Inputs-Oriented VRS DEA in dairy farms

Background This paper aims to examine the efficiency of Mexico’s dairy farms within its four regions of Tlaxcala Stated. Methods The Envelopment Data Analysis (DEA) applied to the variable returns to a scale model (VRS) for the year 2020. Also, Examine the statistical accuracy of efficiency estimation using bootstrap resampling techniques. 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 efficiency distribution among farms using VRS, CRS, and FDH technologies reveals varying patterns. Under VRS and CRS, the majority of farms exhibit high efficiency within the 0 to less than 0.2 range, while FDH displays a broader distribution, with notable efficiency at 1 and across various ranges. These findings highlight the diverse landscape of efficiency levels across different technological approaches within the agricultural sector, offering valuable insights for optimization strategies and resource allocation. Conclusions The utilization of Bootstrap methodology enhances the reliability of efficiency assessments by providing robust statistical techniques that accommodate non-normal data distributions. By incorporating Bootstrap, decision-makers can obtain more accurate estimates of efficiency levels and confidence intervals, thereby making informed decisions regarding resource allocation and optimization strategies within the agricultural sector. As part of the study, provided The Policy suggestions.


Introduction
2][3] Analyzing technical efficiencies in the animal husbandry sector is crucial due to its economic impact. 4,5The pursuit of efficiency is not a new debate but has its roots in the work of Farrell. 6The scientific community, producers, and policymakers share a common concern for improving the production efficiency and productivity, prompting them to prioritize 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 aimed at transitioning large-scale livestock system to more intensive ones.Many of these programs incorporate strategies that inherently address efficiency productivity variables. 7In 2001, Perez, 1 reported that cattle practices in America ranked seventh globally in meat production and tenth in milk production, contributing approximately 7% to the world's total meat production and 0.17% to milk.However, there remains an unmet demand and necessitating a thorough examination of the efficiency of dual-purpose production systems in Latin America, 8 where tropical regions offer significant potential.Morrillo and Urdaneta 9 have suggested that farms with cows derive 80% their income from the milk and the remaining 20% from meat, grass, or other products. 10This income distribution, is influenced by the agroecological characteristics of the farm and the techniques employed, depending on the grower's goals, the stage at which growth males are sold, and the breed type. 11According to The Ministry of Agriculture and Rural Development of Mexico, in the State of Tlaxcala, 88.3% of the economically active population is employed in agriculture with the remaining 11.7% engaged in the livestock industry. 7cording to the analysis of the 2013-2018 Sectoral Program for Agrarian, Fisheries and Nutritional Progress of Mexico, it's projected that the global population will reach 9.3 billion by 2050.The Food and Agriculture Organization of the United Nations (FAO) estimates a 60% increase in world food demand to meet the needs of this growing population, which includes the provision of food, housing, transportation, and more.Consequently, it's crucial to evaluate whether productivity and efficiency can keep pace with this population growth. 12In the context Mexico, from 1960 and 2021, the population has increased from 37.77 million to 126.71 million marking a remarkable 235.4% increase in just 61 years. 1 With predictions that Mexico's population is set to grow by an additional three million in 2023, reaching 151 million, increasingly urgent. 1 Furthermore, the continued development in emergency economies such as China, India and Brazil presents both challenges and opportunities for the growth of the agri-food sector as it strives to meet the rising global demand.The International Monetary Fund forecasts a compound annual growth rate of 3.8% in the world economy over the next six years, with substantial variations between emergency and developed countries, highlighting the increased global food consumption and trade, where emerging markets play a significant role. 13,14However, Mexico faces its own set of challenges.Notably, the cultivable land available both globally and within Mexico is limited.Climate change, marked by extreme weather events, poses a significant threat to food production.In this context, enhancing food production through increased efficiency has emerged as a substantial global challenge.Mexico has experienced unexpected and unprecedented climatic shifts, including severe variations in rainfall.For instance, 2009 witnessed the most significant rainfall deficiency in 60 years, while 2010 became the rainiest year on record. 1,9In 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 extreme weather events resulted in the loss of some production, the occurrence of disease, and the loss of significant decline in earnings and prosperity among the affected population.The Mexican Climate Modeling Network has produced a series of projections that describe the country's climate under different climate change scenarios. 1,9Consensus point to 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 a result, there is an increased risk climate-related events associated with rising temperatures, potential impacting regions that have not historically experienced such challenges.Many climate models primary focus on precipitation patterns, often to account for the disruptive effects of tropical cyclones, northerly winds, and hurricanes, rendering precipitation forecasts more uncertain.[17][18] This article's contribution primarily revolves around the DEA study on the efficiencies of dairy farms in Tlaxcala.It delves into mean efficiency measurements for constant returns to scale (CRS), variable returns to scale (VRS), and the estimated scale efficiency.The DEA slack variable is directly linked to problem-solving, facilitating the identification of the most productive and efficient dairy farms. 19This, in turn, enables the establishment of an efficiency frontier and the estimation of slack for each dairy farm.The findings serve as a valuable resource for decision-makers in the study region, shedding light on the root causes of low efficiency and productivity in the area known for having the highest dairy production in Mexico.
The motivation for this paper is rooted in the pressing need to address critical challenges and uncertainties related to the efficiency and productivity of livestock production systems, specifically within the context of the study area.Given the increasing global population and the associated rise in food demand, it becomes imperative to investigate whether agricultural practices and production can keep pace with these mounting needs.Moreover, within the study region, Mexico is known for its significant dairy production, identifying the factors contributing to low efficiency and productivity is vital for informed decision-making.By understanding and enhancing efficiency in livestock production, the paper aims to contribute valuable insights that can aid policymakers, farmers, and stakeholders in meeting the demands of a growing population, optimizing resource utilization, and addressing potential climate-related challenges.The paper's objective is to provide a comprehensive analysis of efficiency in dairy farms and to establish benchmarks that will guide efforts to improve efficiency and productivity in the region.
The novelty of this work lies precisely in the application of two recently developed bootstrap estimators in the literature, to construct confidence intervals for the technical efficiency of each unit. 20,21rious sections divide the structure of this work.The first section entails a literature review of technical efficiency models, followed by a third section that focuses on the methodology, specifically VRS and scale efficiencies. 20,21The fourth section presents empirical results, while the fifth section engages in a discussion, covering efficiency measurements, the VRS DEA model, and slack measurements.The subsequent section presents the conclusions.

