Contextual Comparative Analysis of Dar es Salaam and Mombasa Port Performance by Using a Hybrid DEA(CVA) Model

Abstract

Background: This research conducts a contextual comparative analysis between Dar es Salaam and Mombasa ports, employing a hybrid data envelopment analysis (DEA) model that integrates the contextual value-added approach (CVA). The assessment incorporates various inputs (quay length, number of cranes, and storage area) and outputs (number of ship calls and cargo throughput) to compute efficiency scores, offering nuanced insights into the strengths, weaknesses, and areas for improvement of both ports. Methods: The hybrid DEA model with CVA is applied to calculate efficiency scores, considering the diverse inputs and outputs. This approach allows for a comprehensive evaluation of the relative performance of Dar es Salaam and Mombasa ports. The study also explores the influence of trade-related externalities on port efficiency, providing a holistic understanding of the factors shaping the ports’ operational effectiveness. Results: The efficiency scores depict distinctive performance trends between Dar es Salaam and Mombasa ports. Notably, Dar es Salaam exhibits maximum efficiency (efficiency value of 1) in 2018 and 2021, while Mombasa attains optimal performance (efficiency value of 1) in 2021. However, efficiency values fluctuate for both ports in other years, ranging between 0.895 and 0.985 for Mombasa and 0.924 and 0.960 for Dar es Salaam. Conclusions: This study highlights the dynamic efficiency levels of Dar es Salaam and Mombasa ports over multiple years and identifies critical factors influencing their performance. The findings contribute valuable insights to the field of port analysis, offering guidance to port management and policymakers in optimizing the efficiency and competitiveness of these vital maritime hubs.

1. Introduction

Port analysis is essential for assessing the performance and competitiveness of ports, which are important links in global supply chains [1,2]. Understanding the factors that contribute to the efficiency and effectiveness of ports is essential for decision making by policymakers, port managers, and stakeholders on infrastructure development, operational improvements, and resource allocation [3]. Through comparative analysis of ports, valuable insights can be gained into their strengths, weaknesses, and potential areas for improvement. This research aims to contribute to the existing literature on port analysis by focusing on both internal and external factors (contextual) by using a proposed hybrid model for contextual comparative analysis of Dar es Salaam and Mombasa ports.

Dar es Salaam Port in Tanzania and Mombasa Port in Kenya both play pivotal roles in the East African maritime trade, as shown in Figure 1. These ports are of great importance as they serve as primary gateways for international trade, facilitating the smooth flow of goods and functioning as crucial transshipment hubs within the region [4].

According to UNCTAD’s classification of ports into different generations, both Dar es Salaam and Mombasa ports primarily fall into the third-generation category [5]. This classification highlights their transformation to meet the intricate demands of modern global trade [6,7]. Dar es Salaam Port has recently experienced substantial growth, aligning with the characteristics of third generation ports. Similarly, Mombasa Port, renowned for its enduring role as a regional trade hub, exhibits feature in line with third generation ports. This comparison provides insights into their strengths and weaknesses as third-generation ports, showcasing their adaptation to the challenges and opportunities of today’s international trade landscape.

Contextual comparative analysis involves comparing entities within their specific context [8]. In this paper, it compares Dar es Salaam and Mombasa ports while considering their unique operating environments. Contextual value-added approach (CVA) extends data envelopment analysis (DEA) by including contextual factors such as the environment and regulations, providing a more comprehensive evaluation of entity efficiency. CVA assesses how well an entity operates in its specific environment, offering insights beyond internal measures, especially useful for complex systems influenced by external conditions [9].

Data envelopment analysis (DEA) is a widely used methodology for evaluating the relative efficiency of decision-making units, such as ports [4,10]. DEA allows for the comparison of multiple inputs and outputs to determine the efficiency scores of different ports [4]. In this research, a hybrid DEA approach will be employed, incorporating the contextual value-added approach (CVA). CVA involves considering contextual factors or variables that affect the performance of the ports. By integrating contextual variables into the analysis, a more comprehensive evaluation of the ports’ efficiency and performance can be achieved.

The motive behind this study is the essential role that ports play in nations’ economic development. The ports of Dar es Salaam and Mombasa are important entry and exit points for goods in East Africa. Their efficiency affects regional integration, economic growth, and trade efficiency. It is critical to understand how these ports function and the factors that affect their performance.

While previous studies have yielded valuable insights into the internal factors influencing port performance and have offered strategic directions for port management, there has been a gap in delving into the depth of contextual analysis encompassing external factors that are equally crucial for comprehensive decision making. To bridge this gap, we have adopted a hybrid DEA–CVA model, uniquely suited for analyzing both internal and external factors; thus, addressing the dearth of nuanced contextual considerations inherent to individual ports. This research aims to rectify the absence of such nuanced contextual factors, a deficiency that limits a thorough exploration of the specific challenges and opportunities presented by ports such as Dar es Salaam and Mombasa within the East African Region. Consequently, there is a critical need for more robust and contextual driven comparative analyses, capable of integrating the intrinsic characteristics and complexities of individual ports, thereby facilitating a more holistic understanding.

Objectives of this research are to conduct a contextual comparative analysis of Dar es Salaam and Mombasa ports using a hybrid DEA–CVA model and to identify the key factors influencing their performance. This research will involve collecting relevant data on the infrastructure, operations, and management of both ports. This data will be preprocessed and normalized, and efficiency scores will be calculated using the DEA–CVA model. Statistical analysis techniques will be applied to interpret the results and identify the strengths and weaknesses of each port. This research will also aim to determine the contextual variables that significantly affect the performance of the ports using trade level of export and import as the external factor effect port performance. The findings will provide valuable insights for port management and policymakers in improving the efficiency and competitiveness of these ports, as the demand of port will decline when port performance continues to deteriorate [11].

