4.1. Analysis of Descriptive Results
As previously mentioned, this study does not follow a systematic review protocol such as PRISMA, nor does it aim to be exhaustive. Instead, it adopts a hybrid and exploratory approach focused on identifying methodological patterns and disciplinary gaps in the intersection between the Bullwhip Effect, Ripple Effect, and supply chain resilience (SCR). The Web of Science (WoS) database was selected due to its high academic selectivity, indexing standards, and relevance for peer-reviewed, high-impact research. The search was performed using the following keyword combination: “Bullwhip Effect” AND “resilience” AND “supply chain”, covering the time window from 2000 to 2023. This narrow keyword strategy intentionally ensured thematic precision and alignment with the research objectives, even at the cost of volume. The resulting number of articles (n = 27) is not presented as a statistically representative sample of all the SCR literature but as a reflection of the limited existing academic focus on the explicit connection between these phenomena. This scarcity, in itself, is an important finding: it highlights a research gap in modeling resilience from the lens of the Bullwhip and Ripple Effects. Inclusion criteria were as follows: (i) studies published in peer-reviewed journals indexed in WoS, (ii) the explicit treatment of the Bullwhip Effect or Ripple Effect regarding supply chain resilience, and (iii) methodological clarity enabling classification. Exclusion criteria included the following: (i) inaccessible full texts, (ii) articles where resilience was only marginally mentioned, and (iii) studies unrelated to methodological modeling. All selection decisions were made manually, and full-text reading was conducted to verify thematic alignment. While modest in size, this curated dataset is analytically sufficient to detect disciplinary trends and methodological preferences, particularly in the context of nonlinear and adaptive modeling approaches such as those grounded in complex systems or AI.
From this sample, the methodologies used by the authors in this research were analyzed, resulting in the following proposed classification:
4.1.1. Linear Analysis
In the papers by Thomas et al. [
30] and Kinra et al. [
8], linear approaches were employed to analyze the effects of Bullwhip and Ripple on supply chains, respectively. These linear approaches, based on simulation models and control engineering techniques, make it possible to simplify the inherent complexity of the dynamic systems involved in supply chains. Thomas et al. [
30] examined resilience and robustness in relation to the Bullwhip Effect through a production and inventory control model. Through this method, one can detect essential parameters and examine their effects on system behavior during disruptive conditions. Conversely, the work of Kinra et al. [
8] developed a linear model to assess the Ripple Effect that allows suppliers to determine their risk exposure without calculating disruption probabilities, enabling them to focus on potential loss sizes. Such approaches generate value by providing an understanding of the system based on the decomposition of complex issues into smaller units over which the contributing factors might be analyzed within the supply chains. The real problem is that it tends to oversimplify the realities of such dynamics, creating a risk of ignoring relevant nonlinear couplings in gaining system insights. The Bullwhip Effect creates barriers to comprehending how differing recovery times affect system resilience. As for the Ripple Effect, simplification might not adequately capture the complexity of global supply networks and the interdependencies between providers.
4.1.2. Nonlinear Analysis
Accompanying articles addressing the analysis of the Bullwhip Effect and the Ripple Effect from a nonlinear perspective used advanced approaches that capture the dynamic complexity and nonlinear interactions in supply chains. Park et al. [
9] investigated how disturbance within distributors’ circular flow systems enables an amplification of the Ripple Effect, thereby creating wider recovery spans and further negative fallout relative to disturbances imposed outside of such circular flows. This nonlinear approach is crucial to understanding the spread of disruptions and their impact on supply chain resilience [
9]. On the other hand, Badakhshan et al. [
1] applied a simulation approach based on system dynamics and genetic algorithms to optimize cash flow management and minimize both the Bullwhip Effect and Bullwhip Cash Flow (CFB) in supply chains. This nonlinear methodological approach has opened up the possibility to capture the inherent complexity within inventory and cash flow decisions. It could serve as a nice tool for liquidity management while helping to achieve a reduction in inefficiencies within the supply chain [
1]. In addition, Garvey and Carnovale [
31] explored how the complexity and interconnectivity of global supply networks can amplify the Ripple Effect, using dynamic Bayesian networks to model and quantify risk spread. This nonlinear approach allows for the identification of optimal supplier selection and order allocation strategies that mitigate risk and improve global resilience [
31]. Pavlov et al. [
32] developed a method based on graph theory and structural genomes to model the dispersion of the Ripple Effect and recovery paths, integrating the detection of disruption scenarios and the optimization of reconfiguration paths in complex supply networks. This nonlinear approach makes it possible to analyze how disruptions propagate and affect different parts of the network, taking into account not only the direct connections but also the indirect and latent ones that could amplify the negative effects [
32].
