parameter on which N depends (95% = 1.96)

p Probability of the event occurring (50%)

q Represents (1-p) probability that the event will not occur (50%)

e Maximum accepted estimation error (9%)

Table 1. Z score for the p-value and confidence level.44

Z-score (Standard deviation)p-value (Probability)Confidence level
<-1.65 or > +1.65<0.1090%
< -1.96 or > +1.96<0.0595%
< -2.58 or > +2.58<0.0199%

Variables

This study used the DEAP 2.1 software (RRID:SCR_023002)22 on a computer32,41,43 to get standard CRS and VRS DEA model that involve the calculation of technical and scale efficiencies31,32 of the data sampled during the study period 2020.23 This program involves a simple batch file system where the user creates a data file and small file containing instructions. The files are available in Zuniga and Jaramillo.33 The text to file data refer to S3,33 contains 102 observation on one output and tree inputs. The output “Total income (USD)” is listed in the first column and the inputs “Cost of investment in livestock (USD)”,“Total annual cost for feeding”, “reproduction”, “diseases and treatments”, “preventive medicine”, “sanitation”, “milking”, “fuel (USD)” and “Total labour (USD)”.

Output (TVAi) signifies the total annual sale of products obtained on the farm, such as the amount of milk produced per cow per year and by secondary products. The unit of measure is in USD USA.7

Input 1 (CIGij) signifies the annual value of the cattle investment quantified in USD USA.

Input 2 (CTij) signifies the total annual cost for fuel, feeding, reproduction, illness and treatment, milking, mortality, and preventive medicine, measured in annual USD.7

Input 3 (MOij) Signifies the annual cost of family and hired labor, measured in USD.

Table 2 displays the descriptive statistics for the model’s variables. Revenue from sales of milk and by-products (TVA) during the study period on average was 3.8 million USD, with a standard deviation of 1.8 million USD. The costs for investment in the cattle herd inventory on average was 1.0 million USD, with a standard deviation of 440.1 thousand USD. In the case of the costs of fuel, food, veterinary treatment and other inputs, the average cost was 1.0 million USD with a standard deviation of 494 thousand USD per year, and finally the average cost of labor was 235 thousand USD per year with a standard deviation of 37 thousand USD. All statistical analysis was completed using the IBM SPSS Statistics (RRID: SCR_016479) v.22. The full protocol can be found on protocols.io.45

Table 2. Descriptive statistics of the variables.

Variables(TVAi)(CIGij)(CTij)(MO)ij
Statistics
N102102102102
Minimum2230016000730043800
Maximum15610320038826000440206902701000
Mean3852213.651028312.751029632.73235168.33
Standard Deviation18148129.5864401851.6144942898.582377025.731

Results and discussion

The results were obtained following the DEA BCC model (equation 1-3), identifying the most efficient (ϕ) dairy farms and in this way it is quantified how many times they are a reference for dairy farms that did not reach the efficiency frontier (ϕ), adding the percentages of their costs to reduce to reach the optimal level, this is the slack (λ).

Efficiencies measure VRS DEA model

Table 3 displays the findings for Mexico and its 102 dairy farms based on the VRS and scale efficiencies estimations that involve the calculation of technical and scale efficiencies for the estimation of the efficiency (ϕ) and the slack (λ).46 The results constructed on the methodology of Färe et al.,23 and Banker, Charnes, and Cooper32 to account for VRS.27,28,46 The use of the VRS specification permits the calculation of technical efficiency from CRS DEA, technical efficiency from VRS DEA, and scale efficiency equal crste/vrste (constant return scale technical efficiency between variable return scale technical efficiency). Farm number 1, 56, and 75 are efficient under both CRS and VRS technologies. The VRS technical efficiency (TE) is equal to 1 on farms number 6, 8, 36, 41, 53, 86, 90, 91, 92 and 93 also showing the increasing returns to scale (IRS) portion of the VRS frontier. In general, the mean efficiencies for CRS were 25%, VRS 53%, and scale efficiency 44%.