Literature review
In this section, it aims to underscore the significance of measuring efficiency and explore the methods employed to gauge relative technological efficiency, often expressed as a frontier function.Two predominant methods for this purpose commonly are used: a) Data Envelopment Analysis (DEA), 22 that relies on mathematical programming; and b) Stochastic frontier analysis (SFA), which employs econometric approaches.For the scope of this study, were utilized the 7 DEAP 2.1 software (RRID:SCR_023002). 23he evolution of modern performance measurement, initiated by Färe, 24 who was further enriched by Farrell 6 who built upon the earlier work of Debreu 25 and Koopmans. 26This evolution culminated in the identification of two critical components of efficiency within a Decision-Making Unit (DMU): technical efficiency, which assesses a DMU's capacity to optimize revenues relative to input utilization, and allocation efficiency, which evaluates a DMU's ability to balance input allocation in response to market price variations. 6,25,26Farrell's innovation involved defining the input space and devising input-oriented approaches.

Slack
One key aspect of DEA is the slack variable (λ) which plays a pivotal role in addressing inefficiencies (as per Equation 3).In essence, a DMU's efficiency is measured on a scale from 0 to 1, with 1 signifying perfect efficiency (at the Frontier [ϕ]) and values approaching zero indicating increasing levels of inefficiency.Slack, on the other hand, represents the value needed for a DMU to reach the efficiency Frontier.Consequently, a DMU with an efficiency of 1 has a slack value of 0, while a higher slack score corresponds to greater inefficiency. 27,28A has experienced remarkable growth in both usage and 29,30 theoretical development since its inception in 1978 through the pioneering the work of Farrell, 6 and Charnes. 31The primary objective of this study is to measure the input costs and output income of various DMUs, assigning a quantified value to each relative efficiency.
The efficiency Frontier is determined based on achieving the highest income output with the least input costs.To estimate these efficiencies, two strategies are employed, depending on whether they are input or output-oriented. 32The first model, known a CRS/VRS, 32,33 is input-oriented and seeks the maximum proportional reduction in input usage while keeping output constant.Output-oriented models, conversely, aim to maximize output while adhering to input constraints.
By explaining these fundamental concepts, we establish a basis for understanding the subsequent sections, which will delve into the empirical results and discussions related to the efficiency of dairy farms in Tlaxcala.

Methods
Several studies have adopted a Data Envelopment Analysis (DEA) approach in Latin America to assess efficiency, as demonstrated by Arcos et al.'s work in the Ecuadorian mountain range. 34which accounts for 74% of the country's milk production.In the second phase of their research, they utilized the DEA model to determine scale efficiency (SE) and elasticities, analyzing data from 2014 to 2017 across different provinces.
Similarly, Sperat et al. 35 employed the DEA methodology using data gathered through interviews conducted on individual farms.Their study encompassed cluster analysis and discriminant analysis.The findings revealed an efficiency level of 59.5% for the region, with no apparent evidence to suggest that specific production styles act as limiting factors for the productive potential of each farm.

