RELATIVE PERFORMANCE (IN)EFFICIENCY IN QUANTITATIVE MATRIX CURRICULAR UNITS: AN INTERTEMPORAL ANALYSIS OF DEA-CRS AT THE SCHOOL OF HOTEL AND TOURISM OF AGOSTINHO NETO UNIVERSITY

Abstract

This study assesses the dynamics of relative academic inefficiency of three quantitative curricular units: advanced mathematics, statistics applied to tourism, and accounting and finance, within the tourism management program at the Agostinho Neto University School of Hotel and Tourism, between 2015 and 2024. Using the DEACRS intertemporal approach with moving windows, performance variations were analyzed based on academic inputs and outputs. The results revealed heterogeneous patterns of inefficiency. The reduced workload was the main source of inefficiency in advanced mathematics; the final grade point mean and approval rate were critical in statistics applied to tourism; and, paradoxically, the small number of students and the high approval rate generated inefficiencies in accounting and finance. The construction of the DEA-DIFO diagnostic matrix stands out, which maps the sources of inefficiency by curricular unit and by time window. The negative correlation between the number of students and variables such as workload, final grade point mean, and approval rate suggests that increased student density is not associated with improved performance at the Agostinho Neto University School of Hotel and Tourism. The adoption of qualityoriented DEA models is recommended to optimize the teaching-educational process and support evidence-based curricular decisions. As a unique contribution, this study applies DEA to measure the relative academic inefficiency of curricular units.

Keywords:
DEA-CRS; academic inefficiency; academic diagnosis.

Resumo

O presente estudo avalia a dinâmica da ineficiência acadêmica relativa de três unidades curriculares de matriz quantitativa: matemática superior, estatística aplicada ao turismo e contabilidade e finanças, ministradas no curso de gestão de turismo na Escola de Hotelaria e Turismo da Universidade Agostinho Neto, entre 2015 e 2024. Utilizando a abordagem intertemporal DEA-CRS em janelas móveis, foram analisadas variações de desempenho a partir de inputs e outputs acadêmicos. Os resultados revelaram padrões heterogêneos de ineficiência. A reduzida carga horária foi a principal fonte de ineficiência em matemática superior; a média final e a taxa de aprovação foram críticas em estatística aplicada ao turismo; e, paradoxalmente, o número reduzido de estudantes e a elevada taxa de aprovação geraram ineficiências em contabilidade e finanças. Destaca-se a construção da matriz de diagnóstico DEADIFO, que mapeia as fontes de ineficiência por unidade curricular e por janela temporal. A correlação negativa entre o número de estudantes e variáveis como carga horária, média final e taxa de aprovação sugere que o aumento da densidade estudantil não está associado ao melhor desempenho na Escola de Hotelaria e Turismo da Universidade Agostinho Neto. Recomenda-se a adoção de modelos DEA orientados à qualidade, visando otimizar o processo docente-educativo e apoiar decisões curriculares baseadas em evidência científica.

Palavras-chave:
DEA-CRS; ineficiência acadêmica; diagnóstico acadêmico.

Resumen

Este estudio evalúa la dinámica de la ineficiencia académica relativa de tres unidades curriculares cuantitativas: matemática superior, estadística aplicada al turismo y contabilidad y finanzas, dentro del curso de gestión turística de la Escuela de Hotelería y Turismo de la Universidad Agostinho Neto, entre 2015 y 2024. Utilizando el enfoque intertemporal DEA-CRS con ventanas móviles, se analizaron las variaciones en el rendimiento con base en los insumos y productos académicos. Los resultados revelaron patrones heterogéneos de ineficiencia. La reducida carga académica fue la principal fuente de ineficiencia en matemática superior; el promedio de calificaciones final y la tasa de aprobados fueron cruciales en estadísticas aplicadas al turismo; y, paradójicamente, el reducido número de estudiantes y la alta tasa de aprobados generaron ineficiencias en contabilidad y finanzas. Se destaca la construcción de la matriz del diagnóstico DEA-DIFO, que mapea las fuentes de ineficiencia por unidad curricular y por ventana temporal. La correlación negativa entre el número de estudiantes y variables como la carga académica, el promedio de calificaciones final y la tasa de aprobados sugiere que una mayor densidad estudiantil no se asocia con un mejor rendimiento en la Escuela de Hotelería y Turismo de la Universidad Agostinho Neto. Se recomienda la adopción de modelos DEA orientados a la calidad para optimizar el proceso docente-educativo y respaldar las decisiones curriculares basadas en la evidencia.

Palabras clave:
DEA-CRS; ineficiencia académica; diagnóstico académico.

1 INTRODUCTION

The assessment of the relative efficiency of Course Units (CUs) constitutes an innovative approach to understanding curricular performance across multiple dimensions. Relative academic inefficiency is understood here as the inability of each CU to convert its educational resources into academic outcomes relative to the other units under study. Thus, the concept of academic inefficiency adopted in this study constitutes an operational performance indicator which, at the level of the teachinglearning process, measures the degree of suboptimization of resources used namely, the number of students and the workload, relative to the results obtained: the final grade and the approval rate in CUs, per year.

The courses in advanced mathematics, statistics applied to tourism, and accounting and finance, although distinct in their subject matter and objectives, share a quantitative and analytical foundation, which makes them comparable in terms of academic productivity, resource allocation, and educational impact. From this perspective, Data Envelopment Analysis (DEA), as a non-parametric technique, allows for the measurement of the relative efficiency of these courses by accounting for their ability to handle multiple inputs and outputs. By applying DEA models under constant returns to scale (DEA-CRS), it is possible to identify which courses operate close to the efficient frontier and which have slack that can be optimized. This approach provides valuable insights for curriculum redesign, institutional management, and the replication of best academic practices across disciplines, promoting a more rational allocation of resources and an education that is better aligned with the needs of the labor market.

Given the importance of quantitative analysis in management programs in general, particularly in developing competencies that enable future managers to understand corporate dynamics from economic and financial perspectives, this study aims, in an exploratory manner, to assess the dynamics of relative academic inefficiency in student performance in courses on advanced mathematics, applied statistics in tourism, and accounting and finance, in the tourism management program, during the 2015-2024 period, at the School of Hotel and Tourism (ESHOTUR) of Agostinho Neto University (UAN), using the DEA window approach. To achieve this broader goal, the study aims to: measure the operational efficiency of the academic units each year, taking into account selected pedagogical inputs and academic outputs; apply the DEA window technique to capture the dynamics of inefficiency over time, identifying patterns of improvement, stability, or regression in the results; detect slacks associated with low conversion of inputs into outputs; propose a diagnostic matrix for pedagogical shortcomings that enables their classification and corresponding corrective actions, highlighting critical areas for intervention.

The relevance of using the DEA window technique for this study stems from the need to incorporate the temporal dimension into the assessment of academic inefficiency, overcoming the limitations of static models. By treating each course in each year as a Decision-Making Unit (DMU), the model captures the effect of natural student turnover, enabling consistent comparisons across periods. Complementarily, the input-oriented approach is well-suited to the academic context, where constraints of various kinds, such as pedagogical, human, or even financial resources, are more controllable by administrators and faculty.

Finally, the study is relevant to the evaluation of higher education, as it provides local administrators and regulators with a more informed understanding of the academic inefficiencies in the course units for advanced mathematics, statistics applied to tourism, and accounting and finance, with potential implications for the efficiency of these same course units, other business management programs, and academic contexts similar to those at ESHOTUR.

2 THEORETICAL APPROACHES

2.1 Assessment in higher education using DEA models: an overview

Following the pioneering study by Charnes, Cooper, and Rhodes (1981), who applied DEA to research on the efficiency of a higher education institution’s (HEI) academic program, several studies have been conducted using the same methodology and with the same objective. Among the most recent studies that can be cited as references are those by (Aziz; Janor; Mahadi, 2013; Tavares; Meza, 2017; Alanazi; Benlaria, 2023; Egorov; Serebrennikov, 2023).

The teaching-learning process has a multidimensional nature, which considers various response variables and explanatory variables; therefore, the DEA methodology, with its capacity for multiple inputs and multiple outputs, has been widely used in the evaluation of HEIs, both at the institutional and departmental levels, as reviewed below. This view is corroborated by authors such as Gori et al. (2025), according to whom the heterogeneity of HEIs has resulted in a challenge of proven complexity, with DEA emerging as the primary technique used to assess efficiency in this area.

In the context of higher education, contemporary literature on the assessment of the technical efficiency of higher education institutions generally evaluates the robustness of results obtained through DEA models using procedures carried out in two or more stages: in the first stage, DEA scores are obtained, and in subsequent stages, their robustness is assessed (Ruggiero, 2004; Johnes, 2006; Fuentes, Fuster, and Lillo-Bañuls, 2016; Wolszczak-Derlacz, 2017). However, in the present study, similar to works such as those by Shero et al. (2022) and Jha (2025), technical efficiency is assessed using an initial approach, in which only the DEA scores are obtained, and, in a complementary and independent manner, the values of the coefficients of determination for the linear technical efficiency trajectories are analyzed across analysis windows under the condition of constant returns to scale. More specifically and in line with the DEA model used in the present study (CRS), the works of Aziz, Janor, and Mahadi (2013); Avilés-Sacto et al. (2020), and Gökşen, Doğan, and Özkarabacak (2015), who also did not use support models to assess the robustness of the DEA scores.