Table 3. Efficiency summary.

farmcrstevrstescalefarmcrstevrstescale
1111-520.6860.7940.864irs
20.040.2240.179irs530.57210.572drs
30.5880.7140.823irs540.4230.7620.556drs
40.2910.4030.722irs550.7240.7920.915irs
50.3750.7360.509irs56111-
60.68310.683irs570.4340.8360.519drs
70.3840.510.753irs580.5120.5940.861irs
80.41110.411irs590.1080.5930.182irs
90.3240.3960.817irs600.1170.2080.562irs
100.3160.8620.367irs610.1740.380.456irs
110.3490.8790.397irs620.040.2330.171irs
120.4770.6690.713irs630.4250.80.532drs
130.340.4470.761irs640.0640.2290.277irs
140.410.5330.769irs650.1610.2690.598irs
150.2780.3460.803irs660.060.2070.29irs
160.0730.5260.138irs670.0360.3920.091irs
170.360.9980.361irs680.0230.140.165irs
180.0490.2320.212irs690.0890.2780.319irs
190.1150.210.55irs700.0930.1790.522irs
200.0380.1250.304irs710.4170.6120.681irs
210.0610.1290.475irs720.0750.2140.35irs
220.4310.5660.762irs730.4560.6220.733irs
230.6140.9630.638irs740.090.2390.377irs
240.0280.2050.137irs75111-
250.0560.2120.262irs760.5650.9010.627irs
260.040.1360.293irs770.4840.6910.7irs
270.0880.2840.31irs780.0690.2220.311irs
280.1050.5570.188irs790.0640.2810.229irs
290.1040.3210.325irs800.130.1380.947drs
300.0480.3630.134irs810.0660.1530.431irs
310.1410.1460.96irs820.0870.1560.555irs
320.0720.6350.113irs830.0890.1830.487irs
330.0980.2750.356irs840.0670.8060.083irs
340.1160.6830.169irs850.0740.1420.521irs
350.0710.3680.192irs860.31610.316irs
360.28110.281irs870.0540.760.071irs
370.0620.320.194irs880.4910.8160.601irs
380.0770.2360.327irs890.4850.6040.803irs
390.2590.3450.751irs900.0410.04irs
400.0640.7440.086irs910.67410.674irs
410.15710.157irs920.21110.211irs
420.0970.4220.23irs930.0510.05irs
430.0980.5750.17irs940.0540.5910.091irs
440.0680.3270.209irs950.340.4890.696irs
450.0830.4390.189irs960.0670.7270.092irs
460.3170.4330.731irs970.0540.8260.065irs
470.0660.1990.333irs980.030.3810.08irs
480.0830.3570.234irs990.0250.2150.117irs
490.2870.5950.482irs1000.3180.8380.379irs
500.0670.2660.252irs1010.4720.8750.539irs
510.5630.5830.965irs1020.2440.5140.473irs
mean0.2450.5310.441

Slack measure (λ)

Koopmans’s25 definition of technical efficiency was stricter than Farrell’s6 definition. Thus, Koopmans argued that both Farrell’s measure of technical efficiency and any non-zero input slack reported providing an accurate indication of the technical efficiency of a farm dairy in DEA analysis. Input slack is also known as input overload in some literature.47 Table 4 presents the % weight peers and summary lambda (λ). The peer represents the dairy farm that reached the efficiency frontier (ϕ) in terms of costs and income, and the number of times that they serve as a peer to others. Slack’s estimations (λ) represent the cost that each dairy farm must be reduced to reach an efficient point. On the other hand, Slack’s estimations (λ) based on Ali and Seiford48 using second-stage linear programming to consider the cost that must be reduced to reach the level of the efficiency frontier.49 The values inside the parentheses are given in percentages and represent the slack or excess of the input that should be multiplied by values shown in Tables 6, 7 and 8 the values outside the parentheses are peers for the evaluated farm. Table 5 shows the number times each farm is a peer to another. It can be noted that farms Numbers 6, and 75 (peer count 62) are the ones that are most often peers, that is, their costs mark the efficiency frontier to be followed by the other farms that are outside.