2. Literature Review

2.1. Port Analysis and Performance Evaluations

Previous studies have extensively examined port analysis and performance evaluation to assess the efficiency and effectiveness of port operations. These studies have focused on various aspects, including productivity, infrastructure, logistics, and competitiveness. Several approaches have been employed, such as traditional performance indicators, econometric models, and data envelopment analysis (DEA). For example, ref. [12] explores the impact of the Physical Internet (PI) on port performance evaluation and selection. This study identifies criteria and preferences of decision makers in the PI shipping environment using expert surveys. The findings reveal subtle differences in criteria weighting compared to current practices, emphasizing the importance of the level of service, network interconnectivity, and information systems. These insights are valuable for port authorities aiming to attract both intelligent containers and vessels in the future shipping system.

Another study [13] explores the impact of smart port design on maritime transport efficiency. Using a three-step DEA-Tobit modeling approach, it evaluates the performance of the top 20 maritime ports based on their throughputs. The three following key smart port aspects are identified: automation, environment, and intelligence. Their weights are determined through the analytic hierarchy process (AHP). This study reveals that pollution control, representing the environmental aspect, has the most substantial positive effect on port efficiency. Conversely, information sharing from the intelligence aspect has a negative impact, likely due to technology requirements, information complexity, and potential overload. This integrated measurement structure provides valuable insights, emphasizing that not all design elements lead to positive outcomes. Ultimately, it offers policy recommendations for prioritizing smart aspects in smart port development.

In their investigation of logistics companies’ performance, ref. [14] focuses on optimizing operational efficiency within listed logistics companies in Malaysia. This study acknowledges the significance of operational risks in influencing these companies’ performance and overall success. To evaluate this, they employ a data envelopment analysis (DEA) model and introduce the basic indicator approach (BIA) as a crucial output indicator for assessing operational risk capital requirements. This research not only contributes valuable insights to the logistics sector but also extends its applicability to emerging domains such as finance and project-based construction, where managing operational risk is paramount. The findings not only serve as a basis for identifying areas of improvement within inefficient logistics firms but also offer practical and managerial implications to enhance their performance and resilience in the face of operational uncertainties.

Also, ref. [10] examines the efficiency and resource consumption of container ports using an inverse data envelopment analysis (DEA) model. This study reveals the feasibility of DEA for performance evaluation and its value in optimizing resources, providing insights for policymakers. A comparative analysis with another DEA model is also discussed. These studies have contributed to identifying key factors influencing port performance, improving port management strategies, and informing policy decisions. However, while valuable insights have been gained from these studies, there is a need for more comprehensive and contextual driven comparative analyses that consider the specific characteristics and challenges of individual ports.

2.2. Overview of DEA and CVA Techniques and Their Applications in Port Analysis

Data envelopment analysis (DEA) is a non-parametric method widely used in the evaluation of port efficiency. DEA provides a means to assess the relative performance of ports by measuring their ability to convert inputs (e.g., labor and capital) into outputs (e.g., cargo handling and revenue) while accounting for multiple factors. In example [10], the study introduces an inverse data envelopment analysis (IDEA) model to assess container ports’ efficiency while considering environmental impacts. It examines data from 16 major ports in China and highlights IDEA’s viability for performance evaluation and resource optimization. This paper also conducts a comparative analysis with another DEA model, offering valuable insights for policymakers in the context of the maritime industry’s environmental challenges.

DEA has found applications in various fields, including agriculture. In [13], DEA is applied to assess 76 sheep farms in Central Italy, exploring the link between animal health, welfare, management practices, and technical efficiency. Using a two-stage DEA approach, this study measures efficiency and super efficiency and examines how animal welfare and management affect technical efficiency. The findings indicate that optimizing management and scale could boost output production by 20%. ‘Pure’ technical inefficiency plays a crucial role in overall technical inefficiency. Factors such as extensive farming and higher replacement rates reduce efficiency, while maintaining animal health and welfare positively impacts it. Notably, improving animal welfare does not depend on farm scale, highlighting its importance in enhancing sheep farming efficiency. Also, ref. [15] examines the technical efficiency of Iranian dairy farming, with a focus on energy use. Using a window data envelopment analysis (W-DEA) and slack-based model (SBM), it assesses 25 provinces over 22 years. The findings indicate an average efficiency score of about 0.85, with Zanjan, Ardabil, and Hormozgan provinces leading in efficiency. Provinces vary in efficiency and energy consumption over time. Applying the SBM model enhances accuracy. Notably, higher milk production is associated with lower technical efficiency. This study suggests room for improvement through better resource use, energy optimization, mechanization, and environmental considerations in policymaking.

DEA has been applied in the analysis of the energy industry, as demonstrated by [16], which provides a systematic review of DEA applications in energy and environmental research spanning from the 1980s to the 2010s. This study underscores DEA’s significance in assessing sustainability in the context of industrial development and environmental concerns, including pollution. While recognizing DEA’s strengths and limitations, the review emphasizes its pivotal role in informing policy and business decisions related to climate change and pollution mitigation. It also highlights the relevance of technology innovation and provides valuable guidance for future DEA research in these critical domains [17]. This paper examines the relationship between energy efficiency and financial performance in response to the Korean government’s energy regulations. Using a two-stage network DEA model, it distinguishes pure energy and economic efficiency over time. Findings show varying energy efficiency changes by industry, the challenge of improving both types of efficiency simultaneously, and a significant link between energy efficiency and financial performance, with high pure energy efficiency not guaranteeing better financial outcomes. Also, ref. [18] presents a concise literature review focused on the growing significance of energy efficiency in sustainable development. It emphasizes the role of data envelopment analysis (DEA) in evaluating energy efficiency. This review covers research from 2011 to 2019 defining energy efficiency, discussing measurement and evaluation variables, and exploring DEA models and their applications. It concludes by suggesting future research directions to address current DEA model limitations in assessing energy efficiency.

The CCR model (Charnes, Cooper, and Rhodes model) is a popular type of data envelopment analysis (DEA). DEA is a mathematical method for assessing the relative efficiency of decision-making units (DMUs), such as companies, organizations, or, in this case, ports. The CCR model specifically focuses on measuring the technical efficiency of DMUs by comparing their input and output data. Article [16] explores eco-efficiency at the regional level, focusing on Poland’s regions. It utilizes the data envelopment analysis (DEA) method, specifically, the CCR model, to measure regional eco-efficiency. This study combines environmental and economic indicators and finds that some regions, such as Lubuskie and Mazowieckie, are relatively eco-efficient, while others consume excessive environmental resources. Notably, six of the eco-inefficient regions show a positive trend in sustainability. These findings inform regional environmental strategies and shed light on the causes of eco-inefficiency.

