Operational risks in supply chains include supplier failures, production delays, transportation issues, and demand fluctuations. These factors disrupt the flow of materials and information, causing delays and increased costs. Mitigation strategies such as inventory stockpiling, supplier diversification, and emergency sourcing are commonly recommended to enhance resilience and maintain continuity.

Security risks involve cyber-attacks, theft, fraud, and sabotage that threaten the integrity and confidentiality of supply chain data and assets. With increasing digitalization, these risks have become more prominent. Effective management requires robust cybersecurity measures, thorough supplier vetting, and strict information security protocols [12] .

Technical risks arise from failures in technology infrastructure, system breakdowns, or insufficient technological capabilities. These disruptions can affect communication, tracking, and automation processes critical for supply chain efficiency. Investments in reliable IT systems, continuous monitoring, and backup solutions are essential to mitigate such risks [13] .

Organisational risks relate to internal processes, human errors, management decisions, and organizational structure. Poor coordination, lack of risk awareness, and inadequate contingency planning can exacerbate disruptions. Strengthening organizational capabilities through training, clear communication, and risk governance frameworks is vital [14] .

Natural risks include events such as earthquakes, floods, hurricanes, and pandemics that can cause sudden and severe disruptions. These risks are often unpredictable and can impact multiple supply chain tiers simultaneously. Common mitigation strategies include flexible supply chain designs, geographic diversification, and disaster recovery plans [11] .

The initial step in risk assessment is to identify all relevant risk factors and organize them into a hierarchical framework. This structure facilitates a clear and systematic understanding of the problem by decomposing it into manageable levels. At the top level lies the overall goal of the risk assessment, followed by criteria that represent key risk dimensions. Each criterion may be further broken down into sub-criteria and, if necessary, additional sub-levels. This hierarchical organization allows decision makers to view the complex problem comprehensively and ensures that all important factors are considered in the analysis.

In assessing supply chain disruption risks, determining the relative importance of each risk factor is crucial. Due to limited historical data, direct calculation of these weights is challenging. The Analytic Hierarchy Process (AHP) provides a structured method to derive weights based on expert judgments.

A group of supply chain experts was consulted to compare the importance of risk factors through pairwise comparisons. These comparisons were used to build judgment matrices, which were aggregated and analyzed using decision-support software to calculate the weights.

Although individual opinions may differ, the combined expert input offers a reliable estimation of each risk factor’s significance, supporting informed risk prioritization and management.

$\begin{array}{c}{w}_i=\frac{\sqrt[n]{{{\displaystyle \prod }}_{j=1}^n{a}_{ij}}}{{{\displaystyle \sum }}_{k=1}^n\sqrt[n]{{{\displaystyle \prod }}_{j=1}^n{a}_{kj}}}\left(i=1,2,\cdots ,n\right)\end{array}$ (1)

$\begin{array}{c}CR=\frac{CI}{RI}\end{array}$ (2)

$CI=\frac{{\lambda }_{\max -n}}{n-1}$

${\lambda }_{\max }=\frac{{{\displaystyle \sum }}_{j=1}^n\frac{{{\displaystyle \sum }}_{k=1}^n{w}_k{a}_{jk}}{w_j}}{n}$

Experts express their assessment of each risk factor RRR by distributing belief degrees over a set of qualitative categories $H=\left\{H_1,H_2,\cdots ,H_K\right\}$, representing different risk levels (e.g., low, medium, high). Each assessment is described by a belief distribution vector:

$\beta =\left[{\beta }_1\text{},{\beta }_2\text{},\cdots ,{\beta }_K\text{}\right]$

${\displaystyle \underset{k=1}{\overset{k}{\sum }}{\beta }_k=1,{\beta }_k\ge 0}$

The Evidential Reasoning Approach aggregates multiple belief distributions weighted by their respective criterion weights $w_i$. For criteria $i=1,2,\cdots ,n$ with belief distributions ${\beta }_i$ and weights $w_i$ the combined belief ${\beta }^{*}$ is computed iteratively by the ER algorithm based on Dempster-Shafer theory.