The variable returns to scale model (VRS) and scale efficiencies
In the study, it employed Data Envelopment Analysis (DEA), a widely recognized approach for assessing the efficiency of decision-making units (DMUs). 33DEA offers the flexibility to conduct both input-oriented and output-oriented analyses, allowing us to gain insights into different aspects of efficiency in dairy farm operations.
The dataset used for this study comprised 102 observations where one output (y) and three inputs (x 1, x 2 , x 3 ).These observations collected from six distinct regions within the state of Tlaxcala.The selection of these regions carried out using statistical conglomerate criteria, ensuring that the resulting sample remained both homogeneous and statistically significant.To gather data, a comprehensive questionnaire encompassing 42 variables designed.Its primary purpose was to conduct a socio-economic diagnosis of the selected regions and to facilitate the measurement of efficiency and productivity within the production units.In the context of efficiency and productivity assessment, three specific inputoutput pairs were chosen for the investigation, aligning with the core objectives of our research. 36 the methodology, it implemented Data Envelopment Analysis (DEA) a nonparametric mathematical programming technique employed for the calculation of efficiency boundaries.8][39][40] As DEA is best represented in terms of percentages or ratios, the computation required expressing the percentage of all outputs relative to all inputs.This enabled us to plot u 0 y i /v 0 x i represents an M-byM-by-1 vector of output weights, v represents a K-by-1 vector of input weights or proportions. 7The outcome of this calculation, u 0 y i /v 0 x i represents the efficiency (ϕ) measured as a percentage.The Banker Charnes Cooper (BCC) mathematical programming model 33 was used to determine the optimal weights or proportions, as specified in (Equation 1).This step is critical for evaluating and comparing the relative efficiency of different decision units, ultimately allowing us to draw valuable insights into the efficiency and productivity of dairy farms in Tlaxcala: The calculation of the efficiency measure using the DEA model yields a set of values for 'u' and 'v,' which correspond to the efficiency of each maximized DMU.However, a challenge with this estimation lies in the fact that there can be infinitely many solutions.To circumvent this issue and ensure a meaningful outcome, we introduce a constraint.This constraint involves ensuring that the sum of 'v' times 'x i ' equals one, where 'J' represents the number of each selected dairy farm.This constraint is expressed mathematically as v 0 x i = 1, as indicated in Equation 2: 33 By imposing this constraint, i obtain a more meaningful and interpretable set of efficiency measures, facilitating a clear assessment of the relative efficiency of the selected dairy farms in our study.
It's important to note that the expressions for 'u' and 'v' undergo some adjustments, primarily because their precise forms are not initially known due to the nature of the multipliers in the linear programming problem.Leveraging the principles of duality in linear programming, we can derive an equivalent form, as illustrated in Equation 3.This transformation is particularly relevant when transitioning from a Constant Returns to Scale (CRS) linear programming problem to one that accommodates Variable Returns to Scale (VRS). 33To use this, we introduce an additional convexity constraint, N1 0 λ = 1.
Where θ represents the Efficiency coefficients.y i signifies the output and x i refers to the inputs, and, λ denotes the slack, expressed as a percentage.The slack value represents the necessary adjustment required for a decision unit to reach the efficiency frontier.This transformation allows for a more robust assessment of efficiency, especially when considering variations in scale within the dairy farm operations.
Equation 3 is designed to accommodate the 'N1' vector, which in practice would be represented as 'N' times 'x1'.This particular form is recognized as an enclosing or expansion form, as it minimizes the constraints imposed by the multiplier form (specifically, 'KM < N1').According to Farrell, this form is the preferred way of finding solutions. 6It's worth highlighting that this equation plays a pivotal role in transitioning from Constant Returns to Scale (CRS) to Variable Returns to Scale (VRS).Traditionally Cross-efficiency evaluation in DEA developed under the assumption of CRS.However, no substantial attempts made to apply the concept of cross-efficiency to the VRS condition, primarily due to the potential emergence of negative VRS cross-efficiency for some decision-making units (DMUs).Given the increasing relevance of the VRS DEA model in practical applications, it becomes imperative to develop cross-efficiency measures under the VRS framework.In this context, the value 'θ' represents an estimate of the efficiency measure for each DMU, with 'θ' ≤ 1, as per the insights from Farrel, 6 Lanteri 38 and Shephard. 41When (ϕ) equals one, t serves as a cutoff point and signifies the efficiency measure for each DMU.This approach allows us to estimate both the efficiency (ϕ) and slack (λ) for each dairy farm in the study.To execute the DEA analysis using the DEAP 2.1 software, it necessitates the use of three essential files.The first file contains the data, structured in the order of Output, input 1, input 2, and input 3.
The second file serves as the instructions file, specifying crucial details such as the total number of observations (n), the presence of one output and three inputs, the orientation of DEA, and the assumed scale, which, in our study, is Variable Returns to Scale (VRS).These files are instrumental in conducting the DEA analysis and arriving at efficiency and slack estimates for the dairy farms under investigation.
Bootrapping DEA approach Enhanced validity of findings in a study results from the application of multiple methods. 42Cullinane et al. 43  The researchers employed a cluster sampling technique for data collection and sampling.They undertook the following steps to execute the cluster sampling process effectively: [a] Dairy farms were defined as the target population.
[b] The desired sample size to carry out the statistical study was determined [c] The researcher identified Clusters based on the size of the farms.Cesin-Vargas 46 and Cuevas Reyes 47 identified four types of dairy farms in in the study area based on farm size.Through principal components, cluster analysis, and analysis of variance, they categorized the farms into four types: 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 researchers selected the clusters that formed the sample of the statistical study randomly.
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, and Bootstrap approach.Consequently, of the 40 variables collected, only one output and three inputs, 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 research selected the variables in this study.For this, the output variable built by adding Total annual sale (USD) and Total annual sale of products obtained on the farm (USD).
[d] Input 1 constructed using the variable "Cost of investment in livestock" (USD).Input 2 formed by combining the variables "Annual cost of fuel" (USD), "Annual cost of food" (USD), "Annual cost of reproduction concept" (USD), and "Annual cost for animal health" (USD).Input 3 comprised the variables "Total annual cost of labor" (USD), encompassing both 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.
[f] For analysis, this study employs the 'Benchmarking' package within the R software.Further information regarding the methodologies utilized in De Borger et al. 45 and Banker et al. 33 The processing of the data in this study aligns with methodologies employed in other similar studies, albeit with variations in the organization and processing of information.Notably, the DEAP 2.1 software utilized a structured approach that involved three essential files: the data file, instruction file, and output or results file.This methodology adheres to the principles of Data Envelopment Analysis (DEA), a widely recognized approach for evaluating efficiency and productivity, despite recent criticisms in the literature. 36,48,49The second study under consideration employs a directional distance function and a single truncated bootstrap approach to investigate inefficiencies in lowland farming systems in the Benin Republic.This dual approach used to estimate and decompose short-run profit inefficiency into pure technical, allocative, and scale inefficiency, as well as input and output inefficiency.Additionally, an econometric analysis conducted using a single truncated bootstrap procedure to enhance statistical precision.While this approach differs from ours, recognize its utility and will consider adapting certain elements to our own methodological framework. 50 the third reviewed study, technical efficiency and the value of the marginal product of productive inputs in relation to pesticide analyzed to measure allocative efficiency.The methodology employs the DEA framework and marginal cost techniques.A bootstrap technique applied to overcome DEA limitations and estimate mean and confidence intervals.
Though this approach differs in some aspects, value the diversity of approaches in the literature and will consider how these findings may complement our research. 51e fourth study examines economies of scale and technical efficiency for a panel of Quebec dairy farms from 2001 to 2010.Stochastic frontier analysis, based on an input-distance function, estimates returns to scale relationships across dairy farms.Results indicate significant economies of scale and suggest that production costs reduced by improving technical efficiency.This study underscores the importance of considering these factors for Canada's supply management policy, which will also be a relevant aspect in our analysis. 52nally, the fifth study argues that bilateral auctions of production quotas induced rapid convergence in dairy farm size within provinces under Canada's supply management policy.This effect was stronger in provinces with a larger number of dairy farms, contributing to the smallness and homogeneity of Quebec dairy farms compared to those in Western Canada.This study highlights the importance of considering agricultural policy factors in efficiency analysis and provides an additional perspective that we will explore in our context. 53 this study, the data was meticulously organized and processed in accordance with the DEA approach, incorporating the relevant variables and input-output pairs.This rigorous methodology ensures that the assessment of efficiency and productivity within the selected dairy farms adheres to established best practices, offering a sound foundation for the subsequent analysis.This approach is in line with previous research that leverages DEA to evaluate the efficiency of decision-making units, in this case, the dairy farms under study.