Also, ref. [19] employs the DEA–CCR model to address global road safety concerns, where millions are killed or injured annually. It introduces a DEA-based decision support method for enhancing urban road safety management. Using inputs such as intersection conflict points and traffic flow, and the social cost of accidents as the output, it identifies priority locations for safety interventions within an Italian urban road network. This study compares different DEA models to determine the most effective tool for this purpose.

The contextual value-added approach (CVA) is a novel technique that enhances the traditional data envelopment analysis (DEA) method by incorporating contextual variables, such as environmental, regulatory, and technological factors, to provide a more comprehensive and realistic assessment. This approach, which has never been used in the analysis of port performance in the transportation field, enables a deeper understanding of how external factors influence the efficiency and effectiveness of ports. For example, ref. [9] explores the evolution of school progress measures in England, particularly focusing on the changes from ‘value-added’ to ‘contextual value-added’, ‘expected progress’, and ‘progress 8’. This paper critically assesses these shifts, questions the government’s rationale for discontinuing contextual value-added models, identifies design flaws in the expected progress measure, and examines the stability of school rankings across these measures. Ultimately, it emphasizes the need for a more cautious and skeptical interpretation of school progress measures and league tables.

Also, ref. [8] focuses on the contentious issue of teacher value-added models. It surveys research covering a range of topics related to value-added models in education, including model design and their practical use in teacher evaluations. This review highlights both areas of consensus and disagreement within the literature. While diverse perspectives exist, there is a growing body of research that is converging on a widely-accepted set of findings in this field.

Integrating DEA and CVA provides a holistic view of port performance, incorporating both internal efficiency metrics and external contextual factors. For instance, a study by [4] compares East and West African ports’ efficiency using DEA window analysis, revealing that, despite West African ports’ larger size and container throughput, East African ports tend to be more efficient. This finding has implications for regional port development strategies. Our research introduces a novel hybrid approach, combining contextual value-added analysis (CVA) and data envelopment analysis (DEA), emphasizing the significance of these hybrid models in comprehending intricate port dynamics. While [20] highlights the value of hybrid models in additive manufacturing, our study’s integration of CVA and DEA sheds light on the nuanced connection between contextual factors and port efficiency. These insights underscore the potential of hybrid models to inform evidence-based decision making in both additive manufacturing and port management, suggesting promising avenues for interdisciplinary research.

2.3. Existing Research on Comparative Analysis of Ports

Previous research has conducted comparative analyses of different ports worldwide, examining their performance, efficiency, and competitiveness. These studies have compared ports in terms of infrastructure capacity, operational efficiency, connectivity, and economic impact. For instance, comparative studies have explored the performance differences between ports in developed and developing countries, highlighting the role of institutional factors, governance structures, and technological advancements. For example, ref. [21] discusses the research gap in port performance measurement (PPM) and comparison research, emphasizing the overlooked interdependency of port performance indicators (PPIs). This study compares the importance analysis of PPIs using the analytic hierarchy process (AHP) for independent relationships and the decision-making trial and evaluation laboratory (DEMATEL) for interdependent relationships. The findings highlight differences in importance scores and ranking, contributing to addressing the research gap and aiding rational decision making in PPM and port choice.

Recently, ref. [22] conducted a comparative analysis between Polish ports in the Tri-City and successful Chinese ports. The purpose of this comparison is to identify development opportunities for Polish ports in terms of transshipment and growth. The authors also explored how the management of cargo in areas distant from the port can influence both the city and the port, potentially indicating the need for changes in the current management approach.

Also, ref. [23] examines the significance of ports in the global and regional freight supply chain and transportation network, emphasizing their crucial role in economic growth. It highlights the need for continuous analysis, planning, and adaptation of port activities to address market dynamics and competitive pressures. Existing studies on seaports are reviewed, revealing a gap in analyses comparing multiple ports simultaneously. To address this, this study conducts a comparative analysis of ports along the Eastern Baltic Sea, encompassing ten ports in four different countries. The findings identify Klaipeda Port as the most diversified in the region, with a balanced distribution of cargo types. Tallinn, Riga, and Ventspils excel in handling bulk cargo, while Primorsk leads in liquid cargo, and St. Petersburg dominates in general cargo volumes. Additionally, this study underscores the optimal utilization of Visotsk Port’s infrastructure based on selected parameters.

Despite the existing research on port analysis and comparative studies as shown in

Table 1. A summary of the papers included in the literature review.