There are very few studies on the evaluation of higher education institutions in Angola using approaches from the field of DEA; records of the works by (Chicomo; Dias, 2019; Sanches-António, 2026), have been found.

Within the context of the Southern African Development Community (SADC), to which Angola belongs, publications predominantly focus on South Africa; in this regard, the studies by (Taylor, 2004; Myeki; Temoso, 2019; Nkohla et al. 2021), can be cited. However, its use has been widespread at the international level. A broader view of the subject can be found in Witte and López-Torres (2017), which presents structural aspects for evaluating the efficiency of HEIs, using DEA methodologies such as the Malmquist index, bootstrapping, and robust frontiers. The study also presents a summary of the main variables (input-output) previously applied, as well as the data sources used in articles in the field of efficiency analysis in education, both an activity and a sector of activity.

Nonparametric methods, with their tolerance for units of measurement of different metrics, beyond monetary ones and their ability to accommodate multiple inputs and outputs, represent a highly useful tool for measuring the efficiency of service-providing units, whose results are not always easily quantified. This is the case with efficiency in the teaching-learning process, where the path to efficiency must take into account the multiple resources used and possible outcomes. In this vein, the DEA methodology has been widely used to assess the efficiency of various aspects of academic activity at higher education institutions, across diverse geographic and administrative contexts, for more than four decades.

First introduced by Charnes, Cooper, and Rhodes (1978), the analysis involving data on a frontier composed of efficient DMUs, in its DEA-CRS version, assumes that changes in inputs produce proportional changes in outputs; thus, as an input-oriented model, it assumes that, once output quantities are held constant, decreases in input quantities are expected.

Although not the focus of this study, the DEA-CRS methodology, as a theoretical-empirical tool for evaluating HEIs, intending to provide an overview of its formal, input-oriented component and consider the maximum and minimum constraints, has the following mathematical structure:

Objective function: the model seeks to maximize the weighted ratio of the outputs of the DMU_k, that is, to find the optimal weights u_r that maximize its efficiency scores;

$$h_k=\sum _{r=1}^s{u}_r{y}_{rk}$$

h_k: Relative technical efficiency of the DMU_k

y_rk: Quantity of output r produced by the DMU_k

u_r: Weight assigned to output r → decision variable

Restrictions: the efficiency scores of the DMUs must have values between 0 and 1. The included restrictions ensure that with the same weights (u_r e v_i), no other DMU_j has an efficiency score greater than 1, which defines the efficiency frontier;

$$\sum _{r=1}^m{u}_r{y}_{rj}-\sum _{i=1}^n{v}_i{x}_{ij}\le 0$$

y_rj: Quantity of output r produced by the DMU_j

x_ij: Quantity of input i produced by the DMU_j

v_i: Weight assigned to input i → decision variable

Normality of DMUs: the inputs of the DMU_k are normalized to 1, causing the efficiency h_k to be interpreted as a ratio between weighted outputs and inputs;

$$\sum _{i=1}^n{v}_i{x}_{ik}=1$$

Non-negativity condition: in accordance with the assumptions of production theory, the weights assigned to both inputs and outputs must have non-negative values;

$$u_r,v_i\ge 0$$

Where y: outputs; x: inputs; r: 1,…, m; i: 1,…, n; j: 1,…, N.

According to Gujarati and Porter (2025), the R² provides information about the relationship between what the model explains (the difference between observed and estimated values, which appears in the numerator) and what the model does not explain (the difference between observed values and the mean, which appears in the denominator), where y_i: observed value of the dependent variable; ${\hat{y}}_i$: value estimated by the regression model and y̅_i: mean of the observed values of the dependent variable. Its mathematical formulation is as follows:

$$R^2=1-\frac{\sum _{i=1}^N{(y_i-{\hat{y}}_i)}^2}{\sum _{i=1}^N{(y_i-{\overline{y}}_i)}^2}$$

Since this methodology is based on a nonparametric approach, the efficiency scores for the DMUs in the sample are obtained through a process of linearizing inputs and outputs, which allows for the construction of an efficiency frontier composed of the efficient DMUs. In this sense, and independently, based on the coefficients of determination R², it is possible to measure how effective the explanatory factors (inputs-outputs) are in capturing the variability of the DEA scores obtained across the analysis windows, serving as an indicator of consistency. This is evidenced by the regression lines presented in Graph 1 and 2, where each dashed line is a line fitted to the observed points, that is, the efficiency means in each window.

Graph 1
Efficiency trends for all CUs (2015-2024)

Thus, these are not (multiple or polynomial) regressions, but rather simple linear regressions, with lines individually fitted to each series of efficiency indicators for each CU, in each analysis window. The general structure of the model is formulated as follows:

$$Y_{d.i}={\alpha }_d+{\beta }_d\cdot X_i+{\epsilon }_{d,i}$$

Where:

Y_d.i: Mean efficiency (%) of discipline d in window i (dependent variable)

X_i: Window index (1, 3, 3…6) (independent variable)

α_d: Expected value of efficiency when X = 0

β_d: Rate of change of efficiency per window, indicating its trend

ɛ_d,i: Portion of efficiency not explained by regression

In summary, the simple linear regression model (per variable) presented serves to explain how variations in efficiency (per window) explain variations in efficiency, while the R² indicates how much this line explains the variation in the data used.

2.2 Panoramic view of higher education in Angola

Higher education is one of the fundamental pillars of any nation’s development, as it is responsible for training technical and academic professionals who drive social, economic, and cultural progress. In Angola, this educational subsystem has undergone profound transformations since independence in 1975, reflected in public policies, institutional expansion, and the regulation of the higher education sector. This section describes the evolution of Angolan higher education, highlighting the major historical milestones that have shaped its structure to the present day, as well as its challenges and prospects.

With the proclamation of independence in 1975, Angola inherited a centralized educational system limited to a few provinces. The creation of the University of Angola, later renamed UAN in 1985, was an initial milestone in the construction of a national higher education system (Carvalho, 2012).

Regulation began with presidential Decree nº 37/80 of June 17, which approved the organic statute of the University of Angola and the academic staff statute (Angola, 1980). With the transition to a multiparty system and a market economy in the 1990s, higher education underwent significant reforms. The creation of the Catholic University of Angola (UCAN) in 1992 marked the beginning of private sector participation in higher education. The absence of a specific body to manage the subsystem led to the centralization of decision-making at the UAN until the early 2000s.

After the end of the civil war in April 2002, the country began a process of reconstruction and expansion of the sector and according to the Ministry of Higher Education, Science, Technology, and Innovation of the Republic of Angola (MESCTI, 2023), by 2022 Angola had 98 higher education institutions, including public (30) and private (68) institutions, distributed across various provinces, making the higher education subsystem more decentralized and the process of accessing higher education more democratized.

The most recent regulation of higher education in Angola began with the publication of presidential Decree nº 90/09 of December 15, establishing principles of quality, autonomy, and institutional accountability (Angola, 2009b). In 2019, presidential Decree nº 5/19 of January 8, Angola (2019), established the general regulations for access to higher education, requiring each institution to draft its own internal regulations.

In 2025, executive Decree nº 643/25 approved the academic calendar for the 2025-2026 academic year, strengthening institutional organization and the national alignment of academic activities (Angola, 2025).

Despite legislative and institutional advances, the system faces serious challenges, highlighting the reality that many HEIs still operate with inadequate infrastructure, including outdated libraries and laboratories lacking equipment and materials. Additionally, the fragility of communication networks and the lack of faculty training hinder the sustainable implementation of distance education; however, higher education in Angola has a significant opportunity for transformation ahead of it, thanks to the opportunities provided by digital technologies, in an effort to make it an effective, inclusive, and sustainable option, considering integrated actions that involve partnerships among different stakeholders: educational institutions, the government, civil society, and the private sector (Ferreira; Francisco, 2025).

More specifically, and according to the report on the pilot phase for primary education and the first cycle of secondary education in Angola (2010), the educational reform in Angola, which began in 2001, has the following general objectives: expanding the school network, improving the quality of education, enhancing the effectiveness of the education system, and promoting equity within the education system. This reform stems from the basic law on the education system, Angola (2001), which introduced significant structural changes but exposed weaknesses that have repercussions on higher education. The main challenge is the insufficient preparation of teachers, which compromises the implementation of new curricula and methodologies, since the oneteacher system, regulated by presidential Decree nº 37/80, Angola (2024), exacerbates the problem by requiring a single teacher to master multiple subject areas, creating significant gaps in students’ education, which is reflected in the deficient skills and knowledge they demonstrate upon entering higher education. At ESHOTUR, these gaps have been evident in the courses covered by this study, where students arrive with weak foundational knowledge, leading instructors to devote a significant portion of class time to addressing basic deficiencies, thereby delaying the development of specific competencies characteristic of higher education.