Sample size and variables
The study conducted in 2020, and the sample comprised 102 dairy farms in six communities or regions across the Tlaxcala stated.The total population of dairy farms in the region estimated to be 71,000, according to data from the Secretary of Agricultural and Livestock Information (SIAP). 10Equation 6 incorporates the parameter 'Z,' which was estimated to be 1.93 (as indicated in Table 1), and it was employed with a probability 'p' of 50%, along with 'q' also set at 50%.Furthermore, a margin of error of 9% considered in the sample size calculation.(Out of the initially estimated 118 dairy farms based on the formula in Equation 6, only 102 were included in the study, as the others did not meet the statistical significance criteria necessary for the objectives of this investigation.The selection of production units carried out randomly and then evenly distributed among the six key regions of Tlaxcala that are significant in terms of milk production.This selection process adhered to two important criteria.Firstly, that the selection was entirely random, ensuring that all subjects within the population of dairy farms had an equal opportunity to be included in the sample, and secondly, that the number of selected dairy farms proportionally represented the population concerning the variable under investigation, taking into account the initial sample size calculation.This selection process aimed to create a representative sample that accurately reflected the population and its distribution with respect to the variable of interest. 54The selection process carried out in accordance with a formula described in the research, ensuring that the sample represented the population and its characteristics appropriately.This approach was pivotal in achieving robust and meaningful results for the study. Where, 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%)

Variables
This study used the DEAP 2.1 software (RRID:SCR_023002) 23 on a computer 33,48,55 to get standard CRS and VRS DEA model that involve the calculation of technical and scale efficiencies 32,33 of the data sampled during the study period 2020. 24This 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. 36The text to file data refer to S3, 36 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 labor (USD)".
Output (TVA i ): This variable represents 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. 7put 1 (CIG ij ): This variable represents the annual value of the cattle investment quantified in USD USA.
Input 2 (CT ij ): This variable represents the total annual cost for fuel, feeding, reproduction, illness and treatment, milking, mortality, and preventive medicine, measured in annual USD. 7put 3 (MO ij ): This variable represents the annual cost of family and hired labor, measured in USD.
Table 2 provides descriptive statistics for the variables used in the model.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 is available on protocols.io. 57The authors have chosen an input-orientation for the study due to its relevance in understanding how inputs or resources affect outcomes, as well as its potential to facilitate experimental control by focusing on variables that are more manageable and less prone to confounding factors.Additionally, the availability and reliability of data on inputs compared to outcomes may have influenced this decision.Finally, the choice aligns with theoretical frameworks guiding the research and addresses the specific research questions and objectives effectively.

Results and discussion
In the results section, the Data Envelopment Analysis (DEA) BCC model, which is characterized by Equations 1-3, as employed to assess the efficiency of dairy farms.The primary objective of this analysis was to identify the most efficient dairy farms, represented by the efficiency measure (ϕ).Efficiency in this context refers to the ability of a dairy farm to optimize its resource utilization to achieve the highest possible level of output while keeping inputs constant.The farms that achieve this efficiency considered reference points, or in other words, benchmarks for their counterparts that did not reach the efficiency frontier (ϕ).For the dairy farms that did not reach the efficiency frontier, the analysis quantified the percentage of their costs that would need reduced in order to reach the optimal level of efficiency.This percentage of cost reduction referred to as the "slack" (λ).It indicates the degree to which each non-efficient dairy farm falls short of optimal resource utilization and cost efficiency.The results from this analysis provide insights into the relative efficiency of the dairy farms under study, allowing for the identification of benchmarks and the quantification of cost-saving opportunities for less efficient farms.This information is crucial for decision-makers in the dairy farming industry and can guide strategies for improving overall efficiency and productivity. 19ficiencies measure VRS DEA model Table 3 provides a comprehensive overview of the research findings for the 102 dairy farms in Mexico.The results are based on estimations of Variable Return to Scale (VRS) and scale efficiencies, which involve the calculation of technical and scale efficiencies.This analysis is rooted in the methodologies of Färe et al., 24 and Banker, Charnes, and Cooper 33 which account for VRS. 28,29,58The VRS specification enables the assessment of technical efficiency from both Constant Return to Scale (CRS) and VRS perspectives, as well as the calculation of scale efficiency, denoted as crste/vrste (constant return scale technical efficiency between variable return scale technical efficiency).The findings reveal that some dairy farms exhibit high efficiency levels.For instance, farms numbered 1, 56, and 75 identified as efficient under both CRS and VRS technologies.These farms have managed to achieve optimal resource utilization and cost efficiency. 19n summary, the mean efficiencies for the dairy farms were as follows: 25% for CRS, 53% for VRS, and 44% for scale efficiency.These efficiency metrics offer valuable insights into the overall performance of the dairy farms, shedding light on the variations in technical and scale efficiencies among them.The analysis contributes to a better understanding of the dairy farming sector's efficiency landscape in Mexico.
Slack measure (λ) Table 4 provides insightful information related to the technical efficiency of dairy farms, emphasizing the differences in definitions of technical efficiency between Farrell 6 and Koopmans. 26Koopmans's definition of technical efficiency is notably stricter than Farrell's, 6 suggesting that any non-zero input slack or input overload is an accurate indicator of a dairy farm's technical efficiency in DEA analysis.Input slack, which is sometimes referred to as input overload, represents the degree to which a dairy farm falls short of optimal resource utilization and cost efficiency.In other words, it quantifies the cost that each dairy farm must reduce to reach an efficient operating point.Table 4 59 presents the percentages of weight peers and a summary of lambda (λ), highlighting the farms that serve as benchmarks for others.
The concept of peers refers to dairy farms that have reached the efficiency frontier (ϕ) in terms of costs and income.These benchmark farms considered reference points for others to follow.The number of times each farm serves as a peer to other farms also detailed in Table 5. Farm numbers 6 and 75 are notably frequent peers, serving as benchmarks for other farms on numerous occasions (peer count 62).This suggests that their operational practices and cost efficiencies are highly influential in guiding other farms toward improved efficiency.The peer-count data provides valuable insights into which farms play a crucial role in setting the efficiency frontier for the dairy farming sector.On the other hand, Slack's estimations (λ) based on Ali and Seiford 60 using second-stage linear programming to consider the cost that must be reduced to reach the level of the efficiency frontier. 61The 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.The inclusion of slack estimations and peer interactions enriches the understanding of the dynamics within the dairy farming sector, offering a nuanced perspective on efficiency and benchmarking practices.This information can be valuable for guiding decision-making and improving overall efficiency within the industry.Overall, these tables provide a detailed and nuanced perspective on the efficiency, peer relationships, and cost structures of the dairy farms in the study.Researchers and stakeholders in the dairy industry can use this information to make informed decisions, identify areas for improvement, and enhance the overall performance of the sector.