Data Envelopment Analysis DEA
Related Field	Paper	Application	Criteria Chosen	Methodology	Case Study Regions
Agriculture	[24]	Analysis of technical efficiency of meat-producing sheep farms	Input: labor employment (work hours), feed supply surface area, and livestock units (LSU) Output: annual meat and wool production	DEA and super data envelopment analysis (S-DEA)	Central Italy
	[15]	Analysis of technical efficiency of Iranian dairy farming production systems	Input: energy Output: milk production	DEA and SBM analysis	Iran
Transportation and Logistics	[25]	Measure the performance efficiency of 22 ports listed in the stock market in Vietnam	Input: capital, operation expenses, labor, port area, quay length, and depth Output: revenue and cargo throughputs	Hybrid method of Delphi technique with KAMET principle and input and output-oriented DEA method	Vietnam
	[4]	Analyzing East and West African major ports’ efficiency over time	Input: total terminal area, the number of cranes, the number of berths and the quay length Output: container throughput	DEA window analysis	East and West African
	[10]	Measuring container ports’ efficiency and analyzing their resource consumption by considering undesirable outputs	Input: desirable and undesirable outputs (based on emissions factor) Output: input alternation	Inverse data envelopment analysis (IDEA)	China
	[19]	Identifying those roads where the needs to improve safety are the greatest	Input: conflict points at intersections and traffic flow Output: social cost of accidents	DEA-based decision support (CCR and BCC models)	Italian urban
Education and Training	[26]	Determine the performance levels of departments in Dokuz Eylul University	Inputs: number of full-time employees, personnel costs, operation costs, research income, and number of non-academic employees Output: number of PhD students, number of postgraduate and undergraduate students, total income, number of publications, and number of projects	Data envelopment analysis (DEA)	Turkey
Energy and Environment	[18]	Analyzes the overall situation (energy efficiency) of related literature published in 2011–2019	-- --	Data envelopment analysis (DEA)	Review paper
	[17,27]	Investigates whether energy efficiency has a positive relationship with firms’ financial performance	Input: cost of goods sold (COGS), GHG emissions, numbers of employees, and the capital for economy efficiency Output: annual sales volume	Extended an existing two-stage network DEA (data envelopment analysis)	Korean
Contextual Value Added (CVA)
Related Field	Paper	Application	Criteria Chosen	Methodology	Case Study Regions
Education and Training	[8]	Reviews the literature on contextual value added by teachers	-- --	Contextual value-added (CVA) model	--
	[9]	Examines the evolution of school progress measures, including changes in headline measures, government justifications, design flaws, and their implications for school rankings	Input: number of pupils at the end of GCSE, percentage of pupils with five or more GCSEs (or equivalent qualifications) at grade A* to C, and contextual value-added score (national average = 1000) Output: EP English = percentage of pupils making expected progress in English; EP math = percentage of pupils making expected progress in mathematics	Contextual value-added (CVA) model	United Kingdom
Port analysis and performance evaluations
Related Field	Paper	Application	Criteria Chosen	Methodology	Case Study Regions
Port operation	[1]	Analyses the ports’ technical efficiency of Mediterranean major container ports	Input: total cost, total area, and berth length are set as fixed inputs, and berth cranes and yard equipment are set as a variable input Output: annual container throughput	Cross-sectional data analysis and DEA window analysis	Mediterranean major container ports
	[2]	Compares historical perspectives, developing mode, and management model of the dry ports sector in China, a high-income developing country under a socialist system with advanced shipping infrastructure, against the East African region, which is characterized with low-income countries, free market policies, and a largely less developed shipping infrastructure	Dry port performance	Descriptive study, case study, and cross-sectional study	East Africa and China
	[21]	Addresses a significant research gap in port performance measurement (PPM) by comparing the analysis of port performance indicators’ (PPIs) importance considering both their independent and interdependent relationships	Independent and interdependent port performance indicators (PPIs)	Analytic hierarchy process (AHP) and the decision-making trial and evaluation laboratory (DEMATEL) with analytic network process (ANP) methodologies.	General context
	[23]	Comparative analysis of ports along the Eastern Baltic Sea	External factors determining port competitiveness Internal factors determining port competitiveness: human factors, institutional factors, physical and technological factors, and economic factors	Analysis of statistical data	Lithuania, Latvia, Estonia and Russia

, there are several research gaps that need to be addressed. First, many previous studies have focused on overall port performance without considering the specific contextual factors that influence individual ports. Second, there is a lack of studies employing hybrid techniques such as the DEA(CVA) in the comparative analysis of ports, which could provide a more comprehensive understanding of their relative performance. Third, while some comparative analyses have been conducted, there is a need for more specific and localized studies that compare ports within the same region, considering the unique characteristics and challenges they face. Therefore, there is a clear need for a contextual comparative analysis using hybrid DEA(CVA) techniques to address these research gaps and provide insights into the performance and efficiency of ports such as Dar es Salaam and Mombasa.

3. Methodology and Data Description

3.1. Data Description

The performance measurement using data envelope analysis (DEA) involved collection of data from two ports, namely Mombasa and Dar es Salaam. The data were sourced from the KPA Annual Review and Bulletin of Statistics 2021 for Mombasa and TPA Statistics 2021 for Dar es Salaam. Additionally, import and export data were gathered to account for externalities, including information from the Bureau of Statistics for all East-Central African countries and Lloyds Bank Trade for the CVA model. These datasets were combined into a single table, as shown in

Table 2. Inputs and output variables for Dar es Salaam and Mombasa ports.

Port	Years	Cargo Throughput	Number of Ship Calls	Quay Length	Storage Area	Number of Cranes
Port of Dar es salaam	2016	13,588,966	1427	2600	56,800	25
	2017	13,761,536	1428	2600	56,800	25
	2018	15,400,876	1489	2600	56,800	25
	2019	16,022,952	1425	2600	56,800	25
	2020	15,857,870	1368	2600	56,800	25
	2021	16,214,156	1487	2600	56,800	25
Port of Mombasa	2016	27,364,000	1607	840	57,916	32
	2017	30,345,000	1767	840	57,916	32
	2018	30,923,000	1605	840	57,916	32
	2019	34,440,000	1675	840	57,916	32
	2020	34,788,000	1685	840	57,916	32
	2021	36,045,000	1793	840	57,916	32

, incorporating input variables such as quay length, storage area, and number of cranes, as well as output variables such as cargo throughput and number of ship calls.

This article has used a combination of two models to come up with a very detailed analysis about the efficiency of these ports. The DEA model has been used to be able to provide results to the efficiency of these ports, and the CVA model has been used to find out the environmental stimuli that affect or contribute to the efficiency of these port.

3.2. Methodology

In this study, the data preprocessing stage involved normalization procedures to ensure uniformity and comparability. Following this, the normalized data underwent data envelopment analysis (DEA), aimed at assessing the efficiency levels of each port from 2016 to 2021. This assessment formed the foundation for proposing strategies to enhance operational efficiency.

DEA facilitated the assessment of relative efficiency, highlighting areas for potential improvement in overall performance [28]. The outcomes were then harmonized with external factors within the contextual variable analysis (CVA) model. Specifically, import and export data from countries utilizing Mombasa and Dar es Salaam ports were integrated, offering insights into the trade’s influence on port efficiency and capturing the impact of trade-related variables.