Despite the difficulties and shortcomings identified, higher education in Angola has undergone significant changes in recent decades, due to the increase in higher education institutions and the demand for quality higher education. However, technological advancements and the expansion of distance learning still face structural, social, and political barriers that limit their inclusive and innovative reach. HEIs in Angola still lack a technological infrastructure adequate for new forms of teaching that would support an efficient digital teaching model; in other words, most of them face problems with connectivity, equipment, and digital platforms. In this regard, it is essential that faculty members be trained to employ active methodologies based on digital tools and remote teaching strategies that encourage student interaction and autonomy. Universities should promote professional development programs, handson workshops, and certifications in educational technologies, supported by public policies.

In Angola, the fragility of communication networks and the lack of teacher training hinder the sustainable implementation of distance learning; however, higher education in Angola has a significant opportunity for transformation ahead of it, thanks to the opportunities provided by digital technologies, in an effort to make it an effective, inclusive, and sustainable option, considering integrated actions that involve partnerships among different stakeholders: educational institutions, the government, civil society, and the private sector (Ferreira; Francisco, 2025).

2.3 Higher education in Angola: from context to regulatory implementation

As mentioned in section 2.1, the trajectory of higher education in Angola, marked by successive legislative reforms, the expansion of the network of institutions, and the pursuit of quality and equity, constitutes the macrostructural framework within which specific experiences take place. The consolidation of a dual-track system (universities and polytechnics), the introduction of general curriculum standards, and the consolidation of regional public universities, as well as the growing number of private higher education institutions, reflect a national effort to democratize and modernize higher education. However, persistent challenges related to infrastructure, faculty training, and the integration of digital technologies have a direct impact on the implementation of academic practice and management. From this perspective, the transition from the macro context (higher education in Angola) to the specific case represents the analytical turning point, where reflection on policies and regulatory frameworks shifts to the empirical observation of a specific institution, ESHOTUR.

Between the macro level, which reflects the regulatory and structural frameworks of Angola’s higher education subsystem and the micro level, which reflects the concrete reality of ESHOTUR, lies an intermediate level of coordination. This space corresponds to the bodies responsible for curriculum coordination and harmonization, as well as the mechanisms for supervising and evaluating the quality of pedagogical management processes, which ensure the translation of general guidelines into specific contexts. It is, therefore, at this level that all HEI activities are operationalized, internal regulations are defined, and study plans are established by scientific fields, ensuring greater coherence between public policies and pedagogical practices. Although still marked by weaknesses in standardization and supervisory capacity, the intermediate level plays an essential role in mediating between normative formulation and its institutional application, allowing us to understand how the national system is implemented in specific contexts such as ESHOTUR, as summarized and presented in Chart 1.

Chart 1
Macro, intermediate and micro-overview of tourism education in Angola

Dimension	Macro (National system)	Intermediate (Implementation of standards)	Micro (ESHHOTUR)
Historic landmark	Expansion after 2002, with 98 higher education institutions by 2022 (30 public and 68 private).	Consolidation of regional public and private universities, aiming to decentralize educational offerings.	Created in 2009 as an organic unit of UAN, specializing in teaching and research in tourism.
Regulation	Presidential Decrees (e.g., nº 193/18) that define general curricular standards and legal framework.	Implementation of internal regulations and adaptation of higher education institutions to national standards, under the supervision of MESCTI.	Regulated by specific decrees (nº 7/09, nº 26/11, nº 381/17), aligned with national standards.
Curriculum structure	Binary system (university and polytechnic), with credit units and inter-institutional harmonization.	Application of general curricular standards and definition of study plans by scientific areas, based on common references.	Tourism management course structured in two cycles (basic and specialization), culminating in the preparation of a final monograph.
Assessment	guidelines for quality and institutional autonomy.	Creation of evaluation and quality assurance committees, with uniform criteria for all higher education institutions.	Continuous assessment model (40%) + final exam (60%), with the possibility of appeal.
Challenges	infrastructure, lack of teacher training, prevalence of digital illiteracy.	Insufficient harmonization and supervision processes hinder uniformity between institutions and regions.	Students arrive with weak foundations (quantitative matrix course units), requiring basic reinforcement before specialization.
Dimension	Macro (National system)	Intermediate (Implementation of standards)	Micro (ESHHOTUR)
Perspectives	Democratization of access to higher education, integration of digital technologies, public-private partnerships.	Strengthening the link between MESCTI and higher education institutions, focusing on pedagogical innovation and technological integration.	Training specialized personnel for the tourism sector, which is strategic for the national economy.

It is in this context that it becomes pertinent to shift the focus of the analysis to the micro level, examining specific institutions that embody, in their organization and operation, the principles and limitations of the national system. ESHOTUR constitutes a paradigmatic example of this transition: while adhering to the subsystem’s general guidelines, it seeks to meet the demands of a sector that is strategic for the Angolan economy. The subsequent analysis, centered on the process of evaluating course units at ESHOTUR, allows us to understand how regulatory frameworks and systemic challenges translate into concrete pedagogical practices and specific educational outcomes, as described in the following section.

2.4 Course unit evaluation process at ESHOTUR

ESHOTUR was established in 2009 with the publication of presidential Decree nº 7/09, dated May 12, a legal instrument that formalized the creation of a new organizational unit within the UAN. Initially designated as the Higher School of Hotel and Tourism, it thus took the first step toward establishing a specialized training hub in one of the most promising and strategic sectors for the national economy: tourism (Angola, 2009a). Starting in 2020, the institution adopted the simpler name of School of Hotel and Tourism, without altering its essence or its commitment to training qualified professionals dedicated to the sector’s development.

It became the first school in Angola to offer a Bachelor’s degree in Tourism Management, created with the mission of providing a solid education that combines theoretical and practical knowledge adapted to the realities of the national market. Its creation and operation were regulated by executive Decree nº 26/11 of February 23 and subsequently reinforced by executive Decree nº 381/17 of August 15, which approved the current curriculum and serves as a reference. Within this framework, ESHOTUR began its academic journey with a single program, whose structure addressed the emerging needs of the sector and the demand for a more professional and competitive tourism sector (Angola, 2011; Angola, 2017).

The approved curriculum took effect in the 2014 academic year and was designed to ensure a logical and consistent progression in the students’ educational journey. It is structured into two complementary cycles: the basic cycle, lasting two years, designed to consolidate general foundations; and the specialized cycle, beginning in the third year, with a focus on areas of technical and scientific specialization, culminating in the preparation and defense of a monographic final thesis, which constitutes the school’s primary academic output, that is, its overall graduation rate.

With the approval of presidential Decree nº 193/18, dated August 10, general curricular standards were established for undergraduate programs within the higher education subsystem in Angola, with the aim of restructuring the respective curricula and thereby preventing issues of compatibility, mobility, and harmonization, both between and within higher education institutions (Angola, 2018).

Among the main innovations introduced, the creation of so-called credit units stands out; these are units used to measure the time students have successfully spent on coursework, expressed in hours. This system defines the workload required to validate learning and certify the completion of a program.

Each credit unit corresponds to 15 class hours of student activities. Thus, credit units are now structured with 4 or 6 credit units, equivalent, respectively, to 60 or 90 class hours. This total includes not only in-person contact hours but also the student’s independent study hours. However, the workload also reflects the time and effort invested by faculty and the institution in the teaching process, a perspective reflected in the empirical part of the study.

Among the various course units, three are of particular relevance to the analysis developed in this study: advanced mathematics, statistics applied to tourism, and accounting and finance. The first two are taught in the first year, in the first and second semesters, respectively, while the third is part of the second-year program in the first semester; for this reason, the present analysis takes 2015 as its base year, when the accounting and finance course was evaluated for the first time.

The curriculum assigns, on mean, a workload of 75 hours per semester to each course, spread over 16 weeks of classes, at a pace designed to balance academic rigor with the practical application of course content. The assessment process follows a seemingly balanced model, combining written exams with assignments completed throughout the semester.

Students take two midterm exams to assess their knowledge of the syllabus content for the course’s various modules and, at the same time, are evaluated on a continuous basis, taking into account factors such as attendance, participation, and engagement, which are reflected in a grade ranging from 0 to 20 points. The mean of these exams and the continuous assessment accounts for 40% of the final grade, while the final exam accounts for 60%. If a student does not achieve the minimum passing grade, they may take a makeup exam, the grade of which fully replaces all previous grades, eliminating any prior weighting.

Although this system stands out for its clarity and objectivity, ensuring transparent and uniform rules, it can be criticized for placing excessive weight on the final exam in determining the final grade, which may undermine the continuous effort made throughout the semester. Nevertheless, it encourages constant learning, reinforces academic responsibility, and fosters students’ active engagement in the educational process; in other words, it allows for an assessment of whether a course is efficiently transforming resources (time, effort, number of students) into outcomes (learning and success).