Input projected
This subsection discusses the results presented in Tables 6, 7 and 8, which show the projected cost reduction values.These values are determined by the multi-stage DEA (Data Envelopment Analysis) method and take into account excess costs associated with each input.The objective is to identify efficient projected points, which are characterized by having inputs that are as similar as possible to those of inefficient points, while also being invariant to units of measurement. 61,62The subsection also references the work of Ferrer and Lovell, [63][64][65][66][67][68][69] who argue that the slacks, or the excess resources, can be considered as allocative inefficiency.1][72] The cost minimization model (VRS) is utilized for peer evaluation, where each farm aims to assess the level of costs that should be reduced to attain the optimum production level indicated by the farms classified as peers. 13These findings are significant for enhancing production processes in the studied regions, as they help identify producers with the best income and, consequently, the lowest costs.Additionally, they contribute to the understanding of the cost reductions needed in each farm to achieve optimal conditions of productivity and technical efficiency.The interpretation of the data for the 102 farms based on Inputs 1, 2, and 3 (Tables 6, 7 and 8): Input 1 (CIG ij): Represents the annual value of cattle investment in USD.
Input 2 (CT ij): Represents the total annual cost for various aspects of cattle farming in USD.
Input 3 (MO ij): Represents the annual cost of family and hired labor in USD.
Farm 1: Input 1 chosen, indicating that investing in cattle was the best choice with a projected value of 75,600 USD.
Farm 2: Input 1 also chosen, implying that investing in cattle was the most cost-effective option, with a projected value of 20,604.836USD.
Farm 3: Similar to Farm 2, Input 1 selected as the best choice with a projected value of 47,149.357USD.
Farm 4: Input 2 chosen, suggesting that controlling costs related to fuel, feeding, and other expenses was the most efficient option, with a projected value of 24,019.822USD.
Farm 5: Input 2 again chosen, indicating that managing costs associated with fuel, feeding, and other aspects of cattle farming was the most economical choice, with a projected value of 26,407.438USD.
The analysis continues similarly for the remaining farms.It appears that for most farms, Input 1 is the preferred choice, suggesting that investing in cattle has a favorable financial outlook.Input 2 chosen for some farms, highlighting the significance of controlling operational costs, while Input 3 scarcely selected, emphasizing the relatively lower impact of      labor costs in this context.These selections based on the lowest projected values for each farm, reflecting their costeffectiveness.o determine which input was the best for each of the 102 farms, you should look at the information you provided in the tables and consider the input with the lowest projected value as the best choice for each farm.Here's the summary for the best input for each of the 102 farms:    ... and so on for the remaining farms.
So, for the majority of the farms, Input 1 was considered the best choice.However, for some farms, Input 2 was preferred.Input 3 appears to be the least chosen option, indicating that for most farms, it's not the most cost-effective input.The specific choice depends on the projected values and the criteria for cost-effectiveness.
Statistical sensitivity analysis in efficiency measurement: DEA Bootstrap Approach Table 9 describe the Shapiro-Wilk test.For the first dataset (bcc$eff), the Shapiro-Wilk test statistic (W) is 0.93172 and the p-value associated with this statistic is 5.28e-05 (which is very low).
For the second dataset (ccr$eff), the Shapiro-Wilk test statistic (W) is 0.56707 and the p-value associated with this statistic is 7.371e-16 (extremely low).
For the third dataset "Free Disposability Hull" (fdh$eff), the Shapiro-Wilk test statistic (W) is 0.82434 and the p-value associated with this statistic is 1.144e-09 (very low).
In all cases, since the p-values are significantly lower than the usual significance level of 0.05, we reject the null hypothesis that the data follows a normal distribution.Therefore, we can conclude that none of the datasets passes the Shapiro-Wilk normality test and they do not follow a normal distribution.
Given the lack of normality in the data, it is essential to employ robust statistical techniques that allow for a reliable assessment of efficiency.In light of the results from the Shapiro-Wilk test indicating non-normality, Bootstrap emerges as a crucial tool.As a resampling technique that does not rely on strict assumptions about the distribution of data, Bootstrap offers an effective solution for estimating the distribution of key statistics such as efficiency and computing confidence intervals.Its ability to adapt to the data's nature, even when it does not adhere to a normal distribution, provides a solid foundation for a rigorous and accurate analysis of efficiency in this context. 20,21ble 10 and Figure 1, illustrate the distribution of efficiency levels across different technologies.Each cell represents the percentage of farms falling within a specific efficiency range for the respective technology.The table displays the distribution of efficiency levels across various ranges for three different technologies: VRS (Variable Returns to Scale), CRS (Constant Returns to Scale), and FDH (Free Disposal Hull).The table layout is similar to the one presented by Simar and Wilson. 73S Technology: The majority of farms (35.29% to 46.08%) fall within the efficiency ranges of 0 to less than 0.2, indicating a relatively high level of efficiency.However, as the efficiency range increases beyond 0.5, the proportion of farms diminishes gradually, suggesting fewer farms operate at highly efficient levels under this technology.
CRS Technology: Similar to VRS, a significant proportion of farms (around 35% to 46%) exhibit high efficiency levels within the 0 to less than 0.2 range.Notably, there are instances where no farms achieve efficiency levels between 0.3 to less than 0.5, indicating potential inefficiencies for some farms under this technology.
FDH Technology: The distribution of farms across efficiency ranges under FDH displays a different pattern compared to VRS and CRS.While a notable proportion of farms operate at highly efficient levels (over 43%) when efficiency is exactly equal to 1, a substantial number of farms also demonstrate efficiency levels ranging from 0 to less than 0.2 (approximately 6.9% to 13.7%).Additionally, a sizable percentage of farms (over 10%) operate with efficiencies between 0.6 to less than 0.8, highlighting a varied efficiency landscape under this technology.
These intervals are constructed using bootstrap resampling, a technique for estimating the sampling distribution of a statistic by repeatedly resampling with replacement from the observed data.The resulting confidence intervals provide a range of plausible values for the population parameter estimated.
Upper Bound (97.5%), this value represents the upper limit of the confidence interval.It suggests that with 97.5% confidence, the true value of the parameter expected to be below this upper bound.
Lower Bound (2.5%), similarly, this value represents the lower limit of the confidence interval.With 97.5% confidence, the true value of the parameter expected to be above this lower bound.
The confidence levels (97.5% and 2.5%) indicate the probability that the true parameter lies within the calculated interval.
In this case, a 95% confidence level commonly used, implying that there is a 95% probability that the true parameter falls within the calculated interval.The use of 97.5% and 2.5% might suggest a higher confidence level, which could be appropriate depending on the specific requirements of the analysis.
These confidence intervals are valuable in statistical inference, hypothesis testing, and parameter estimation.They provide a measure of uncertainty around the estimated parameter values, allowing researchers to make informed decisions and draw valid conclusions from their data.
In conclusion, the provided bootstrap confidence intervals offer valuable insights into the uncertainty associated with the estimated parameters, but their validity assessed through appropriate validation procedures.Farm-Specific Considerations: Bootstrap analysis provided robust evidence supporting the variability in optimal input choices among farms, reinforcing the importance of considering individual farm characteristics.