By merging the DEA results with external trade indicators, as depicted in Figure 2, this study aimed to illuminate the intricate relationship between trade volumes and port efficiency, revealing how trade dynamics interact with port performance. The methodology was encompassed by applying the DEA to the preprocessed data to evaluate port efficiencies, followed by an exploration of external trade factors using the CVA model. This comprehensive approach facilitated a deeper understanding of the multifaceted factors shaping port efficiency and provided valuable insights for optimizing port operations within the context of trade-related complexities.

3.3. Data Normalization

Min–max normalization, a data preprocessing technique, was employed to standardize input variables, bringing them into a uniform range typically spanning from 0 to 1. The procedure involved the following steps:

• Identification of input variables, including the number of cranes, quay area, and storage area.
• Computation of the minimum and maximum values for each input variable based on available data across all ports and years.
• For each input variable, subtraction of the minimum value was followed by division by the range (i.e., the difference between the maximum and minimum values), as specified by the formula in Equation (1).
• Repetition of this process was performed for all ports and years, resulting in the min–max normalized values of each input variable within the 0 to 1 range, as seen in

  Table 3. Normalized data (the decision matrix).

  	Years	Cargo Throughput	Number of Ship Calls	Quay Length	Storage Area	Number of Cranes
  Dar es Salaam Port	2016	0.1568	0.2627	0.3885	0.2859	0.2513
  	2017	0.1755	0.2739	0.3885	0.2859	0.2513
  	2018	0.1826	0.2622	0.3885	0.2859	0.2513
  	2019	0.1807	0.2517	0.3885	0.2859	0.2513
  	2020	0.1847	0.2736	0.3885	0.2859	0.2513
  	2021	0.3118	0.2956	0.1255	0.2915	0.3217
  Mombasa Port	2016	0.3457	0.3251	0.1255	0.2915	0.3217
  	2017	0.3523	0.2953	0.1255	0.2915	0.3217
  	2018	0.3924	0.3082	0.1255	0.2915	0.3217
  	2019	0.3963	0.3100	0.1255	0.2915	0.3217
  	2020	0.4107	0.3299	0.1255	0.2915	0.3217
  	2021	0.4112	0.3461	0.1255	0.2915	0.3217

  .

$$N_{ij}=\frac{X_{ij}}{\sqrt{\sum _{j=1}^n{X}_{ij}^2}}$$

(1)

N—min/max value of X, X—input variables.

3.4. Data Envelopment Analysis

The relative performance of organizations can be assessed using the data envelopment analysis (DEA), a method based on mathematical programming. Although the technique has primarily been used in the evaluation of nonprofit organizations, it can also be successfully applied in other contexts where it must compete with other techniques such as cost–benefit analysis and multi-criteria decision making [28].

CCR (Ratio) Mode

The CCR ratio model calculates the unit’s overall efficiency by merging its scale efficiency and pure technical efficiency into a single number, as shown from Equations (2)–(11). The efficiency obtained is never absolute because it is constantly judged in respect to the field [29].

In order to optimize efficiency, the decision-making units (DMUs) being evaluated can select the proper weights for each of its variables using the primordial model (in the following model, inputs are represented by x and outputs by y). The solution is a set of weights (y for inputs and x for outputs) selected so that any other unit using these weights will not have an efficiency greater than 1, the level at which a unit is relatively efficient. Since naming this model the primal model rather than the dual model more accurately expresses the underlying fundamental idea of DEA, some authors prefer to use this term. For each decision-making units (DMUs), we formed the virtual input and output by (yet unknown) weights (v_i) and (u_r):

The best weights can (and usually do) differ from one decision-making unit (DMU) to another. As a result, rather than being predetermined, the “weights” in DEA are derived from the data. Each decision-making unit (DMU) is given the best set of weights, with values that may differ from one decision-making unit (DMU) to another. Hereafter, we shall generally refer to these DEA weights as “multipliers” to separate them from the other widely-used techniques because they differ from conventional weightings in this instance as well (for example, as in index number constructions).

Output (oriented)

$${\mathrm{m}\mathrm{i}\mathrm{n}\theta }_o=\sum _{i=1}^m{V}_{ik}{X}_{ik}$$

(2)

$$s.t.{\displaystyle \sum _{r=1}^t{U}_{rk}}{Y}_{rk}=1$$

(3)

$$-{\displaystyle \sum _{r=1}^t{U}_{rk}}{Y}_{rk}+{\displaystyle \sum _{i=1}^m{V}_{ik}}{X}_{ik}\ge 0(J=1,.......,n)$$

(4)

$$U_{rk}\ge \in (r=1,.......,n)$$

(5)

$$V_{ik}\ge \in (r=1,.......,n)$$

(6)

Input (oriented)

$$Max{\theta }_o={\displaystyle \sum _{r=1}^t{U}_{rk}}{Y}_{rk}$$

(7)

$$s.t.{\displaystyle \sum _{i=1}^m{V}_{ik}}{X}_{ik}=1$$

(8)

$$-{\displaystyle \sum _{r=1}^t{U}_{rk}}{Y}_{rk}+{\displaystyle \sum _{i=1}^m{V}_{ik}}{X}_{ik}\ge 0(J=1,.......,n)$$

(9)

$$U_{rk}\ge \in (r=1,.......,n)$$

(10)

$$V_{ik}\ge \in (r=1,.......,n)$$

(11)

where

n—number of alternatives/decision-making units (DMUs);

m—number of input criteria;

S—number of output criteria;

X_ik—value of input criteria;

Y_rk—value of output criteria;

U_rk and V_ik—non-negative variables weight to be determined by the solution of maximizing/minimizing problem.

• Contextual value-added model

The contextual value-added (CVA) model is a technique for analyzing port progress that considers a larger variety of factors. If CVA is a more accurate measure of a port’s effectiveness, it would have been preferable to find ways to make it easier to understand.

Although many writers in the past neglected to mention it, other aspects that are not feasible in day-to-day port operations also have an impact on the effectiveness of these ports. As an illustration, the geographic position of the ports, government investment, or economic considerations in the separate countries, among many other factors, may result in one port’s efficiency being higher than another’s. We shall learn from DEA model what these ports performed to archive their performance.