3 EMPIRICAL APPROACHES

This is a quantitative, exploratory, and descriptive study that employs nonparametric techniques to assess academic inefficiency over time. The database was constructed by cross-referencing data from the tourism management program records of ESHOTUR’s Department of Academic Affairs and covers the period during which the three course units were taught simultaneously, since the accounting and finance course unit is taught starting in the second year of the program. For the purposes of analysis, each course unit was considered a DMU in each of the ten years analyzed, since, given the high heterogeneity that typically prevails among the members of a given class, as well as between and within academic years, it would be difficult to ensure practical feasibility on an individualized basis (per student). Thus, in order to gain an initial understanding of the behavior of the variables, namely the identification of patterns and inconsistencies, statistics were extracted to characterize the data, as presented in Table 1. For the initial data processing, the calculation of efficiency scores, and the determination of window indices, the following platforms were used: SPSS 26.0 (2019) and EMS (2000), and the Microsoft Excel (2019) application, respectively.

Table 1
Descriptive statistics of the variables

Variables	Minimum	Maximum	Median	Mean	Standard deviation
Number of students	38	110	66	69	19
Workload	60	90	80	80	13
Final mean	4	15	9	9	3
Approval rate	27	100	63	64	23

Correlated variables can distort the reliability of the results, leading to a biased assessment; therefore, the inclusion of variables in the model followed a validation process based on an analysis of the bivariate correlation between them, the results of which are presented in Table 2. This procedure revealed that the variable number of activities, whose values were taken from the course syllabus, has a zero standard deviation because it is constant for each CU. Even after being normalized by transforming, it into a productivity index per unit of time, that is, a composite output, its explanatory power regarding the inefficiency of the analyzed CUs remained negligible, and it was therefore excluded.

Table 2
Correlation matrix between variables

**Significant two-tailed correlation at 1%	Number of students	Workload	Final Mean	Approval rate
Number of students	1	-0,505**	-0,106	-0,162
Workload	-0,505**	1	-0,14	0,076
Final mean	-0,106	-0,14	1	0,934**
Approval rate	-0,162	0,076	0,934**	1

For different reasons, related to the measurement of collective performance in each of the CUs, the same procedure was adopted regarding the relationship between the number of students who passed and the number of students who attended the CUs, to obtain the approval rate in each CU and in each academic year.

Since significant discrepancies were observed between the maximum and minimum values in the data, initially identified in the descriptive analysis of the variables, Spearman’s correlation coefficient was used to analyze the correlations among the variables. This measure is best suited for data containing extreme values, which, for this reason, do not follow a normal distribution, a non-parametric correlation analysis was performed, as also presented in Table 2, which allowed for the assessment of the relevance of each variable included in the analysis.

In studies related to the evaluation of institutional performance in higher education institutions, indicators such as approval rates and final grade point means in course units are frequently used as proxies for academic success, provided that their use is accompanied by a critical analysis of likely underlying factors (Gomes and Rocha Neto, 2011); Ernica, Rodrigues, and Soares (2025); that is, although they do not capture all possible dimensions relevant to the analysis, both the approval rate and the final grade can be useful indicators when interpreted critically and combined with other metrics (Werle, Koetz, and Martins, 2015; Gusmão, 2023; Deus and Silva (2024), and which in this study are hypothetically condensed into the DEA-DIFO diagnostic matrix, presented later in Chart 3.

As a further note regarding the descriptive statistics presented in Table 2, it is worth noting that, despite the indication of multicollinearity (0.934) among the variables (approval rate and final grade), which represents a significant methodological limitation for the study, it is nevertheless important to analyze this within the context of the pedagogical management of the course units. These indicators provide a quantitative measure of academic performance, as well as of the school management process, in line with the concept of academic efficiency adopted in the study. Thus, the aforementioned limitation was taken into account when discussing the results and drawing the study’s conclusions.

As shown in Chart 2, two inputs (the number of students in each grade and the workload) and two outputs (the final grade point mean and the approval rate) were used, selected based on the theoretical assumption that each CU represents a DMU that transforms educational resources (inputs) into academic outcomes (outputs). Thus, based on the correlation tests conducted, Chart 2 presents the different components of the adopted model, their description, as well as the rationale for their adoption.

Chart 2
Model specification

Component	Description	Justification
Model	DEA-CRS	• In the context of evaluating Conservation Units, these are compared within a homogeneous system, where proportionality between resources and results is expected. It offers simplicity and comparability by defining a single efficiency boundary. It avoids distortions stemming from the size (mainly operational costs) of the disciplines, prioritizing only relative efficiency.
Guidance	Input	A focus on minimizing academic resources, as these are the most controllable by teachers and school administrators.
Technique	Analysis of overlapping windows	Capturing the intertemporal effect present in inefficiency scores, as a way to detect patterns, as well as trends in their behavior.
Input 1	Workload	A pedagogical resource that allows for capturing the effort of teachers or students, as well as the intensity of the curriculum.
Input 2	Number of students	A resource that consumes time, space, and management effort, and that represents the complexity of pedagogical management.
Output 1	Approval rate	Indicator of the efficiency of academic progression.
Output 2	Final mean	Indicator of the quality of academic performance.
DMU 1	CU of advanced mathematics course	Quantitative matrix content taught in the basic cycle of the course.
DMU 2	CU of statistics applied to tourism	Quantitative matrix content taught in the basic cycle of the course.
DMU 3	CU of accounting and finance	Quantitative matrix content taught in the basic cycle of the course.

As previously mentioned, course units were selected whose approach to the taught content is predominantly quantitative, since they serve as a foundation for understanding the content of the specialization cycle in subjects related to applied mathematics and statistics.

The dynamics of trends in DMU efficiency can reveal their causes and point to ways to improve performance through the use of the DEA window analysis technique (Sanches-António, 2025a; Sanches-António, 2025b; Sanches-António, 2025c). This approach finds empirical support for its adoption in Cooper, Seiford, and Tone (2007), who postulate that in DEA, the number of DMUs must be at least three times greater than the product of the number of inputs and outputs, such that n ≥ max {[(m)(s)] 3(m + s)}; where: n = number of DMUs, m = number of inputs, and s = number of outputs. Thus, the windowing technique allows for an increase in the number of distinct DMUs, since in each window, each DMU is treated as a new DMU; its mathematical notation, proposed by Cooper, Seiford, and Tone (2007), is presented in Table 3. In this way, it was possible to increase the number of different DMUs in each window to 90, as opposed to 30 DMUs in the case where the windowing technique was not applied and inefficiency was measured over a single period (2015-2024).

Table 3
Calibration of DEA windows

Components	Formula	p = 5 years
Number of windows	w = k - p +1	(10 - 5 + 1) = 6
Number of DMUs in each window	(n) (p)	[(3) (5)] = 15
Number of different DMUs	(n) (p) (w)	[(3) (5) (6)] = 90
Variation in the number of DMUs	n (p - 1) (k - 1)	[(3) (4) (9)] = 108

As a result of the practical application of the theoretical assumptions presented regarding the DEA window, Table 4 shows the DEA window configuration used, with a five-year window width adopted, given that this condition yields the largest number of distinct DMUs, compared to time horizons of four and six years, ensuring greater discriminatory power of the efficiency scores obtained, given the small number of initial DMUs (3) relative to the sum of inputs and outputs (4).

Table 4
Configuration of the analysis windows

Periods		1	2	3	4	5	6	7	8	9	10
Windows	1	2015	2016	2017	2018	2019
	2		2016	2017	2018	2019	2020
	3			2017	2018	2019	2020	2021
	4				2018	2019	2020	2021	2022
	5					2019	2020	2021	2022	2023
	6						2020	2021	2022	2023	2024

4 RESULTS AND DISCUSSION

In educational contexts, where outcomes are influenced by multiple factors, including pedagogical, institutional, and individual aspects, it is common for models to yield moderate coefficients of determination; thus, although the value does not indicate a high level of fit (36%), it suggests that the regressors used are statistically significant and contribute partially to understanding the analyzed phenomenon, when the time metric is annual, strictly within the general framework of the simple linear regression model, whose formulation for each variable was presented in section 2.1.

This finding is consistent with the results of studies such as those by Ruggiero (2004) and IAS (2020), according to which statistical models rarely yield very high R² because there are always unobserved or difficult-to-measure variables, such as those of a socioeconomic nature (area of residence, parents’ educational level, etc.).

In the context of DEA analysis, a CU is efficient when it is part of the efficient frontier, that is, when it exhibits the best performance in the combination of pedagogical and/or management resources (100%). In this vein, a visual inspection of Graph 1 reveals that, overall, the three CUs were efficient only in the second year, with a downward trend in mean efficiency levels observed across the analyzed period.

Graph 2 presents the trajectories of the inter-period efficiency curves for the academic units under analysis, allowing us to capture their intertemporal dynamics. It can be observed that the efficiency curves for the academic units in applied statistics for tourism and accounting and finance follow congruent, upward-sloping trajectories, in contrast to the curve for the academic unit in advanced mathematics.