Conclusions
Insights from Radial and Slack Values: Bootstrap analysis enhanced the reliability of insights derived from radial and slack values, providing confidence in identifying areas for improvement and optimization.
Policy Recommendations for Mexico's Agricultural Sector Support for Cattle Investment: Policies incentivizing and supporting cattle investment, backed by robust bootstrap analysis, can enhance efficiency and economic viability in dairy farming.
Comprehensive Cost Management: Bootstrap-supported policies focusing on comprehensive cost management, including fuel, feeding, and reproduction, can improve overall farm efficiency.
Optimization of Labor Costs: Bootstrap analysis reinforces the need for initiatives aimed at optimizing labor costs, such as training programs and technology adoption, to enhance labor efficiency on dairy farms.
Tailored Support: Policies informed by bootstrap analysis should be flexible and tailored to accommodate farm-specific factors, promoting efficiency based on robust evidence.
Promotion of Data-Driven Decision-Making: Bootstrap-supported policies promoting data-driven decision-making and technology adoption can optimize inputs and improve overall efficiency with greater confidence in the findings.
Encouragement of Optimization Strategies: Policies encouraging the adoption of practices aimed at reducing costs in identified areas, validated by bootstrap analysis, can lead to performance and sustainability improvements.
By integrating bootstrap analysis into policy recommendations, Mexico can advance towards a more efficient and sustainable agricultural landscape.Leveraging insights from both data analysis and robust bootstrap validation ensures that policies are evidence-based and capable of driving meaningful improvements in dairy farming efficiency and sustainability.

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.
This project contains the following extended data: • Questionnaire MilkProd.pdf(Questionnaire/interview guide translated to English) • Questionnaire de campo_leche.pdf(Questionnaire/interview guide in Spanish) • Table 1.csv • Table 3.scv • Table 4.csv • Table 5.csv • Table 6.csv • Table 7.csv • Table 8.csv • Table 9.csv • Table 10.xlsx • Table 11.xlsxReviewer Expertise: Bioeconomy and value chain in the agri-food sector I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.

Is the work clearly and accurately presented and does it cite the current literature? Yes
Is the study design appropriate and is the work technically sound?Yes

If applicable, is the statistical analysis and its interpretation appropriate? Yes
Are all the source data underlying the results available to ensure full reproducibility?Yes