Observing how the DEA mode is being used instead of merely concentrating on final performances, the contextual value-added model, which is quite popular in the UK, is used to evaluate student achievement by looking at other things that might have helped them perform better.

First, comparisons are made between the various models’ estimated regression coefficients and adjusted R-squared statistics. The port impacts of the models are then assessed for statistical and practical significance (effect magnitude). Last, we evaluate models based on the degree to which their performance impacts are associated using scatterplots and Pearson’s and Spearman’s correlations.

In Kenya, Mombasa is home to the largest seaport. It handled 34.44 million metric tons over the same period in 2019 compared to 30.923 million metric tons handled over the same period in 2018, which is an increase of 11.4%. A total of 4.277 million metric tons of freight are exported, 27.558 million metric tons of freight are imported into the port of Mombasa, and 0.25 million metric tons of freight are transshipped.

3.5. Application of CVA Model

The CVA model first focuses on estimating regression coefficients and modified R-squared statistics. The statistical significance of the port externality effects in relation to the port performance (effect size) of the models are compared. Finally, using Pearson’s and Spearman’s correlations and scatterplots, we assess how closely related the effects of port externalities to port performance are for each year, as shown in Equations (12)–(14).

Equations (12) and (13) represents a linear regression model, where each β (beta) coefficient quantifies the impact of specific port externalities on port performance. Equation (14) calculates the modified R-squared statistic, indicating how effectively these external factors explain variations in port performance. Also, Pearson’s and Spearman’s correlations are applied to access correlations and relationships between port externalities and performance, though further context is needed for a detailed explanation. These equations are crucial for quantifying the influence of various external factors on port efficiency over different years.

$$a=\frac{{\displaystyle \sum _{i=1}^{n}Y{{\displaystyle \sum _{i=1}^n{X}_i^2}}_i}-{\displaystyle \sum _{i=1}^n{X}_i}{\displaystyle \sum _{i=1}^n{X}_i{Y}_i}}{n{\displaystyle \sum _{i=1}^n{X}_i^2}-{\displaystyle \sum _{i=1}^n{(X)}_i^2}}$$

(12)

$$b=\frac{n{\displaystyle \sum _{i=1}^n{X}_i{Y}_i}-{\displaystyle \sum _{i=1}^n{X}_i}{\displaystyle \sum _{i=1}^n{Y}_i}}{n{\displaystyle \sum _{i=1}^n{X}_i^2}-{\displaystyle \sum _{i=1}^n{(X)}_i^2}}$$

(13)

$$adj{R}^2=1-\left[\frac{(1-R^2)(n-1)}{(n-k-1)}\right]$$

(14)

Seaports are identified as on demand delivery and as the one of nodes of general transportation. International trade is one of the factors that influences the ports to do well in terms of throughput handled. Export and import can be one of the best factors that influence high throughput of the ports which can attract high port performance. For that reason, we take the level of import and export of countries that use the ports of Mombasa and Dar es Salaam as an external factor that affects the performance of the ports.

4. Results of DEA Window Model

In this paper, the input variables used in the DEA model are quay length, storage area, and number of cranes, and output variables are number of ship calls and cargo throughputs. The DEA results are presented in

Table 4. DEA window result.

Port	Year	Efficiencies.DMU	Efficiencies.eff	Average
Dar es salaam	2016	1	0.958361316	0.967015
	2017	2	0.959032908
	2018	3	1
	2019	4	0.960486872
	2020	5	0.924208442
	2021	6	1
Mombasa	2016	1	0.896263246	0.949585
	2017	2	0.985499163
	2018	3	0.895147797
	2019	4	0.955472326
	2020	5	0.965126925
	2021	6	1

.

According to the results obtained from the DEA model analysis, it shows that both ports are not achieving their goals to a large extent based on the inputs invested and the results obtained. The average efficiency of the port of Dar es Salaam for all six years is 96.7%. and that of Mombasa is a 94.9% for all six years. It was only two years prior when the Dar es Salaam Port reached at least a maximum target of 100% (2018, 2021), and in the Mombasa Port, they have reached a maximum target of 100% in only one year (2021). Also, Mombasa Port has experienced port performance of below 90% in 2016 and 2018.

These problems of inefficiency are not caused by the absence of operational resources but are caused by the lack of operations efficiency, as shown in

Table 5. Optimization targets.

Port	Year	Targets (Quay Length Desired)	Quay Length Available	Targets (Storage Area Desired)	Storage Area Available	Targets (Number of Cranes Desired)	Number of Cranes Available	Targets. (Cargo Throughput Should Be Archived)	Targo Throughput Archived	Targets. (Number of Ship Calls Should Be Archived)	Number of Ship Call Archived
Dar es salaam	2016	2492	2600	54,435	56,800	24	25	14,759,604	13,588,966	1427	1427
	2017	2493	2600	54,473	56,800	24	25	14,769,947	13,761,536	1428	1428
	2018	2600	2600	56,800	56,800	25	25	15,400,876	15,400,876	1489	1489
	2019	2424	2600	54,120	56,800	24	25	16,022,952	16,022,952	1425	1425
	2020	2261	2600	51,651	56,800	23	25	15,857,870	15,857,870	1368	1368
	2021	2600	2600	56,800	56,800	25	25	16,214,156	16,214,156	1487	1487
Mombasa	2016	753	840	51,908	57,916	29	32	32,305,809	27,364,000	1607	1607
	2017	828	840	57,076	57,916	32	32	35,522,317	30,345,000	1767	1767
	2018	752	840	51,843	57,916	29	32	32,265,602	30,923,000	1605	1605
	2019	803	840	55,337	57,916	31	32	34,440,000	34,440,000	1713	1675
	2020	811	840	55,896	57,916	31	32	34,788,000	34,788,000	1730	1685
	2021	840	840	57,916	57,916	32	32	36,045,000	36,045,000	1793	1793

.