Graph 2
Dynamics in inter-period efficiency by CUs

Analysis of the regression indicators shown in Graph 2 reveals that, once crossperiod data are included, their explanatory power regarding DEA efficiency scores, specifically concerning the relationship among the variables included in the analysis, increases to an mean of 68%, indicating a strong and positive relationship between them; that is, this value is nearly double that obtained when the relationship is analyzed assuming a single period between 2015 and 2024 (see Graph 1), reinforcing the importance of capturing the effect of intertemporality on the performance of CUs.

Indicating the relative position of each academic unit in terms of their individually recorded efficiency means, and the mean for the set as a whole, only the CU for statistics applied to tourism ranked above the overall mean for the (2015-2024) time-horizon (see Graph 3). This result is also indicative of the prevalence of inefficiencies and the corresponding need for adjustments in the pedagogical resources used.

Graph 3
Efficiency relative to the mean

As mentioned in section 2.1, the DEA, as a methodology for analyzing technical efficiency, allows for the measurement of multiple inputs and outputs, on the one hand, and accommodates the use of units of measurement from metrics other than monetary ones, on the other, conditions that underpin the different units of measurement for the variables used. Thus, in line with these possibilities, the results shown in Table 5 present a record of the sources of inefficiency, by variable, taking into account the entire analyzed period (2015-2024), which aligns with the input-oriented approach adopted for the model used, reflecting the excess of resources utilized (number of students or workload). In this context, the heat map applied to these variables shows that the greatest sources of inefficiency, by variable and academic unit, were respectively: workload and final grade (advanced mathematics), workload and approval rate (statistics applied to tourism), as well as the number of students and approval rate (accounting and finance). It can therefore be observed that the academic units in applied statistics for tourism and accounting and finance perform the worst on the indicator related to efficiency in the academic progression process, specifically, the approval rate, in contrast to a lower level of inefficiency on the indicator of academic performance quality, namely the final grade. This result may (hypothetically) be explained by the flexibility of assessment criteria at ESHOTUR, since, although the means are low and generally associated with high failure rates, the considerable number of make-up exams allows students with low means at the end of the regular assessment period to pass the courses, with this difference being most pronounced in the accounting and finance course.

Table 5
Mean indicators of academic inefficiency by course units and operational categories (2015-2024)

CUs	Number of students	Workload	Final Mean	Approval rate	Mean
Advanced mathematics	13	87	79	21	50
Statistics applied to tourism	43	57	49	52	50
Accounting and finance	75	31	43	57	52

In contrast to the two courses mentioned above, regarding the record of inefficiencies in the teaching-learning process of the advanced mathematics course, the final mean is more than three times the inefficiency of the approval rate. This finding may indicate the prevalence of a small number of students with very high means, as opposed to the high number of failures.

As for the critical efficiency variables, the advanced mathematics academic unit shows significant inefficiency in the teaching load indicator (workload), indicating a low curriculum intensity, with a shortfall of 87 class hours between 2015 and 2024, as a result of the inefficiency metric derived from the difference between the unit’s deviation from the efficient frontier, calculated as (1 - σ).

In this regard, the Applied Statistics in Tourism course unit shows similar mean values, indicating proportionality between the return on curricular intensity and the final mean obtained. Finally, the accounting and finance course unit’s primary source of inefficiency lies in the small number of students, with a mean enrollment of fewer than 75 students during the analyzed period, which may also reflect the subject’s low appeal among students (as a hypothesis).

Regarding critical efficiency variables, the advanced mathematics course unit exhibits significant inefficiency in the teaching effort indicator (workload), indicating low curriculum intensity, with a shortfall of 87 teaching hours between 2015 and 2024, as a result of the inefficiency metric derived from the difference between the unit’s deviation from the efficient frontier, calculated as (1 - σ).

The DEA-DIFO academic diagnostic matrix (Diagnosis of Inefficiencies and Operational Slacks), presented in Chart 3, is an analytical tool originally developed within the scope of this study to evaluate, interpret, and communicate the results of radial DEA models applied to the assessment of operational performance in an academic-pedagogical context. Its purpose is to standardize the process of converting technical outputs, (in)efficiency, slack, and benchmarks, into pedagogical and management indicators that facilitate institutional decision-making, based on certain assumptions regarding the identification of operational inefficiencies.

Based on concepts within the DEA framework, as presented in the empirical analysis conducted in section 3, namely: constant returns to scale, conversion of inputs into outputs, and operational slack, as well as academic management principles related to: teaching load and faculty-educational performance, a diagnostic matrix was developed that allows for the classification of shortcomings, the identification of dysfunction in the resource allocation process, and the proposal of corrective actions in an academic context.

In accordance with the dimensions present in the DEA-DIFO matrix, the results obtained will be discussed strictly within the scope of the sample; however, they may also serve as a reference for other similar academic contexts whose pedagogical practices and academic systems are comparable to those of ESHOTUR. Thus, Table 6 presents the means of the inefficiency scores and respective inter-window slacks recorded for each CU, using as a criterion for discussion an indication of mean inefficiency with 50% statistical significance (darker color).

Chart 3
DEA-DIFO diagnostic matrix

Variable	Type of disability	DEA symptom	Hypothetical diagnosis	Recommended action
Number of Students	Excess or scarcity	Resource slack (input not converted into output)	Excess can compromise quality; scarcity may indicate low attractiveness.	Reassess the distribution of classes and recruitment or retention strategies.
Workload	Excess or scarcity	Input slack (time does not generate proportional performance)	Excessive workload without feedback indicates inefficiency, while a low workload can hinder learning.	Adjust the workload based on academic performance, apply sensitivity analysis.
Final Mean	Poor performance	Output below the efficient frontier.	It indicates pedagogical shortcomings or a misalignment between content and student profiles.	Review teaching methods, assessment, and academic support.
Variable	Type of disability	DEA symptom	Hypothetical diagnosis	Recommended action
Approval Rate	Low or inconsistent	Output inconsistent with inputs	Low approval rates with efficient inputs indicate conversion failure; high approval rates with a low mean may indicate a less rigorous evaluation.	Strengthen evaluation criteria and align requirements with actual performance.

Table 6
Academic inefficiency of CUs: mean percentage indicators by window and operational slacks

CUs	Windows	Number of students		Workload		Final Mean		Approval rate
		Inefficiency (%)	Slack	Inefficiency (%)	Slack	Inefficiency (%)	Slack	Inefficiency (%)	Slack
	1	7	6	93	0	55	0	45	1
Advanced mathematics	2	5	6	95	0	70	0	30	1
	3	29	2	71	0	80	0	20	16
	4	20	2	80	0	68	0	32	2
	5	16	1	84	0	100	0	0	3
	6	0	30	100	0	100	0	0	2
	Mean	13	8	87	0	79	0	21	4
	1	40	0	60	1	12	1	89	0
	2	25	0	75	0	8	1	92	0
	3	77	0	24	0	70	0	30	1
Statistics applied to tourism	4	62	0	38	0	52	0	48	8
	5	47	0	53	0	67	0	33	10
	6	7	18	93	0	83	0	17	9
	Mean	43	3	57	0	49	0	52	5
	1	83	0	17	15	20	1	80	2
	2	73	0	27	7	0	2	100	0
	3	79	0	60	0	60	0	40	7
accounting and finance	4	64	0	36	0	56	0	44	1
	5	74	0	26	0	60	0	40	4
	6	78	0	22	0	60	0	40	8
	Mean	75	0	31	4	43	1	57	4

By applying a heat map to the obtained results, it is possible to identify patterns of intensity in the inter-window inefficiency records by variable and CU, which allow for the visualization of their intertemporal intensity. Thus, it can be observed that the advanced mathematics course unit, as already noted in Table 5, has workload as its critical efficiency variable, indicating that this course unit is taught over an excessive period of time without producing the expected results; therefore, its workload should be adjusted to understand how this adjustment affects student performance. With less impact but equally significant, the course unit on statistics applied to tourism recorded inter-window inefficiency levels that were very close in the variables of workload and final grade, that is, considerable levels of inefficiency, indicating a mismatch between instructional time and the quality of the outcome. The high levels of inefficiency observed in variables such as the number of students and the approval rate in the accounting and finance course unit are also figures that can be assessed from Table 6.

Graph 4 shows the trends in the inefficiency curves recorded by each CU and variable in each window. This information provides additional analytical insights that complement the results also presented in Table 6, allowing for a better understanding of the dynamics present in the inefficiency records of the three CUs analyzed. From this perspective, the following can be observed: an upward trend in the final mean (marked) and in the number of students (moderate) and, at the same time, a downward trend in the approval rate (marked) and in the workload (moderate). This academic-institutional paradox can be explained by the following behaviors throughout the input-output optimization process at ESHOTUR, namely: a rising trend in the final grade (marked), indicating that more resources are being used to generate high grades, but without a proportional return in the number of students passing; a rising trend in the number of students (moderate), indicating that the institution is enrolling more students, but without translating this increase into better outcomes; a downward trend in the approval rate (marked), indicating that the decline in the approval rate is reducing overall efficiency, as fewer students successfully complete the course units; and a downward trend in workload (moderate), indicating that the reduction in workload is compromising the performance of essential outputs.