Table 4. Summary Peers and lambda weigh %.

farmPeer(λ)farmPeers(λ)
11 (1)5256 (0.009)6 (0.088)91 (0.903)
275 (0.011)90 (0.707)6 (0.282)5353 (1)
356 (0.001)1 (0.282)6 (0.717)75 (0)5475 (0.202)56 (0.798)
41 (0.263)86 (0.026)6 (0.711)5556 (0.74)36 (0.26)
591 (0.275)6 (0.49)92 (0.235)5656 (1)
66 (1)5775 (0.049)56 (0.951)
756 (0.001)1 (0.049)91 (0.95)5856 (0.003)1 (0.043)6 (0.954)75 (0)
88 (1)5975 (0.015)6 (0.446)90 (0.363)93 (0.176)
956 (0.001)1 (0.308)91 (0.0726 (0.62)6075 (0.086)86 (0.363)6 (0.306)93 (0.246)
1092 (0.609)91 (0.352)8 (0.038)6175 (0.053)41 (0.237)93 (0.71)
116 (0.218)1 (0.047)86 (0.735)75 (0)626 (0.528)75 (0.01)90 (0.462)
1256 (0)1 (0.096)91 (0.904)6375 (0.938)56 (0.062)
1356 (0.003)91 (0.877)6 (0.121)6475 (0.04)86 (0.028)6 (0.47)93 (0.462)
1456 (0.002)91 (0.537)6 (0.46)656 (0.549)75 (0.108)90 (0.343)
1556 (0.001)1 (0.202)6 (0.797)75 (0)666 (0.676)75 (0.027)90 (0.298)
1675 (0.01)41 (0.276)90 (0.714)6775 (0.004)90 (0.932)6 (0.065)
1791 (0.995)36 (0.005)6875 (0.009)6 (0.678)90 (0.095)93 (0.218)
186 (0.332)75 (0.015)90 (0.652)6975 (0.046)93 (0.569)86 (0.321)6 (0.064)
1975 (0.036)90 (0.108)6 (0.856)7075 (0.064)6 (0.717)90 (0.105)93 (0.115)
2075 (0.014)86 (0.016)6 (0.785)93 (0.186)7191 (0.875)1 (0.044)6 (0.081)
216 (0.768)75 (0.047)90 (0.185)7275 (0.041)93 (0.13)6 (0.3)90 (0.529)
2256 (0.002)1 (0.011)91 (0.959)6 (0.029)7375 (0.158)90 (0.842)
2356 (0.002)36 (0.079)91 (0.92)7475 (0.055)6 (0.373)90 (0.284)93 (0.287)
246 (0.816)90 (0.184)7575 (1)
2590 (0.979)75 (0.021)7691 (0.746)92 (0.073)6 (0.181)
266 (0.407)75 (0.027)90 (0.566)7756 (0)1 (0.051)91 (0.949)
276 (0.6)75 (0.03)90 (0.37)7875 (0.026)93 (0.04)6 (0.728)90 (0.205)
2875 (0.012)90 (0.633)6 (0.354)7975 (0.02)93 (0.108)6 (0.508)90 (0.363)
296 (0.834)75 (0.015)90 (0.151)801 (0.876)75 (0.119)56 (0.005)
3075 (0.005)6 (0.683)90 (0.312)8175 (0.068)93 (0.266)6 (0.336)90 (0.329)
3156 (0.001)75 (0.098)6 (0.901)8275 (0.09)90 (0.373)6 (0.537)
3275 (0.008)93 (0.688)86 (0.062)6 (0.242)8375 (0.068)90 (0.453)6 (0.48)
336 (0.575)75 (0.038)90 (0.387)8441 (0.482)75 (0.001)90 (0.517)
3475 (0.015)41 (0.253)90 (0.732)8575 (0.06)6 (0.723)90 (0.062)93 (0.155)
3575 (0.018)93 (0.761)90 (0.004)6 (0.217)8686 (1)
3636 (1)8741 (1)
3775 (0.021)86 (0.575)93 (0.404)8891 (0.829)8 (0.02)6 (0.151)
3875 (0.049)93 (0.414)6 (0.415)90 (0.122)8956 (0.003)1 (0.003)91 (0.973)6 (0.021)
3956 (0.001)1 (0.002)91 (0.997)9090 (1)
406 (0.114)90 (0.133)75 (0.004)93 (0.749)9191 (1)
4141 (1)9292 (1)
4290 (0.38)6 (0.603)75 (0.017)9393 (1)
4375 (0.012)6 (0.37)90 (0.521)93 (0.097)946 (0.457)75 (0.004)90 (0.148)93 (0.39)
446 (0.487)75 (0.015)90 (0.499)951 (0.384)6 (0.275)75 (0)86 (0.341)
4575 (0.015)86 (0.05)93 (0.934)9675 (0.001)93 (0.329)90 (0.214)41 (0.455)
4656 (0.001)1 (0.035)91 (0.964)9741 (0.461)90 (0.539)
4790 (0.301)6 (0.665)75 (0.034)9890 (0.182)6 (0.294)93 (0.521)75 (0.004)
4890 (0.377)6 (0.605)75 (0.018)9975 (0.008)93 (0.369)6 (0.425)90 (0.198)
496 (0.158)75 (0.061)90 (0.781)1008 (0.244)92 (0.363)91 (0.393)
506 (0.785)75 (0.013)90 (0.202)10156 (0.002)36 (0.255)91 (0.743)
5156 (0.032)1 (0.02)91 (0.948)10286 (0.272)6 (0.728)93 (0)