At each step, combined belief degrees are updated by:

$\begin{array}{c}{\beta }_k^{*}=\frac{{{\displaystyle \sum }}_{i=1}^n{w}_i{\beta }_{i,k}{{\displaystyle \prod }}_{j\ne i}\left(1-w_j{\displaystyle {\sum }_{m=1}^K{\beta }_{j,m}}\right)}{1-{{\displaystyle \prod }}_{i-1}^n\left(1-W_i\right)}\end{array}$ (3)

where ${\beta }_i{{}_{,}}_k$ is he belief degree of criterion i in category k.

After aggregating the belief degrees, a crisp risk score U is derived via expected utility:

$\begin{array}{c}U={\displaystyle \underset{k=1}{\overset{K}{\sum }}u\left(H_k\right){\beta }_k^{*}}\end{array}$(4)

where:

This weighted average converts qualitative assessments into a single numerical value facilitating risk ranking and decision-making.

Uncertainties are inherently present in different influencing factors. Since the proposed methodology provides a numerical estimation of disruption risk without identifying the most important input event, sensitivity analysis (SA) is a systematic approach that can provide managerial insight in evaluating quantitative information in order to identify the weakest points or areas of a system in order to improve its designs [21] .

To evaluate the robustness of the proposed risk assessment model, a limited sensitivity analysis will be conducted. This involves introducing small changes to one or two selected input parameters while maintaining the necessary normalization constraints. For each variation, the aggregated belief degrees and the resulting utility score UUU will be recalculated using the Evidential Reasoning algorithm.

The sensitivity index $S=\frac{\Delta U}{\Delta Input}$ will be used to quantify the impact of these

changes. This study employed the SA approach to test how sensitive the model output is to a minor change in the input data.

This phase of the analysis involves the identification of risk factors associated with supply chain disruption risks at port of Cotonou through a robust literature research and port authority reports and maritime logistics studies pertinent to Benin and similar developing countries. The identified risk factors are presented in Table 1 .

At this stage, the identified risk factors from Table 1 are represented in a hierarchical structure and depicted in Figure 3 . Based on the available information in Section 2, a specific model is constructed to demonstrate the applicability of the methodology. Following a review of [13] , which suggests that linguistic terms for safety expression typically range from four to seven for effective information processing, this research adopts four to five linguistic terms to represent the assessment of disruptions based on the available data.

This section outlines the process of calculating the relative weights of the identified risk factors for supply chain disruptions in maritime logistics at the Port of Cotonou, Benin, using the Analytic Hierarchy Process (AHP). Due to the unavailability of primary data from surveys or interviews, this study relies on a robust literature review, port authority reports, and maritime logistics studies pertinent to Benin and similar developing countries to simulate expert judgments. These sources provide insights into the relative importance of risk categories and sub-criteria, enabling the construction of pairwise comparison matrices. The AHP methodology involves structuring the problem hierarchically (as shown in Figure 3 ), performing pairwise comparisons, calculating weights, and ensuring consistency to prioritize risks effectively. Based on the theoretical data derived, fuzzy numbers are not explicitly used here due to the focus on crisp AHP for simplicity, though the approach can be adapted to fuzzy AHP if needed.

Data Simulation Process

Since direct expert consultation was limited, expert-based judgments were simulated using a systematic literature-driven approach. Relevant academic papers, port management reports, and regional logistics studies were reviewed to extract qualitative descriptions of major risk factors affecting West African ports, particularly Cotonou. These qualitative insights were then translated into quantitative pairwise comparison values following the Saaty 1 - 9 fundamental scale. For example, if multiple sources emphasized environmental risks as more frequent or impactful than technical failures, a value of 5 (“strongly more important”) was assigned in the matrix.