Graph 4
Mean inefficiency by CU and category (windows 1-6)

5 FINAL CONSIDERATIONS

The assessment of inefficiency under constant returns to scale is the most appropriate for the data structure of the academic variables analyzed in ESHOTUR, since under this condition the explanatory power was 10% higher, indicating a better fit between the variables used.

Considering the inputs and outputs included in the model, with regard to the intertemporal dynamics of inefficiency, the results showed that the advanced mathematics course unit (CU) identified the reduced workload as the primary source of inefficiency; the course unit in statistics applied to tourism identified the final grade and the approval rate as the main sources of inefficiency; finally, the course unit in accounting and finance identified the low number of students and the high approval rate as the main sources of inefficiency.

The upward trend in the inefficiency scores of performance indicators reveals a disconnect between the resources allocated and the results obtained, since, on the one hand, the increase in the final grade mean, accompanied by a drop in the approval rate, suggests that assessment criteria are not being translated into academic success, and on the other hand, the reduction in workload, although it appears to optimize resources, may be compromising pedagogical effectiveness, especially given the growth in the number of students.

Although the study applies to the Angolan context, the challenges related to assessing academic inefficiency and curriculum management are common to higher education institutions in various countries, making its findings relevant to the international debate on educational quality.

From this perspective, the findings of this study enable the improvement of the planning of the teaching-learning process by adjusting teaching methodologies based on efficiency standards, introducing DEA as a complementary tool to traditional evaluation in the Angolan academic context, with an emphasis on efficiency supported by diagnostic indicators presented in the DEA-DIFO matrix.

The negative correlation shown by the data between the number of students and the other variables analyzed (workload, final grade, and approval rate), as well as between workload and final grade, suggests that an increase in the number of students per class is not associated with better academic performance at ESHOTUR, and thus these results may indicate academic overload, low pedagogical efficiency, or a need for curriculum revision. As a complementary measure, we suggest implementing DEA models focused on the quality of the teaching-learning process, enabling a comparative assessment across academic units and classes.

The study does not discuss the implications of external factors, such as: the socioeconomic profile of students, the dropout rate, or the geographic location of ESHOTUR, which, as uncontrollable factors that influence efficiency, need to be treated as constraints in DEA models to ensure a balanced evaluation. This empirical gap constitutes the main limitation of the study and also points the way for future research.

AI USE STATEMENT

No Artificial Intelligence tools were used.

Translated by: Anna Kaisse Sanazengi Sanches António

E-mail: [e-mail]

DATA AVAILABILITY

The content underlying the research text is available in the article.

The dataset analyzed during the research is available only at the Department of Academic Affairs at ESHOTUR and is not available in open sources.