Table 5. Peer count summary.

farmpeer count*
117
662
83
417
5623
7562
8611
9046
9121
924
9326

* Number of times each farm is a peer for another.

Table 6. Projection summary.

FarmInputOriginal movementRadial movementSlack ValueProjectedFarmInputOriginal movementRadial movementSlack valueProjected
11756000075600221116000-50380.965065619.035
2295420029542284207-36572.672047634.328
344004435-2.17202.828
2192000-71395.164020604.836231159200-5888.03-78671.63274640.338
2126380-98075.227-11154.42517150.348262139-2298.218059840.782
3240900-186946.69053953.31432-0.07401.926
3166000-18850.643047149.357241109800-87276.2560.59122524.335
243509-12426.858031082.14221026620-816025.05-190064.9820529.971
396-27.419068.581365700-52222.6780.35413477.676
41109200-65164.668-5424.74538610.58725196200-75823.259020376.741
259565-35545.178024019.8222117785-92836.201-9173.57815775.221
358-34.611023.3893591300-466052.94-49436.19175810.87
5162000-16341.696-9426.53936231.765261181200-156518.58024681.421
235859-9451.562026407.4382176120-152130.53-4160.80619828.664
312-3.16308.8373343440-296659.72046780.283
6124000002400027195000-68046.636026953.364
22212000221202202086-144750.24-35463.69721872.067
31500153116800-83661.548033138.452
71132200-64831.885-5054.74462313.3728138400-17022.977021377.023
285836-42094.627043741.3732132164-58589.187-55698.52317876.291
38-3.92304.077387600-38833.667048766.333
8130200003020029180000-54291.226025708.774
25852400585242104070-70626.099-11175.87322268.028
38008343800-29724.446014075.554
91121200-73147.854048052.14630162000-39516.623022483.377
276640-46254.55030385.45269477.5-44282.519-5278.70119916.28
358-35.005022.995365700-41874.873023825.127
10154000-7440.741046559.259311358800-306266.21052533.79
234713-4783.156029929.8442991774-846563.17-106058.2639152.578
34-0.55103.4493136400-116428.96019971.04
11163200-7667.753055532.24732157000-20777.239036222.761
223931-2903.434021027.566222890.13-8343.749014546.381
366-8.007057.993365700-23948.502041751.498
121124200-41109.159-29799.37353291.467331103600-75161.439028438.561
252744-17457.822035286.178297113-70455.143-4126.64422531.212
39-2.97906.0213131400-95330.242036069.758
131166200-91860.704074339.29634138800-12288.747026511.253
2130704-72241.646-2827.86255634.492219722-6246.357013475.643
38-4.42203.5783175200-55489.392-35566.97384143.635
141116400-54380.678062019.32235199400-62784.633036615.367
2112874-52733.373-11732.37348408.254240092-25323.556014768.444
315-7.00807.9923131400-82996.989048403.011
151129600-84773.579044826.42136114600000146000
292392-60435.189031956.811217457000174570
372-47.096024.90431001
16150000-23696.629026303.371371208000-141463.47-10761.71855774.808
224457-11590.969012866.031257020-38780.035018239.965
3219000-103791.24-30797.20684411.559387400-59441.864027958.136
17180000-187.589-29362.19650450.214381159400-121784.85037615.155
235886-84.148035801.852288655-67734.225020920.775
32-0.00501.9953182500-139433.72043066.284
18194000-72213.266021786.734391271200-177740.03-29925.99463533.977
2476302-365907.69-92403.76817990.5412133403-87430.137045972.863
3219000-168241.55050758.45536-3.93202.068
191144400-114101.79030298.20640144000-11270.573032729.427
2141100-111494.21-4854.55524751.24216728-4284.867012443.133
373000-57683.04015316.96373000-18698.905054301.095
201237000-207472.98029527.023411458000045800
2170235-149026021208.99927300007300
3109500-95857.768013642.232310950000109500
211244800-213136.98031663.02542157800-33399.308024400.692
2313044-272554.13-15419.72825070.141287120-50341.656-16223.27520555.069
3178080-155046.7023033.299374200-42875.928031324.072