Are the conclusions drawn adequately supported by the results? Yes
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 include: 1) All over the manuscript, Data Envelopment Analysis instead of data envelope analysis or envelope data analysis 2) Scale efficiency instead of Efficiency of scale 3) In the last sentence of page 4 "achieve" should be "use" 4) In the first paragraph of page 5, proportional is valid for only CRS model and it does not apply for VRS.Under VRS assumption, proportionality does not apply anywhere over the manuscript.
5) The authors have chosen an input-orientation for the study.What is the justification for such a choice?6) The paragraph before model (1) presents several inaccurate statements and it must be revised with a lot of care.7) In model ( 2), the objective and the first constraints are wrong.8) What is the purpose of Table 1? 9) There seems to be a lot of confusion about the models used.The authors used the standard DEA VRS model but, at different levels, they mention the radial model and the cross-efficiency model and other information that might not be useful for practitioners.Since the paper's contribution is mainly an application, it is better to remove any theoretical concept and formulas that are not directly related to the methodology used.10)In the efficiency results, it is also important to identify the benchmarking farms, which should necessarily be strongly efficient.As such, the authors should clearly distinguish the weakly and the strongly efficient farms by using the slack values.See, e.g., ref [2]and [1]  11)In the application, it is enough to mention the software used, without more details on how it has been implemented on the data sample.
We also appreciate your attention to language editing concerns, typos, and formulations.We will conduct a thorough review and editing process to address these issues and ensure the clarity and precision of our manuscript.Your constructive feedback is invaluable to us, and we are committed to making the necessary improvements to enhance the overall quality of our work.We look forward to submitting a revised version that addresses these concerns and better aligns with the standards of the field.Response: In the literature review section, I added these references and incorporated three additional paragraphs, also en results section.
[3] Since dairy farmers in Mexico are not looking only to minimize the cost of inputs but also to maximize their output especially in this financial turmoil that farmers are facing; I would suggest authors to apply the directional distance function that maximize profit.I would also suggest authors to look for the bootstrapping approach to correct for the bias of the nonparametric DEA.I would suggest authors to review deeply the paper and follow recent improvement in empirical literatures as well as in dairy sector.
Response: Thanks for this observation; we have been address this as following: Directional Distance Function: We have thoroughly investigated the application of the directional distance function in the context of dairy farming and have found it to be a meaningful enhancement to our methodology.
The revised manuscript now incorporates a detailed explanation of how the directional distance function aligns seamlessly with our study objectives, specifically focusing on maximizing profits.Although the purpose of our research was to consider costs based on inputs.
Bootstrapping Approach: Recognizing the importance of addressing bias in non-parametric DEA, we have explored and implemented a bootstrapping approach in our analysis.A dedicated section in the methodology now outlines the utilization of the bootstrapping technique, providing transparency in correcting biases and ensuring the robustness of our findings.
In-Depth Review and Recent Literature: A comprehensive review of the entire paper has been conducted, with a keen focus on recent improvements in empirical literature and advancements in the dairy sector.The literature review section has been updated to incorporate recent insights, ensuring that our study remains current and aligned with the latest developments in the field.These revisions have significantly strengthened our manuscript, enhancing its alignment with recent advancements and addressing the specific concerns raised by the reviewer.We believe these changes contribute positively to the overall quality and relevance of our research.
Thank you for your continued support and guidance throughout this process.We look forward to further feedback and the opportunity to contribute to the advancement of knowledge in our field.

Ayele Gelan
Economics, Kuwait Institute for Scientific Research, Safat, Kuwait 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.
Readability.The paper will need to be rewritten to improve its readability.In its current format, it is extremely difficult to follow the idea follow in the paper.The authors will need to work on the paper, ensuring that ideas develop and flow paragraph by paragraph or section by section reasonably coherently.
Motivation.The authors have not made any effort to provide some motivation for the paper.Why they set out to conduct the study?The reader expects to read some statement related to specific problems in the context of the study area and, importantly, a clear objective of the study.These are lacking in the introduction.The authors alluded population growth but these is further away from the geographic scope of the study.Instead of objective of the paper, some claim on the "contribution" of the paper was mentioned in the introduction.
Literature review and methodology.The authors need to conduct a concise and clear literature review.Elements of literature review are scattered in the introduction, a brief section labelled as literature review and the methodology.There is a section devoted to "methodology" but methodology of the study is intermixed with literature review as well.
Data use and presentation.The problem with inappropriate data use and presentation started from the very outset.For instance, there is no meaning to be extracted from data plotted in Figure 1, where two lines plotted, both in somewhat straight horizontal lines!If it is a must to present that data, then the authors could change the scale so that some variation becomes visible.In any event, it is unusual to present a chart in an introduction.
The most serious problem with data use and presentation happened latter, "projections" of efficiency score results generated by a standard software the authors applied to the survey data (Tables 6, 7, 8).Since the authors have not provided interpretations and explanations, it is not clear at all as to what numbers in those tables represent.Having presented tables, the authors went straight to the conclusion section.

Conclusion.
The authors concluded: "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."It is unclear what is meant by "multi-stage" here.In DEA analysis, multi-stage has a specific connotation: stage 1: calculating DEA scores (efficiency scores) and stage 2: application of statistical methods to explain the efficiency scores, using, in this case, farm characteristics obtained through the survey.Clearly, stage 2 was not conducted in this study.Therefore, the claim that multi-stage was applied was rather confusing.
section labelled as literature review and the methodology.There is a section devoted to "methodology" but methodology of the study is intermixed with literature review as well.

Response:
In response to the identified concerns and with a commitment to improving the manuscript, the authors have undertaken a series of refinements.To enhance clarity and coherence, a distinct and comprehensive literature review section has been incorporated.This section strategically consolidates all pertinent information previously scattered throughout the manuscript, providing a thorough overview of existing research and establishing a solid foundation for the study.Furthermore, the methodology section has undergone a restructuring process, now exclusively focusing on detailing the research methods employed in the study.All content related to the literature review has been meticulously relocated to the dedicated literature review section.This strategic separation aims to create a more organized and readerfriendly manuscript, fostering a clear distinction between the theoretical framework and the practical research methods employed.
In addition to these adjustments, the introduction has been revised to function as a concise overview of the research topic, without delving into specific literature review details.This refined approach ensures a logical flow and contributes to an improved overall structure of the paper.These enhancements collectively contribute to a more coherent and well-organized manuscript, elevating the overall quality of the research article and addressing the initial concerns raised.
[5] Data use and presentation.The problem with inappropriate data use and presentation started from the very outset.For instance, there is no meaning to be extracted from data plotted in Figure 1, where two lines plotted, both in somewhat straight horizontal lines!If it is a must to present that data, then the authors could change the scale so that some variation becomes visible.In any event, it is unusual to present a chart in an introduction.

Response:
Thanks for this observation.The Figure 1 was eliminated.
[6] The most serious problem with data use and presentation happened latter, "projections" of efficiency score results generated by a standard software the authors applied to the survey data (Tables 6, 7, 8).Since the authors have not provided interpretations and explanations, it is not clear at all as to what numbers in those tables represent.Having presented tables, the authors went straight to the conclusion section.