4.1.3. Resilience Low-Focus Analysis
Articles that address the analysis of the Bullwhip and Ripple Effects from nonlinear approaches present a relatively weak description in terms of their direct application to supply chain resilience. Although these studies, such as those by Mu et al. [
33], Badakhshan et al. [
1], and Garvey and Carnovale [
31], among others, employed advanced methodologies and complex models to quantify the effects of disruptions on supply chains, they tend to focus more on the theoretical modeling and simulation of the specific effects rather than offering a practical and applicable integration of their findings into resilience strategies for supply chains. Such shortcomings are shown by the poor guidance contained in these articles on specific ways that businesses can adopt their models to be more attuned to resilience against various disruptions. Also, these journal articles do not specify nor discuss in-depth how their model deliverables can be translated into concrete action on either risk mitigation or resilience strengthening, and this is an area of opportunity. The inclusion of practical case studies, implementation approaches, or even specific recommendations for resilience management would greatly allow for the immediate and grounded application of their findings. Thus, as robust as the work by Kinra [
8] and other co-authors of 2019 was, the proposed models lack the applicability and sense of direction to enhance real-world supply chain resilience.
While the critique of existing studies in this category is justified—particularly their lack of direct, practical integration with supply chain resilience strategies—it is equally important to provide a constructive alternative. This study addresses that gap by proposing an initial conceptual framework informed by the interdisciplinary signals emerging from our neural network analysis. Specifically, our SHAP-based results and LSTM time-series models consistently highlight Business, Engineering, Environmental Science, and Decision Science as the most influential fields driving resilience-oriented research output. Rather than approaching resilience in isolation or as a theoretical abstraction, we suggest that future models adopt a hybrid interdisciplinary approach that structurally integrates the following: (i) Engineering for system-level modeling and simulation of disruptions; (ii) Business and Decision Sciences for tactical decision-making and inventory policies; (iii) Environmental Sciences for embedding sustainability and external shock resilience (e.g., climate or energy volatility). This integration can enable models that not only capture the complexity of Ripple or Bullwhip dynamics but also translate those dynamics into resilience-enhancing decisions—such as multi-tier supplier optimization, recovery time prediction, or resource reallocation under disruption. Moreover, the patterns revealed by our LSTM-based forecasting provide temporal insights that support anticipatory resilience strategies, where firms can act before vulnerabilities escalate. While this paper does not claim to develop a prescriptive model, it provides an empirically grounded, methodologically explicit roadmap for future research to bridge theoretical modeling with practical resilience applications.
4.1.4. Resilience High-Focus Analysis
The accompanying articles apply a remarkable focus on supply chain resilience, offering several important contributions to the field. For example, Thomas et al. [
30] explored the relationship between resilience, robustness, and the Bullwhip Effect through control engineering and simulation techniques, establishing that it is possible to improve resilience and reduce the Bullwhip Effect through an appropriate selection of control parameters. This makes the interrelationship between inventory management and a supply chain recovery from disturbance comprehensible. Looking more closely at some of the key studies in the field reveals just how fragmented the methodological landscape still is. For example, Park et al. [
9] used simulation-based network models to study Ripple Effects in supply chains, with a focus on how disruptions spread through different network structures. While their approach does a good job of revealing structural weak points in the network, it falls short when it comes to linking those insights to actual decision-making or control strategies, making it harder to apply in real-world settings. In contrast, Badakhshan et al. focused more on operational control, working to optimize factors like lead times and service levels. Their work offers actionable insights for managers, but it tends to overlook how disruptions Ripple through the broader network or how systems respond over time. Garvey and Carnovale [
31] offered a data-driven perspective by assessing risk exposure across supply tiers, but their model lacks dynamic components and assumes relatively static system behaviors. Similarly, Kinra et al. proposed an econometric model to assess exposure levels in global supply chains, yet their work remains isolated from operational resilience modeling or adaptive dynamics. Pavlov et al. [
32] contributed a hybrid simulation framework that blends structural modeling with some control logic. However, their model is highly abstract and complex to operationalize in real-time decision environments. Ivanov [
32], a key contributor to the digital supply chain resilience literature, introduced the concept of the “Ripple Effect” in dynamic settings using discrete-event and hybrid simulation; however, his models often prioritize scenario coverage over model parsimony, raising concerns about generalizability.