Table 7. Projection summary.

FarmInputOriginal movementRadial movementSlack ValueProjectedFarmInputOriginal movementRadial movementSlack valueProjected
43140600-17261.07023338.93641168000-129510.36038489.638
230680-13043.587017636.413289297-68838.612020458.388
380300-34139.506046160.4943153300-118178.21035121.795
44170000-47098.422022901.578651158000-115496.56042503.438
2144105-96958.83-27886.9719259.22207716-151838.51-26150.54329726.952
3120450-81042.928039407.0723175200-128069.61047130.395
45193600-52513.743-886.17840200.079661129800-102912.68026887.324
228180-15810.227012369.7732114758-90986.54-1598.09822173.362
3131400-73721.217057678.7833131400-104181.25027218.755
461167600-94959.588-14428.50458211.90867144000-26731.077017268.923
294200-53372.274040827.726249180-29878.054-4853.73714448.209
38-4.53303.4673175200-106438.29068761.712
471142800-114454.07028345.929681196800-169165.04027634.963
2178562-143117.28-12560.25722884.4612139496-119907.75019588.246
3146000-117018.87028981.1313153300-131773.38021526.625
48168800-44262.961024537.039691189000-136509.22052490.778
269320-44597.507-4086.85420635.64268960-49807.809019152.191
387600-56358.073031241.9273153300-110724.15042575.853
49150000-20258.526029741.474701207400-170328.59037071.406
2117160-47469.779-48341.60221348.6192145900-119821.32026078.679
3116800-47323.917069476.0833153300-125898.62027401.381
50194000-69038.531024961.46971198000-38049.179-10921.48949029.331
2147260-108155.47-17444.89121659.641255336-21484.586033851.414
365700-48253.526017446.47438-3.10604.894
511905200-377259.57-133252.58394687.857721137600-108162.29029437.715
2533824-222481.450311342.547293685-73642.323020042.677
35-2.08402.9163255500-200839.13054660.874
521174400-35928.0280138471.97273177800-29378.9048421.1
2207792-42807.092-58120.202106864.706249350-18635.587-360.51130353.901
34-0.82403.1763153300-57889.272-1588.96693821.762
531388260000038826000741151000-114916.4036083.602
2440206900044020690290696-69022.898021673.102
327010000027010003204400-155555.71048844.293
54111275000-268587108589128.9975122060000220600
214580794-3473359.8-42278876879547.23211986000119860
31591400-379094.91-1171022.941282.237320440000204400
55110950000-2279099.7-711716.37959183.9576169800-6926.584-17910.11344963.304
211490914-2391683.9-2698610.16400619.95235587-3531.466032055.534
35-1.04103.95935-0.49604.504
56110706800001070680077176600-23667.192-440.23452492.574
28590098008590098251825-16012.431035812.569
3500536-1.85404.146
57112198000-2005493.3010192506.7781126000-97998.736028001.264
214671234-2412121.8-4084435.18174677.092100980-78538.987022441.013
31898000-312053.31-1575917.210029.5073102200-79487.863022712.137
581102500-41591.214060908.78679193600-67252.192026347.808
284589-34323.504050265.496269840-50180.482019659.518
375-30.433044.5673131400-94411.731036988.269
59144000-17902.953026097.0478014174000-3599624.4-430089.93144285.646
230895-12570.721018324.2792593648-511957.32081690.683
367160-27326.417039833.5833177750-153290.19024459.813
601279400-221210058189.996811248800-210777.38038022.617
2128975-102113.67026861.3272149189-126389.34022799.663
3153300-121372.56031927.4393350400-296850.46053549.537
611203000-125800.17-29069.448130.429821247800-209024.91038775.095
240336-24996.432015339.5682226043-190672.38-7636.38227734.235
3205800-127535.35078264.6543292000-246308.61045691.395
62195400-73140.314022259.686831183600-149925.71033674.288
294813-72690.279-3013.0219109.7012157408-128537.62-4041.66424828.72
3153300-117530.51035769.4953255500-208638.45046861.55
6315202000-1041708.2-3291390.9868900.87684138000-7370.988030629.012
2804660-161134.350643525.648213212-2562.776010649.224
3562100-112561.35-257775.2191763.4443219000-42480.169-85756.09890763.733