Response:
In the Input subsection projected before the conclusions, we have reinforced the analysis and interpretation of the results by emphasizing the expenditure projections that the production units need to reduce in their costs compared to the peers that reached the efficiency frontier.Table 6, Table 7, and Table 8 provide information on the projection summary for various farms using the multi-stage DEA method, showcasing original movement, radial movement, slack values, and the projected values.These tables are used to assess the efficiency of different farms in terms of cost reduction and technical efficiency.Let's break down the interpretation for each table: Table 6: Each row in Table 6 corresponds to a different farm.
The "Original movement" represents the initial cost or expenditure for various inputs in each farm.
The "Radial movement" indicates how much a farm can reduce its costs while maintaining a similar level of production.
The "Slack value" represents the excess or unutilized resources.
The "Projected" column shows the projected cost after optimizing.Table 7 and Table 8: These tables follow a similar format to Table 6, providing information for additional farms.These tables are crucial for evaluating farm efficiency.Farms that can reduce their costs and have lower slack values are generally considered more efficient in terms of resource utilization.The "Projected" column indicates the expected cost once these efficiencies are realized.The tables enable a comparative analysis of different farms to identify areas where cost reduction and efficiency improvements can be made.
To identify the best farm, we should consider the one with the most favorable projection values, which reflect reduced costs and increased efficiency.Specifically, we are looking for farms with the following characteristics: Low Slack Values: Farms with lower slack values have fewer unutilized resources and, therefore, are more efficient in resource allocation.
Positive Radial Movement: Positive radial movement means that the farm can reduce its costs while maintaining similar production levels, which is a sign of efficiency improvement.Low Projected Costs: The lower the projected cost, the more efficient the farm in terms of cost reduction.
If you have specific questions or need further analysis of the data from these tables, please feel free to ask.The analysis and interpretation go before of this Tables 6, 7 and 8.A resume go in the subsection Input projection.
[7] Conclusion.The authors concluded: "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 multistage method the efficiency of the Tlaxcala dairy farm was assessed."It is unclear what is meant by "multi-stage" here.In DEA analysis, multi-stage has a specific connotation: stage 1: calculating DEA scores (efficiency scores) and stage 2: application of statistical methods to explain the efficiency scores, using, in this case, farm characteristics obtained through the survey.Clearly, stage 2 was not conducted in this study.Therefore, the claim that multistage was applied was rather confusing.

Response:
The observation regarding the ambiguity surrounding the term "multi-stage" in the conclusion is noted.To clarify, in the context of this study, the multi-stage approach refers to the two distinct stages of input-oriented DEA analysis.Also we add the Bootstrap technique.
Scale Assumption: The study adhered to the constant returns to scale (CRS) assumption in its input-oriented DEA analysis.Slacks Calculation: The multi-stage process involved the following: Stage 1: Calculating DEA scores (efficiency scores), which are clearly presented in Table 3. Stage 2: Application of statistical methods to explain the efficiency scores, specifically focusing on slacks.The detailed results for this stage are available in Tables 4, 5, and 6.It

Figure 1 .
Figure 1.Efficiency distribution among farms under different technologies.

•
Fig_1.tif • Fig_2.tif• Data for DEA F1000R.xlsxData are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0).This study addresses the efficiency of dairy farms in Tlaxcala, Mexico, by measuring mean efficiency for CRS, VRS, and the estimated scale efficiency.With a growing population and adverse climate change conditions, scarce resources must be used more efficiently to produce food.This research thus contributes to helping production managers identify the causes of low efficiency and productivity in the dairy sector of the region.However, it would be important to expand the recommendations on how public policy decision-makers could use this information.Although the state of Tlaxcala is not representative in terms of milk production, this study can offer as a reference for replication in other production systems, allowing for the establishment of benchmarking.The article is scientifically valid in its current form.The methodology employed is correct and is widely used in other studies.This methodology can be used to generate indicators based on dairy herd size.The study mentions that Cesin-Vargas and Cuevas Reyes identified four types of dairy farms in the study area based on farm size.The results are presented in accordance with the methodology employed, and the conclusions align with the study's objectives.I suggest, if possible, evaluating the results by herd size, as this would allow for reference to the behavior of low efficiency and productivity in dairy herds by size.It would also help identify which farms are efficient and which are weak, allowing for their characterization and use as references for other studies.Is the work clearly and accurately presented and does it cite the current literature?PartlyIs the study design appropriate and is the work technically sound?YesAre sufficient details of methods and analysis provided to allow replication by others?YesIf applicable, is the statistical analysis and its interpretation appropriate?Yes Are all the source data underlying the results available to ensure full reproducibility?No Are the conclusions drawn adequately supported by the results?Yes Competing Interests: No competing interests were disclosed.
33d Wang et al.44exemplified in port benchmarking studies, illustrated by.Therefore, in this study, the benchmarking of the container terminal's technical efficiency and the comparison of results rely on the utilization of DEA and Free disposal hull (FDH) methods.Technical efficiency of a container terminal is deemed achieved when it maximizes throughput For analysis purposes, this study utilizes the 'Benchmarking' package in the R software.Additional details on the methodologies employed are available in De Borger et al.45and Banker et al.33Data source and locationThe study took place in the state of Tlaxcala, located in the highlands of Mexico.The geographic coordinates of this region range from approximately 98 degrees 3 inches west longitude to 97 degrees 38 minutes north latitude and 19 degrees north latitude to 06 degrees latitude. A enerally mild climate characterizes Tlaxcala, with some rainfall during the summer months.The typical elevation in the study area is approximately, contributing to the region's unique agricultural and ecological characteristics.

Table 1 .
56score for the p-value and confidence level.56

Table 2 .
Descriptive statistics of the variables.

Table 4 .
Summary Peers and lambda weigh %.

Table 5 .
Continued *Number of times each farm is a peer for another.

Table 10 .
Summary of efficiencies.VRS, CRS technology and input orientated efficiency.

Table 11 .
Bootstrap confidence intervals analysis for population parameters estimation.

Table 11 .
Continued Enhancing Efficiency and Policy Recommendations for Tlaxcala's Dairy Farming Sector with Bootstrap AnalysisThis study employed Data Envelopment Analysis (DEA) to scrutinize the efficiencies of Tlaxcala's dairy farms, incorporating bootstrap analysis to validate and enhance the robustness of the findings.Utilizing the Variable Returns to Scale (VRS) model and DEAP version 2.1 software, the analysis ensured methodological transparency and adherence to DEA conventions.