The comparative judgments in Tables 2-6 were based on the relative importance of each risk category reported in previous studies [22] [23] . Environmental and natural risks were assigned higher weights due to Cotonou’s recurrent flooding and coastal erosion [24] , while security risks were rated strongly relative to organizational risks based on frequent cargo theft and smuggling incidents documented in port safety reports.

The consistency ratio was measured by applying the established AHP consistency check method and was found to be acceptable. The pairwise matrices of the operational, security, technical, organizational, and environmental & natural risk factors are presented. Following the procedure of calculations, the weights of the sub-criteria within each risk category are determined, and their consistency ratios are verified. The results are presented in Table 7 .

This section details the assignment of belief degrees to qualitative risk levels for the identified sub-criteria of supply chain disruption risks at the Port of Cotonou, Benin, within the hybrid AHP-ERA framework. These sources guide the allocation of belief degrees across qualitative categories, namely Low, Medium, and High, reflecting the perceived likelihood and impact of each risk factor. The belief degrees are normalized to sum to 1 for each sub-criterion, ensuring a consistent and probabilistic representation of risk severity.

Continued

The belief degrees are assigned based on the perceived frequency and impact of each risk factor, derived from the reviewed literature and contextual knowledge of the Port of Cotonou. The normalization constraint (sum of belief degrees = 1) is maintained for each sub-criterion, ensuring compatibility with the ER approach. These belief degrees are presented in Table 8 and will be integrated with the AHP weights in the next section using the Evidential Reasoning approach to synthesize the final risk prioritization scores.

This section describes the synthesis of weighted belief assessments for supply chain disruption risks at the Port of Cotonou, Benin, using the Evidential Reasoning Approach (ERA) within the hybrid AHP-ERA framework. The ERA integrates these belief degrees assigned across qualitative categories (Low, Medium, High) with their respective weights to produce a synthesized risk assessment for each risk category. The methodology follows the standard ERA procedure, normalizing the assessments and aggregating them hierarchically to reflect the overall risk profile.

The results shown in Table 9 will be used in Section 4.5 to derive crisp numerical values for risk prioritization, with potential refinements based on additional data or sensitivity analysis.

This section outlines the derivation of crisp numerical values for the supply chain disruption risks at the Port of Cotonou, Benin, using the expected utility approach. The expected utility approach converts the qualitative belief distributions (Low, Medium, High) into a single numerical score by assigning utility values to each category and weighting them by their respective belief degrees. For this study, Low is assigned a utility of 0.2, Medium 0.5, and High 0.8, reflecting increasing risk severity. For each risk category, compute the expected utility as the weighted sum of the utility values multiplied by their synthesized belief degrees. Crisp numerical values for each risk category are then calculated and presented in Table 10 .

The utility scale (Low = 0.2, Medium = 0.5, High = 0.8) follows conventions from previous multi-criteria decision-making studies [25] [26] , where linear interval values are used to preserve proportional relationships among linguistic assessments while maintaining computational simplicity within the expected utility framework.

This section presents an expanded sensitivity analysis to assess the robustness of the crisp numerical values derived for all supply chain disruption risk categories at the Port of Cotonou. The sensitivity analysis evaluates the impact of small perturbations (±10%) in the belief degrees of the dominant sub-criteria within each risk category on the expected utility scores with a focus on the belief degrees of the most weighted sub-criterion in each risk category. The results, summarized in Table 11 , show that the model maintains consistent ranking stability even under moderate variations in input parameters.

where EU stands for Expected Utility.

To broaden the robustness analysis, additional tests with ±20% and ±30% perturbations were performed on both belief degrees and AHP weights. Results showed consistent ranking stability, with only minor shifts (<5%) in expected utility values. This confirms the resilience of the model against moderate parameter variation. Future research could integrate Monte Carlo simulations or bootstrapping for a more probabilistic representation of uncertainty.

While the current analysis treats risks as independent figure, real-world disruptions often interact across categories. For example, storms causing congestion and organizational delays. Future extensions could integrate influence diagrams or Bayesian networks to capture such cascading interdependencies between risk categories.