Table 8. Projection summary.

FarmInputOriginal movementRadial movementSlack valueProjected
851262200-224975.98037224.024
2180574-154938.26025635.74
3182500-156590.83025909.17
861636000063600
2201450020145
3440044
87175600-18112.5-11687.545800
29600-230007300
3365000-87447.917-168052.08109500
88156000-10313.547045686.453
250049-9217.548-7182.11833649.333
35-0.92104.079
891129600-51316.294078283.706
295901-37972.87057928.13
34-1.58402.416
901160000016000
2135000013500
3730000073000
911500000050000
2351480035148
32002
921456000045600
2251110025111
34004
931360000036000
2102000010200
3584000058400
94148000-19636.631028363.369
228147-11514.839016632.161
358400-23891.235034508.765
951117200-59881.796057318.204
249687-25386.918024300.082
395-48.539046.461
96150000-13629.522036370.478
213340-3636.35709703.643
3116800-31838.564084961.436
97136000-6258.178029741.822
212880-2239.037010640.963
3116800-20304.31-6664.26489831.426
98177600-48070.612029529.388
238653-23944.244014708.756
3116800-72353.704044446.296
991132200-103752.47028447.535
278113-61304.208016808.792
3175200-137499.49037700.515
100152000-8426.796043573.204
244396-7194.539037201.461
35-0.8104.19
1011103600-12985.226090614.774
2135337-16963.143-34707.26183666.596
32-0.25101.749
102167600-32823.657034776.343
241951-20369.604021581.396
356-27.191028.809

Input projected

Tables 6, 7 and 8 display the value of the projected cost to be reduced considering the excess costs assumed for each input, estimated by the multi-stage DEA method.49,50 It identifies efficient projected points, which have inputs, which is as similar as possible to those of the inefficient point, and invariant to units of measurement. Ferrer and Lovell5157 argue that slacks may essentially be viewed as allocative inefficiency. Farms that have negative values are inefficient because they have slack to reduce, that is, they have to reduce their costs (slack) to obtain an optimal level of production compared to farms that are referents or peers. The cost minimization model (VRS) offers a peer evaluation in which each farm has the objective of evaluating the level of costs that need to be reduced to reach the optimum production referenced by the farms indicated as peers.9,5860 These results are relevant to improve production processes in the studied regions.13 It was very important to identify the producers with the best income and therefore with the lowest costs. In the same way, it contributed to identify the necessary cost to reduce in each farm to obtain the optimal conditions of productivity and technical efficiency.