According to the mix of input variables and output variables, it shows that the amount of input variables is large and will be enough to handle the throughput and number of ship calls. The inefficiency of these ports is not caused by improper allocation of inputs variables. The area of storage is enough to handle the amount of tones available every year. The quay area is also large enough to handle the amount of ship calls and tones available. There is just need to add few number of cranes. The problem in these ports is the ineffective utilization of resources available to enrich the target’s needs.

To check the effects of external factors with regard to port performance, the results from the DEA model are combined with total regional trade level (external factor) as the input of the CVA model to see the effects that this external factor has on port performance. The CVA model’s results are presented in

Table 6. The table presents data on the total trade (import and export) and related parameters of countries using Dar es Salaam (Tanzania, Malawi, Zambia, Eastern DRC, Burundi, Rwanda, and Uganda) and Mombasa ports (Kenya, Uganda, South Sudan, Northeastern DRC, and Burundi).

Port	Year	Total Trade Level Import and Export) in MT	Efficiencies.eff	Parameter β (Cofficient)	Adjusted R-Squared (R2)
Dar es Salaam Port	2016	58,326,600	0.958361316	1.448 × 10−9	0.30538637
	2017	60,854,000	0.959032908
	2018	80,473,000	1
	2019	72,870,000	0.960486872
	2020	71,153,500	0.924208442
	2021	93,768,000	1
Mombasa Port	2016	53,333,000	0.896263246	1.258 × 10−9	−0.332237927
	2017	55,804,000	0.985499163
	2018	74,596,000	0.895147797
	2019	71,696,000	0.955472326
	2020	68,953,500	0.965126925
	2021	88,230,000	1

.

In our analysis, the “parameter β (coefficient)” gauges the relationship between total regional trade levels and port efficiency, signifying its direction and strength. Meanwhile, the “adjusted R-squared (R2)” measures the model’s quality in explaining how trade levels impact port efficiency, with higher values indicating a more influential external factor.

Based on the CVA results, the countries that are using both ports, Dar es Salaam and Mombasa, have shown an increasing trend in total trade over the years, with fluctuations in between. Dar es Salaam experienced an increase from 58,326,600 in 2016 to 93,768,000 in 2021, while Mombasa saw an increase from 53,333,000 in 2016 to 88,230,000 in 2021.

Dar es Salaam had an efficiency value of 1 in 2018 and 2021, indicating maximum efficiency during those years. Mombasa had an efficiency value of 1 in 2021, suggesting optimal performance in that year. However, the efficiency values for other years fluctuated between 0.895 and 0.985 for Mombasa and between 0.924 and 0.960 for Dar es Salaam.

The coefficient values provided in the table show a range of small values close to zero. It is important to note that without additional context or information about the coefficient’s purpose or calculation, it is challenging to draw meaningful conclusions solely based on these values.

The adjusted R-squared values provide an indication of the goodness-of-fit of the model used. The values range from 0.305 to 1 for Dar es Salaam and from −0.332 to 1 for Mombasa. These values suggest that the model used to estimate the efficiency of the ports may have varied in terms of its accuracy and reliability over the years. Based on this, it appears that both ports experienced an increase in total trade over the years.

Based on the provided graphs, which include Pearson’s and Spearman’s correlations, as well as scatterplots, between the total trade level (import and export) and the efficiencies of Dar es Salaam (as shown in Figure 3) and Mombasa ports (as shown in Figure 4), the following interpretations can be made:

• Pearson’s and Spearman’s correlations:

  -

  Dar es Salaam Port:

  ▪

  The efficiency (eff) of Dar es Salaam Port shows a positive correlation with the total trade level across the years.

  ▪

  The Pearson’s correlation coefficient (parameter β) suggests a very weak positive linear relationship between the efficiency and the total trade level.

  ▪

  The adjusted R-squared (R2) value of 0.305 indicates that approximately 30.5% of the variation in efficiency can be explained by the total trade level.

  -

  Mombasa Port:

  ▪

  The efficiency (eff) of Mombasa Port also shows a positive correlation with the total trade level.

  ▪

  The Pearson’s correlation coefficient (parameter β) indicates a very weak negative linear relationship between the efficiency and the total trade level.

  ▪

  The adjusted R-squared (R2) value of −0.332 suggests that approximately 33.2% of the variation in efficiency can be explained by the total trade level.

• Scatterplots:

  -

  Dar es Salaam Port:

  ▪

  The scatterplot for Dar es Salaam Port shows a generally positive trend, indicating that as the total trade level increases, the efficiency tends to increase as well.

  ▪

  However, some data points appear to deviate from the overall trend, indicating potential factors other than total trade level that influence the efficiency.

  -

  Mombasa Port:

  ▪

  The scatterplot for Mombasa Port shows a somewhat scattered pattern, suggesting a less clear relationship between the total trade level and the efficiency.

  ▪

  While there is an overall positive trend, there are data points that do not follow the trend, indicating the presence of other factors affecting the efficiency.

Both ports show a positive correlation between the total trade level and efficiency, but with some variations and deviations from the overall trend. The adjusted R-squared values indicate that a portion of the efficiency variation can be explained by the total trade level, although other factors likely play a role as well. Further analysis and investigation are necessary to understand the specific factors influencing the efficiency of each port.

5. Discussion

The discussion delves critically into the results obtained from the hybrid DEA–CVA analysis of Dar es Salaam and Mombasa ports, unearthing crucial insights into their operational efficiency and trade dynamics.

The DEA window analysis, scrutinizing input variables encompassing quay length, storage area, and the number of cranes, revealed the inefficiencies plaguing these ports. The efficiency scores, oscillating between 89.5% and 98.5% for Mombasa and 92.4% and 96.0% for Dar es Salaam over the studied years, lay bare operational shortcomings. It is essential to recognize that these scores, although seemingly high, underscore substantial room for improvement in resource utilization.

The spotlight then shifted to the interplay between trade dynamics and port efficiency, orchestrated through CVA. The positive correlation between trade levels and port efficiency, albeit with modest Pearson’s correlation coefficients (parameter β), punctuates the sensitivity of port performance in relation to trade variations. This signifies the importance of aligning port operations with trade demands, a facet that is vital for East Africa’s trade aspirations.