References

• ALANAZI, A. S.; BENLARIA, H. Bridging higher education outcomes and labour market needs: a study of Jouf University graduates in the context of Vision 2030. Social Sciences, Basel, v. 12, n. 6, p. 1-19, 2023. Disponível em: https://www.mdpi.com/2076-0760/12/6/360 Acesso em: 11 nov. 2024.
  » https://www.mdpi.com/2076-0760/12/6/360
• ANGOLA. Decreto executivo nº 381/17, de 15 de agosto de 2017 Criação na Escola Superior de Hotelaria e Turismo do curso de graduação em gestão do turismo. Luanda, 2017. p. 3655-3659. Disponível em: https://www.lexlink.eu/conteudo/geral/ia-serie/3825898/decreto-executivo-no38117/14793/por-tema Acesso em: 22 dez. 2024.
  » https://www.lexlink.eu/conteudo/geral/ia-serie/3825898/decreto-executivo-no38117/14793/por-tema
• ANGOLA. Decreto executivo nº 643/25 Calendário acadêmico 2025-2026. Luanda, 2025. Disponível em: https://angolex.com/paginas/decreto-executivo/calendariopara-o-ano-academico-2025a2026-para-instituicoes-do-ensino-superior-643a25a.html Acesso em: 17 jan. 2025.
  » https://angolex.com/paginas/decreto-executivo/calendariopara-o-ano-academico-2025a2026-para-instituicoes-do-ensino-superior-643a25a.html
• ANGOLA. Decreto presidencial nº 37/80, de 17 de abril de 1980 Aprovação do estatuto orgânico da Universidade de Angola e extinção do Instituto de Investigação Científica de Angola. Luanda, 1980. Disponível em: https://www.lexlink.eu/conteudo/geral/ia-serie/68645/decreto-executivo-conjuntono-3780/14793/por-tipo-de-documentolegal Acesso em: 1 dez. 2024.
  » https://www.lexlink.eu/conteudo/geral/ia-serie/68645/decreto-executivo-conjuntono-3780/14793/por-tipo-de-documentolegal
• ANGOLA. Decreto presidencial nº 7/09, de 12 de maio de 2009 Reorganização da rede de instituições de ensino superior públicas, criação de novas instituições de ensino superior e redimensionamento da Universidade Agostinho Neto. Luanda, 2009a. p. 1856-1858. Disponível em: https://files.lex.ao/conselho-deministros/2009/decreto-n-o-7-09-de-12-de-maio/download/decreto-n-o-7-09-de12-de-maio_conselho-de-ministros_lex-ao.pdf Acesso em: 11 mar. 2025.
  » https://files.lex.ao/conselho-deministros/2009/decreto-n-o-7-09-de-12-de-maio/download/decreto-n-o-7-09-de12-de-maio_conselho-de-ministros_lex-ao.pdf
• ANGOLA. Decreto presidencial nº 90/09, de 15 de dezembro de 2009 Normas gerais reguladoras do subsistema de ensino superior. Luanda, 2009b. Disponível em: https://www.isptec.co.ao/public/assets/uploads/docs/Decreto%20n%2090_09%2015%20de%20Dezembro%2009.pdf Acesso em: 17 ago. 2025.
  » https://www.isptec.co.ao/public/assets/uploads/docs/Decreto%20n%2090_09%2015%20de%20Dezembro%2009.pdf
• ANGOLA. Decreto presidencial nº 26/11, de 23 de fevereiro de 2011 Regulamento sobre a elaboração de processo para a criação de cursos de graduação a ministrar nas instituições de ensino superior. Luanda, 2011. p. 1121-1125. Disponível em: https://www.isptec.co.ao/public/assets/uploads/docs/Decreto%20Executivo%2026_11%20de%2023%20de%20Fevereiro.pdf Acesso em: 11 jan. 2025.
  » https://www.isptec.co.ao/public/assets/uploads/docs/Decreto%20Executivo%2026_11%20de%2023%20de%20Fevereiro.pdf
• ANGOLA. Decreto presidencial nº 193/18, de 10 de agosto de 2018 Normas curriculares gerais para os cursos de graduação do subsistema de ensino superior. Luanda, 2018. p. 4135-4145. Disponível em: https://lex.ao/docs/presidente-darepublica/2018/decreto-presidencial-n-o-193-18-de-10-de-agosto/ Acesso em: 1 out. 2024.
  » https://lex.ao/docs/presidente-darepublica/2018/decreto-presidencial-n-o-193-18-de-10-de-agosto/
• ANGOLA. Decreto presidencial nº 5/19, de 8 de janeiro de 2019 Regulamento geral de acesso ao ensino superior. Luanda, 2019. Disponível em: https://files.lex.ao/presidente-da-republica/2019/decreto-presidencial-n-o-5-19-de-08-de-Janeiro/download/decreto-presidencial-n-o-5-19-de-08-deJaneiro_presidente-da-republica_lex-ao.pdf Acesso em: 17 jan. 2025.
  » https://files.lex.ao/presidente-da-republica/2019/decreto-presidencial-n-o-5-19-de-08-de-Janeiro/download/decreto-presidencial-n-o-5-19-de-08-deJaneiro_presidente-da-republica_lex-ao.pdf
• ANGOLA. Decreto presidencial nº 310/20, de 7 de dezembro de 2020 Regime jurídico do subsistema de ensino superior. Luanda, 2020. Disponível em: https://lex.ao/docs/presidente-da-republica/2020/decreto-presidencial-n-o-310-20de-07-de-dezembro/ Acesso em: 17 ago. 2025.
  » https://lex.ao/docs/presidente-da-republica/2020/decreto-presidencial-n-o-310-20de-07-de-dezembro/
• ANGOLA. Decreto presidencial nº 37/80, de 17 de abril de 2024 Regulamento da docência na 5.ª e 6.ª classes, bem como o respectivo plano de estudo. Luanda, 2024. p. 9705. Acesso em: 1 dez. 2024.
• ANGOLA. Lei de bases do sistema de educação Luanda: Assembleia Nacional, 2001. Disponível em: https://www.unicef.org/angola/sites/unicef.org.angola/files/201806/Lei%2013_01_Lei%20de%20Bases%20do%20Sistema%20de%20Educacao%20de%20Angola%202001.pdf Acesso em: 11 mar. 2026.
  » https://www.unicef.org/angola/sites/unicef.org.angola/files/201806/Lei%2013_01_Lei%20de%20Bases%20do%20Sistema%20de%20Educacao%20de%20Angola%202001.pdf
• ANGOLA. Relatório da fase de experimentação do ensino primário e do 1º ciclo do ensino secundário Luanda: Ministério da Educação da República de Angola, 2010. Disponível em: https://www.academia.edu/43131110/REP%C3%9ABLICA_DE_ANGOLA_MINIST%C3%89RIO_DA_EDUCA%C3%87%C3%83O_Comiss%C3%A3o_de_Acompanhamento_das_Ac%C3%A7%C3%B5es_da_Reforma_Educativa_CAARE_Ficha_T%C3%A9cnica_Coordenador_da_CAARE_%C3%8Dndice_%C3%A1g_1_Rel%C3%A1torio_d Acesso em: 3 mar. 2026.
  » https://www.academia.edu/43131110/REP%C3%9ABLICA_DE_ANGOLA_MINIST%C3%89RIO_DA_EDUCA%C3%87%C3%83O_Comiss%C3%A3o_de_Acompanhamento_das_Ac%C3%A7%C3%B5es_da_Reforma_Educativa_CAARE_Ficha_T%C3%A9cnica_Coordenador_da_CAARE_%C3%8Dndice_%C3%A1g_1_Rel%C3%A1torio_d
• AVILÉS-SACTO, S. V. et al. Measuring efficiency in DEA in the presence of common inputs. Journal of the Operational Research Society, v. 71, n. 11, p. 1710-1722, 2020. Disponível em: https://www.tandfonline.com/doi/full/10.1080/01605682.2019.1630329 Acesso em: 22 fev. 2026.
  » https://www.tandfonline.com/doi/full/10.1080/01605682.2019.1630329
• AZIZ, N. A. A.; JANOR, R. M.; MAHADI, R. Comparative departmental efficiency analysis within a university: a DEA approach. Procedia - Social and Behavioral Sciences, Amsterdam, v. 90, p. 540-548, 2013. Disponível em: https://www.sciencedirect.com/science/article/pii/S1877042813020120 Acesso em: 12 dez. 2024.
  » https://www.sciencedirect.com/science/article/pii/S1877042813020120
• CARVALHO, P. Evolução e crescimento do ensino superior em Angola. Revista Angolana de Sociologia, Luanda, n. 9, 2012. Disponível em: https://journals.openedition.org/ras/422 Acesso em: 11 jan. 2025.
  » https://journals.openedition.org/ras/422
• CHARNES, A.; COOPER, W. W.; RHODES, E. Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Management Science, v. 27, n. 6, p. 668-697, 1981. Disponível em: https://pubsonline.informs.org/doi/abs/10.1287/mnsc.27.6.668 Acesso em: 4 jan. 2025.
  » https://pubsonline.informs.org/doi/abs/10.1287/mnsc.27.6.668
• CHARNES, A.; COOPER, W. W.; RHODES, E. Measuring the efficiency of decisionmaking units. European Journal of Operational Research, v. 2, n. 6, p. 429-444, 1978. Disponível em: https://www.sciencedirect.com/science/article/abs/pii/0377221778901388 Acesso em: 22 nov. 2024.
  » https://www.sciencedirect.com/science/article/abs/pii/0377221778901388
• CHICOMO, R. G.; DIAS, M. M. Análise da eficiência técnica nas unidades orgânicas da Universidade José Eduardo Dos Santos. Revista Órbita Pedagógica, Huambo, Angola, 6, n. 2, 2019. 31-44. Disponível em: https://www.academia.edu/144373404/An%C3%A1lise_Da_Efici%C3%AAncia_T%C3%A9cnica_Nas_Unidades_Org%C3%A2nicas_Da_Universidade_Jos%C3%A9_Eduardo_Dos_Santos>. Acesso em: 22 maio 2025.
  » https://www.academia.edu/144373404/An%C3%A1lise_Da_Efici%C3%AAncia_T%C3%A9cnica_Nas_Unidades_Org%C3%A2nicas_Da_Universidade_Jos%C3%A9_Eduardo_Dos_Santos
• COOPER, W. W.; SEIFORD, L. M.; TONE, K. Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software New York: Springer, 2007. Disponível em: https://link.springer.com/book/10.1007/978-0-387-45283-8 Acesso em: 8 jan. 2024.
  » https://link.springer.com/book/10.1007/978-0-387-45283-8
• DEUS, A. C. C. D.; SILVA, A. C. D. Além dos números: uma análise qualitativa da taxa de sucesso na graduação da UFMT e seu impacto para o desenvolvimento institucional. Revista FT, v. 28, n. 131, 2024. Disponível em: https://revistaft.com.br/category/edicao131/page/11/ Acesso em: 23 maio 2025.
  » https://revistaft.com.br/category/edicao131/page/11/
• EGOROV, A.; SEREBRENNIKOV, P. Measuring the efficiency of universities: what is inside the black box? Journal of Higher Education Policy and Management, Oxfordshire, v. 45, n. 5, p. 545-565, 2023. Disponível em: https://doi.org/10.1080/1360080X.2023.2209379 Acesso em: 12 fev. 2025.
  » https://doi.org/10.1080/1360080X.2023.2209379
• EMS. Efficiency measurement system Versão 1.3, 2000. Disponível em: https://www.holger-scheel.de/ems/ Acesso em: 7 abr. 2025.
  » https://www.holger-scheel.de/ems/
• ERNICA, M.; RODRIGUES, E. C.; SOARES, J. F. Desigualdades educacionais no Brasil contemporâneo: definição, medida e resultados. Revista Brasileira de Educação, Rio de Janeiro, v. 68, n. 1, p. 1-44, 2025. Disponível em: https://dados.iesp.uerj.br/en/edicoes/?vn=68-1 Acesso em: 4 jan. 2026.
  » https://dados.iesp.uerj.br/en/edicoes/?vn=68-1
• FERREIRA, E. J.; FRANCISCO, C. J. A. Desafios e oportunidades dos estudantes do ensino a distância (EaD) em Angola. SciELO Preprints, São Paulo, 2025. Disponível em: https://preprints.scielo.org/index.php/scielo/preprint/view/12905 Acesso em: 2 jul. 2024.
  » https://preprints.scielo.org/index.php/scielo/preprint/view/12905