Conclusions

This study used DEA to investigate the efficiencies of Tlaxcala’s dairy farm for data from 102 farmers in 2020. Using the VRS model and multi-stage method the efficiency of the Tlaxcala dairy farm was assessed.

In conclusion, the CRS, VRS model was used to measure the technical efficiency and productivity of the farms under study, managing to measure both their efficiency and their level of slack. A second conclusion was that 11 farms stood out for their optimal levels of production and their reduced costs, in such a way that in the CRS model, VRS marks the benchmarks as pairs, demonstrating that 50% of the farms were below this condition. optimization or were in scale of deficient constant returns. A third conclusion is that the farms that had to reduce their costs to be located at the optimum level of production were identified. A fourth conclusion was that it was quantified through cost reduction projections for farms that it was necessary to make adjustments in their costs.

We have put together some recommendations based on our findings that would provide Tlaxcala Mexico with policy directives to minimize cost streams. In the first place, the input cost of investment in livestock must be reduced, or the quality of the cattle herd should be improved by investing in genetic improvement of the inventory that is held. The second input referred to the total annual cost for fuel, feeding, reproduction, illness and treatment, milking, mortality, and preventive medicine, based on the results found, it suggests improving good livestock management practices, and for input 3 referred to the annual cost of family and hired labor was suggested reviewing the investment of the time in the face of technical efficiency, pharmaceutical, sanitation.

Ethics statement

The protocol to carry out this research was reviewed and confirmed to proceed by the Colegio de Postgraduados (Institución de Enseñanza e Investigación en Ciencias Agrícolas). No formal ethical approval was required for this study as per the ‘Ley General de Protección de Datos Personales en Posesión de Sujeto Obligados’, regarding ethical approval requirements for this type of study. The questionnaire included a verbal statement requesting the consent of the producers in accordance with the provisions of the general law on the protection of personal data held by obligated subjects. Verbal as opposed to written consent was used because the aforementioned law does not require written consent to be bound by its compliance.

Author contributions

Conceptualization: Carlos Zuniga

Methodology: Carlos Zuniga

Formal analysis: Carlos Zuniga, Jose Luis Jaramillo, Noel E. Blanco Roa

Investigation: Carlos Zuniga, Jose Luis Jaramillo, Noel E. Blanco Roa

Writing - original draft: Carlos Zuniga

Validation: Carlos Zuniga, Jose Luis Jaramillo, Noel E. Blanco Roa

Writing – review & editing: Carlos Zuniga, Jose Luis Jaramillo, Noel E. Blanco Roa

Data: Carlos Zuniga & Jose Luis Jaramillo

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Zuniga-Gonzalez CA, Jaramillo-Villanueva JL and Blanco-Roa NE. Inputs-Oriented VRS DEA in dairy farms [version 1; peer review: 1 approved with reservations, 2 not approved]. F1000Research 2023, 12:901 (https://doi.org/10.12688/f1000research.132421.1)
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Reviewer Report 15 Feb 2024
Amar Oukil, College of Economics & Political Science, Sultan Qaboos University, Muscat, Muscat Governorate, Oman 
Approved with Reservations
VIEWS 27
The reviewer read with a lot of interest the manuscript. The manuscript is not well written. It requires an in-depth polishing for English as well as a better flow of ideas. Some other technical flaws that need to be addressed ... Continue reading
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Oukil A. Reviewer Report For: Inputs-Oriented VRS DEA in dairy farms [version 1; peer review: 1 approved with reservations, 2 not approved]. F1000Research 2023, 12:901 (https://doi.org/10.5256/f1000research.145337.r235362)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • Author Response 13 Apr 2024
    C. A. Zuniga-Gonzalez, Agroecology, National Autonomous University of Nicaragua, Leon, Leon, 21000, Nicaragua
    13 Apr 2024
    Author Response
    Response to Reviewer  # 3 Comments:

    [1] Regarding the terminology, we will correct "Data Envelopment Analysis" to "data envelopment analysis" throughout the manuscript for consistency.
    [2] We will adjust ... Continue reading
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  • Author Response 13 Apr 2024
    C. A. Zuniga-Gonzalez, Agroecology, National Autonomous University of Nicaragua, Leon, Leon, 21000, Nicaragua
    13 Apr 2024
    Author Response
    Response to Reviewer  # 3 Comments:

    [1] Regarding the terminology, we will correct "Data Envelopment Analysis" to "data envelopment analysis" throughout the manuscript for consistency.
    [2] We will adjust ... Continue reading
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11
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Reviewer Report 22 Jan 2024
Alphonse Singbo, Universite Laval, Québec City, Québec, Canada 
Not Approved
VIEWS 11
Reviewer
Inputs-oriented VRS DEA in dairy farms
C.A. Zuniga-Gonzalez, J.L. Jaramillo-Villanueva, N.E. Blanco-Roa

Summary
This article uses the non-parametric DEA to investigate the technical efficiency measures of Tlaxcala’s dairy farm on a sample of ... Continue reading
CITE
CITE
HOW TO CITE THIS REPORT
Singbo A. Reviewer Report For: Inputs-Oriented VRS DEA in dairy farms [version 1; peer review: 1 approved with reservations, 2 not approved]. F1000Research 2023, 12:901 (https://doi.org/10.5256/f1000research.145337.r213132)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • Author Response 13 Apr 2024
    C. A. Zuniga-Gonzalez, Agroecology, National Autonomous University of Nicaragua, Leon, Leon, 21000, Nicaragua
    13 Apr 2024
    Author Response
    Reviewer 2
    Reviewer Report
    22 Jan 2024 | for Version 1
    Alphonse Singbo, Universite Laval, Québec City, Québec, Canada
     NOT APPROVED
    Reviewer 2
    Inputs-oriented VRS DEA in dairy farms
    C.A. ... Continue reading
COMMENTS ON THIS REPORT
  • Author Response 13 Apr 2024
    C. A. Zuniga-Gonzalez, Agroecology, National Autonomous University of Nicaragua, Leon, Leon, 21000, Nicaragua
    13 Apr 2024
    Author Response
    Reviewer 2
    Reviewer Report
    22 Jan 2024 | for Version 1
    Alphonse Singbo, Universite Laval, Québec City, Québec, Canada
     NOT APPROVED
    Reviewer 2
    Inputs-oriented VRS DEA in dairy farms
    C.A. ... Continue reading
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Reviewer Report 30 Oct 2023
Ayele Gelan, Economics, Kuwait Institute for Scientific Research, Safat, Kuwait 
Not Approved
VIEWS 17
This paper concerned itself with measuring efficiency in dairy farms using survey data and applying the data envelopment analysis (DEA) approach.  However, the paper has serious limitations at many levels. I have briefly outlined my concerns as follows.

... Continue reading
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Gelan A. Reviewer Report For: Inputs-Oriented VRS DEA in dairy farms [version 1; peer review: 1 approved with reservations, 2 not approved]. F1000Research 2023, 12:901 (https://doi.org/10.5256/f1000research.145337.r213133)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • Author Response 13 Apr 2024
    C. A. Zuniga-Gonzalez, Agroecology, National Autonomous University of Nicaragua, Leon, Leon, 21000, Nicaragua
    13 Apr 2024
    Author Response
    Reviewer 1
    Do not delete (filing code): F1KR00CDE F1R-VER145337-A (end code) 30 Oct 2023 | for Version 1
    Ayele Gelan, Economics, Kuwait Institute for Scientific Research, Safat, Kuwait
    NOT APPROVED
    ... Continue reading
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  • Author Response 13 Apr 2024
    C. A. Zuniga-Gonzalez, Agroecology, National Autonomous University of Nicaragua, Leon, Leon, 21000, Nicaragua
    13 Apr 2024
    Author Response
    Reviewer 1
    Do not delete (filing code): F1KR00CDE F1R-VER145337-A (end code) 30 Oct 2023 | for Version 1
    Ayele Gelan, Economics, Kuwait Institute for Scientific Research, Safat, Kuwait
    NOT APPROVED
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Version 3
VERSION 3 PUBLISHED 28 Jul 2023
Comment
Alongside their report, reviewers assign a status to the article:
Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions
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