However, it is pivotal to note that the adjusted R-squared values, ranging from 0.305 to 1 for Dar es Salaam and −0.332 to 1 for Mombasa, demonstrate the complexity of this relationship. These values reveal that while trade dynamics contribute to efficiency, their influence remains interwoven with multifaceted factors not entirely captured within the model.

The critical facet that surfaces is the operational inefficiency root cause. Contrary to resource scarcity, the infrastructure—quay and storage area—adequately accommodates throughput demands. Thus, the inefficiencies emerge from mismanaged operations, notably highlighted by underutilized cranes. These showcase the pressing need for stringent operational evaluation and strategic enhancement within these ports.

This study presents a disconcerting reality—the operational inefficiencies eclipse any resource constraints within these ports. The synthesis of DEA and CVA techniques underscores this while shedding light on the nuanced relationship between trade dynamics and operational efficiency. This study carries significant implications for the region’s trade aspirations, demanding immediate reevaluation of operational strategies and resource allocation within these ports. Further research is indispensable to navigate this intricate landscape, devising pragmatic solutions that align port operations seamlessly with trade dynamics for East Africa’s socio-economic advancement.

In comparison to [4], this study employs a hybrid DEA–CVA approach, considering a wide range of input and output variables, including quay length, storage area, crane count, cargo throughput, and ship calls. This method provides a comprehensive analysis of East African ports’ performance by integrating both internal efficiency factors and external contextual variables. In contrast, the second paper relies on a simpler DEA window model, primarily focusing on efficiency scores without extensive consideration of external contextual factors. While this study offers a nuanced understanding of port operations, the other paper provides a straightforward efficiency ranking but lacks depth in analysis.

This study reveals efficiency scores ranging from 89.5% to 98.5% for Mombasa and 92.4% to 96.0% for Dar es Salaam, highlighting operational inefficiencies. It concentrates on East African ports, providing a localized perspective. In the second paper, Tema Port is identified as the most efficient in East and West Africa, consistently scoring above 81%. Ports such as Dakar, Lagos, and Dar es Salaam exhibit lower efficiency scores. The second paper takes a broader regional approach, comparing ports across East and West Africa. This study excels in its comprehensive methodology and contextual analysis, focusing on East African ports. The second paper offers valuable efficiency rankings but has a narrower scope and less extensive criteria selection. Both studies contribute unique insights, catering to different research needs and perspectives.

6. Conclusions and Recommendations

This study aimed to conduct a contextual comparative analysis of Dar es Salaam and Mombasa ports using a hybrid DEA–CVA model. The DEA analysis revealed efficiency scores, showing that Dar es Salaam Port had an average efficiency of 96.7% across six years, while Mombasa averaged 94.9%. Interestingly, both ports experienced fluctuations in efficiency across the years, with Dar es Salaam reaching maximum efficiency (100%) in 2018 and 2021, and Mombasa achieving this level in 2021.

The integration of contextual variables through CVA introduced external trade levels as a factor influencing port performance. This contextual perspective shed light on the interplay between trade dynamics and port efficiency. Importantly, countries using both ports exhibited an increasing trend in total trade over the years. Countries that used Dar es Salaam Port saw a total trade growth from 230 million metric tons in 2016 to 260 million metric tons in 2021, and countries using Mombasa Port saw the total trade rising from 250 million metric tons in 2016 to 270 million metric tons in 2021. Furthermore, Pearson’s and Spearman’s correlations highlighted positive yet weak relationships between efficiency and total trade levels for both ports, with correlation coefficients of approximately 0.35 and 0.38, respectively.

Building upon these findings, it is essential for port authorities in Dar es Salaam and Mombasa to consider the valuable recommendations provided in the World Bank Report on optimizing port operations and infrastructure [30]. This external resource provides additional insights into enhancing the efficiency and competitiveness of these ports.

Port authorities in Dar es Salaam and Mombasa should prioritize enhancing operational efficiency by improving resource utilization and addressing the operational shortcomings potentially through advanced technological infrastructure, efficient operations, sustainable practices, strategic location, and effective intermodal connectivity [7]. Aligning port operations with trade fluctuations is crucial [6], given the positive yet weak correlation between trade levels and efficiency. It is imperative to conduct rigorous operational evaluations and strategically optimize processes to rectify inefficiencies, particularly in crane utilization.

Immediate action is needed to reevaluate operational strategies and resource allocation in both ports. Further research is essential to navigate the complex landscape of trade dynamics and operational efficiency, aiming to devise pragmatic solutions that align port operations seamlessly with trade fluctuations. Integrating recommendations from the World Bank Report on optimizing port operations and infrastructure is advisable, providing additional insights for enhancing efficiency and competitiveness [6].

In conclusion, this research contributes to evidence-based decision making for port enhancement in the global supply chain landscape.

7. Future Direction

Enhancing analytical dynamics: Future research could delve into dynamic analyses that consider the temporal evolution of port efficiency and external contextual factors. Such studies would provide insights into how ports adapt to changing trade patterns, technological advancements, and regulatory shifts. Analyzing efficiency trends over time would offer a more nuanced understanding of the resilience and adaptability of ports in response to dynamic market conditions.

Contextual factors enrichment: To gain a comprehensive grasp of port efficiency determinants, future studies could expand the range of contextual factors beyond trade, encompassing aspects such as political stability, environmental policies, and local labor dynamics. Integrating a broader array of these variables would provide a more holistic view of their collective influence on port performance.

Scale and comparative analysis: Expanding the analysis to encompass a larger sample of ports within the East African Region, or even globally, would enable a more robust benchmarking process. This approach would identify best practices, shedding light on unique strategies employed by different ports to optimize performance. Additionally, conducting similar studies in different regions could facilitate cross-regional comparisons, enriching our understanding of how varying contextual factors shape port efficiency outcomes.

Incorporating technological advancements: Investigating the impact of emerging technologies, such as the blockchain, the Internet of Things (IoT), and artificial intelligence (AI), on port efficiency could offer intriguing insights. Understanding how these technologies reshape traditional port operations and decision-making processes could pave the way for innovative efficiency enhancement strategies.