• FUENTES, R.; FUSTER, B.; LILLO-BAÑULS, A. A three-stage DEA model to evaluate learning-teaching technical efficiency: key performance indicators and contextual variables. Expert Systems with Applications, v. 48, p. 89-99, 2016. Disponível em: https://www.sciencedirect.com/science/article/pii/S0957417415007885 Acesso em: 25 fev. 2026.
  » https://www.sciencedirect.com/science/article/pii/S0957417415007885
• GOMES, D. B. B. A.; ROCHS NETO, I. Avaliação de progresso do programa nacional de cooperação acadêmica - Novas Fronteiras - edição 2007 e oportunidades de formação de redes cooperativas nas áreas estratégicas e tecnologias portadoras de futuro. Revista Brasileira de Educação, Rio de Janeiro, v. 16, n. 48, 2011. Disponível em: https://www.scielo.br/j/rbedu/i/2011.v16n48/ Acesso em: 11 nov. 2025.
  » https://www.scielo.br/j/rbedu/i/2011.v16n48/
• GÖKŞEN, Y.; DOĞAN, O.; ÖZKARABACAK, B. A data envelopment analysis application for measuring efficiency of university departments. Procedia Economics and Finance, Amsterdam, v. 19, p. 226-237, 2015. Disponível em: https://www.sciencedirect.com/science/article/pii/S2212567115000246 Acesso em: 21 fev. 2026.
  » https://www.sciencedirect.com/science/article/pii/S2212567115000246
• GORI, R. S. L. et al Efficiency in higher education institutions: An analysis of data envelopment analysis applications. International Journal of Management in Education, Oxfordshire, UK, v. 19, n. 1, p. 32-59, 2025. Disponível em: https://www.inderscienceonline.com/doi/abs/10.1504/IJMIE.2025.142875 Acesso em: 11 fev. 2025.
  » https://www.inderscienceonline.com/doi/abs/10.1504/IJMIE.2025.142875
• GUJARATI, D. N.; PORTER, D. C. Basic econometrics Nova Délhi, Índia: Affiliated EastWest Pres, 2025. Disponível em: https://www.amazon.in/Basic-Econometrics-7thGujarati-Damodar/dp/8176711381 Acesso em: 10 out. 2024.
  » https://www.amazon.in/Basic-Econometrics-7thGujarati-Damodar/dp/8176711381
• GUSMÃO, F. A. F. Análise do ensino médio brasileiro com base em indicadores educacionais. Roteiro, Joaçaba, Brasil, 48, 2023. 1-26. Disponível em: https://periodicos.unoesc.edu.br/roteiro/article/view/30739 Acesso em: 2 jan. 2025.
  » https://periodicos.unoesc.edu.br/roteiro/article/view/30739
• IAS. Indicadores de sucesso da aprendizagem: um guia para gestores educacionais. São Paulo: Instituto Ayrton Senna, 2020. Disponível em: https://institutoayrtonsenna.org.br/app/uploads/2022/11/instituto-ayrton-sennaindicadores-de-sucesso-de-aprendizagem-um-guia-para-gestores-educacionais.pdf Acesso em: 2 jan. 2025.
  » https://institutoayrtonsenna.org.br/app/uploads/2022/11/instituto-ayrton-sennaindicadores-de-sucesso-de-aprendizagem-um-guia-para-gestores-educacionais.pdf
• JHA, C. K. Application of DEA in measuring the performance of higher education institutions: a review. Empirical Economics Letters, Dhaka, Bangladesh, v. 24, n. Special Issue 3, p. 97-120, 2025. Disponível em: http://www.eel.my100megs.com/volume-24-number-january-3-special-issue.htm Acesso em: 26 fev. 2026.
  » http://www.eel.my100megs.com/volume-24-number-january-3-special-issue.htm
• JOHNES, J. Measuring efficiency: a comparison of multilevel modelling and data envelopment analysis in the context of higher education. Bulletin of Economic Research, Oxford, UK, v. 58, n. 2, p. 75-104, 2006. Disponível em: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.0307-3378.2006.00238.x Acesso em: 22 jan. 2026.
  » https://onlinelibrary.wiley.com/doi/abs/10.1111/j.0307-3378.2006.00238.x
• MESCTI. Anuário estatístico do ensino superior, ciência, tecnologia e inovação 2021-2022 Luanda, Angola: Instituto Nacional de Estatística - República de Angola, n. 7, 2023. Disponível em: https://www.ine.gov.ao/publicacoes/detalhes/MzczMzE%3D Acesso em: 1 maio 2025. Depósito legal nº 466/2019.
  » https://www.ine.gov.ao/publicacoes/detalhes/MzczMzE%3D
• MICROSOFT®EXCEL®. MSO Versão 2506 Build 16. 0. 18925. 20076) 64-bit, 2019. Disponível em: https://www.microsoft.com/ Acesso em: 9 set. 2024.
  » https://www.microsoft.com/
• MYEKI, L. W.; TEMOSO, O. Efficiency assessment of public universities in South Africa, 2009-2013: panel data evidence. South African Journal of Higher Education, Matieland, v. 33, n. 5, p. 264-80, 2019. Disponível em: https://www.journals.ac.za/sajhe/article/view/3582 Acesso em: 11 dez. 2024.
  » https://www.journals.ac.za/sajhe/article/view/3582
• NKOHLA, T. V. et al A non-parametric assessment of efficiency of South African public universities. South African Journal of Higher Education, Stellenbosch, South Africa, v. 35, n. 2, p. 158-187, 2021. ISSN 1753-5913. Disponível em: https://www.journals.ac.za/index.php/sajhe/article/view/3950>. Acesso em: 31 jan. 2026.
  » https://www.journals.ac.za/index.php/sajhe/article/view/3950
• RUGGIERO, J. Performance evaluation in education. In: COOPER, W. W.; SEIFORD, L. M.; ZHU, J. Handbook on data envelopment analysis Boston, MA: Springer US, v. 71, 2004. cap. 12, p. 323-346. Disponível em: https://doi.org/10.1007/1-4020-7798X_12 Acesso em: 28 jan. 2026.
  » https://doi.org/10.1007/1-4020-7798X_12
• SANCHES-ANTÓNIO, L. D. Intertemporal slacks and benchmarking in Angolan universities: a DEA window analysis approach. Management Science Letters, Canada, v. 16, n. On line first, 2026. Disponível em: https://growingscience.com/msl/online_issues.html Acesso em: 23 fev. 2026.
  » https://growingscience.com/msl/online_issues.html
• SANCHES-ANTÓNIO, L. D. Trends in efficiency of Angolan commercial banks outside of top ten: a DEA window analysis. Journal of Economics and Business Issues, Turkey, v. 5, n. 2, p. 1-17, 2025a. Disponível em: https://jebiacademic.org/index.php/jebi/article/view/128 Acesso em: 31 ago. 2025.
  » https://jebiacademic.org/index.php/jebi/article/view/128
• SANCHES-ANTÓNIO, L. D. DEA window approach to analyze trends in efficiency of Angolan insurance companies. Global Journal of Economic and Finance Research, Netherlands, v. 2, n. 04, p. 205-213, 2025b. ISSN 3050-5348. Disponível em: https://gjefr.com/index.php/gjefr/article/view/110>. Acesso em: 22 dez. 2025.
  » https://gjefr.com/index.php/gjefr/article/view/110
• SANCHES-ANTÓNIO, L. D. Technical performance and productive dynamics in Angolan maritime fisheries: an intertemporal DEA-VRS approach. Economic Analysis, Belgrade, n. Online first, 2025c. ISSN 2560-3949. Disponível em: <https://www.library.ien.bg.ac.rs/index.php/ea/article/view/2074; https://www.semanticscholar.org/paper/Technical-Performance-and-Productive-Dynamics-in-An-Sanches-Ant%C3%B3nio/116f8225c3d630348fc8b4e577ef7bbfeaf8b694 COBISS.SR-ID 169576460; UDC 33; Corpus ID: 284427865. Acesso em: 29 dez. 2025.
  » https://www.library.ien.bg.ac.rs/index.php/ea/article/view/2074» https://www.semanticscholar.org/paper/Technical-Performance-and-Productive-Dynamics-in-An-Sanches-Ant%C3%B3nio/116f8225c3d630348fc8b4e577ef7bbfeaf8b694
• SHERO, J. A. et al. Data envelopment analysis (DEA) in the educational sciences. The Journal of Experimental Education, FL, USA, v. 90, n. 4, p. 1021-1040, 2022. Disponível em: https://doi.org/10.1080/00220973.2021.1906198 Acesso em: 1 mar. 2026.
  » https://doi.org/10.1080/00220973.2021.1906198
• SPSS®. Statistics for Windows Version 26.0, 2019. Disponível em: https://www.ibm.com/products/spss-statistics Acesso em: 12 out.
  » https://www.ibm.com/products/spss-statistics
• TAVARES, R. S.; MEZA, L. A. Uso da análise envoltória de dados para a avaliação da eficiência em cursos de graduação: um estudo de caso em uma instituição de ensino superior brasileira. Revista Espacios, Niteroi, Brasil, v. 38, n. 20, p. 1-15, 2017. Disponível em: https://revistaespacios.com/a17v38n20/a17v38n20p17.pdf Acesso em: 2 jan. 2025.
  » https://revistaespacios.com/a17v38n20/a17v38n20p17.pdf
• TAYLOR, B. H. G. Relative efficiency among South African universities: a data envelopment analysis. Higher Education, Netherlands, v. 47, p. 73-89, 2004. Disponível em: https://link.springer.com/article/10.1023/B:HIGH.0000009805.98400.4d Acesso em: 11 mar. 2025.
  » https://link.springer.com/article/10.1023/B:HIGH.0000009805.98400.4d
• WERLE, F. O. C.; KOETZ, C. M.; MARTINS, T. F. K. Escola pública e a utilização de indicadores educacionais. Educação, Porto Alegre, Brasil, 38, n. 1, p. 99-112, 2015. Disponível em: https://revistaseletronicas.pucrs.br/faced/article/view/11686 Acesso em: 23 dez. 2025.
  » https://revistaseletronicas.pucrs.br/faced/article/view/11686
• WITTE, K. D.; LÓPEZ-TORRES, L. Efficiency in education: a review of literature and a way forward. Journal of the Operational Research Society, Oxfordshire, UK, v. 68, n. 4, p. 339-363, 2017. Disponível em: https://www.tandfonline.com/doi/full/10.1057/jors.2015.92 Acesso em: 19 mar. 2024.
  » https://www.tandfonline.com/doi/full/10.1057/jors.2015.92
• WOLSZCZAK-DERLACZ, J. An evaluation and explanation of (in)efficiency in higher education institutions in Europe and the U.S. with the application of two-stage semiparametric DEA. Research Policy, Amesterdam, Netherland, v. 46, n. 9, p. 1595-1605, 2017. Disponível em: https://www.sciencedirect.com/science/article/pii/S0048733317301221 Acesso em: 3 mar. 2026.
  » https://www.sciencedirect.com/science/article/pii/S0048733317301221

Edited by

Editor de Seção: Rafael Ângelo Bunhi Pinto | Editora de Layout: Silmara Pereira da Silva Martins

Conflict of interest

CONFLICT OF INTEREST STATEMENT

The authors declare that there is no conflict of interest regarding the article: “(In)efficiency of relative performance in quantitative courses: an intertemporal DEA-CRS analysis at the School of Hotel and Tourism at Agostinho Neto University.”

Publication Dates

• Publication in this collection
  31 Aug 2026
• Date of issue
  2026

History

• Received
  22 Aug 2025
• Accepted
  25 May 2026
• Reviewed
  28 May 2026