Altogether, these studies paint a picture of a fragmented field. Some focus on network structures, others on optimization or statistical risk assessment—but very few try to bring these perspectives together into a single, cohesive modeling approach. Even though they often tackle similar problems, they tend to work in isolation, each within its own disciplinary framework, without engaging with one another’s assumptions or methods. This lack of connection makes it harder to build cumulative knowledge and slows the development of practical, flexible tools that supply chains can actually use to manage disruptions. Our study identifies this methodological dispersion and calls for integrative modeling approaches that bridge structural dynamics, control systems, and uncertainty management in the context of Bullwhip and Ripple Effects under a resilience lens. Finally, the aforementioned analysis is succinctly and clearly summarized in
Table 2 and
Figure 6.
Figure 6.
Classification of methodologies and modeling approaches in supply chain resilience studies from 2000 to 2023. The diagram shows the distribution of articles by year, focus on resilience (low vs. high), analytical approach (linear vs. nonlinear), type of effect studied (Bullwhip or Ripple), and dominant modeling technique. Source: Authors’ own work, based on [
1,
6,
8,
9,
10,
11,
12,
30,
31,
32,
33,
34,
35,
36,
37].
Figure 6.
Classification of methodologies and modeling approaches in supply chain resilience studies from 2000 to 2023. The diagram shows the distribution of articles by year, focus on resilience (low vs. high), analytical approach (linear vs. nonlinear), type of effect studied (Bullwhip or Ripple), and dominant modeling technique. Source: Authors’ own work, based on [
1,
6,
8,
9,
10,
11,
12,
30,
31,
32,
33,
34,
35,
36,
37].
Table 2.
Modeling framework and applied techniques. The classification of studies as having a “low application in resilience” was based on a qualitative assessment through the direct reading and observation of each article. Studies were considered to have low application if their resilience analysis was broad and general rather than explicitly focused on supply chain resilience. Only those articles that deeply examined resilience within supply chain contexts were categorized as having a high application. A checkmark (✔) indicates that the corresponding study explicitly addresses the Bullwhip or Ripple effect. Source: Authors’ own work.
Table 2.
Modeling framework and applied techniques. The classification of studies as having a “low application in resilience” was based on a qualitative assessment through the direct reading and observation of each article. Studies were considered to have low application if their resilience analysis was broad and general rather than explicitly focused on supply chain resilience. Only those articles that deeply examined resilience within supply chain contexts were categorized as having a high application. A checkmark (✔) indicates that the corresponding study explicitly addresses the Bullwhip or Ripple effect. Source: Authors’ own work.
Author | Year | Nonlinear | Bullwhip | Ripple | Resilience Approach | Technique |
---|
Mu et al. [33] | 2023 | yes | | ✔ | Low | Network topology |
Brusset et al. [34] | 2022 | yes | | ✔ | Low | Susceptible–Infected–Susceptible (SIS) |
Sindhwani et al. [12] | 2022 | yes | | ✔ | Low | Bayesian network |
Park et al. [9] | 2021 | yes | | ✔ | High | Real-world data and structures/discrete event simulation models (DESMs) |
Anuat et al. [37] | 2021 | yes | | ✔ | High | Bayesian network/Markov chains |
Thomas et al. [30] | 2020 | no | ✔ | | High | Inventory- and order-based production control system (IOBPCS) |
Badakhshan et al. [1] | 2020 | yes | ✔ | | Low | Genetic algorithms/Beer game |
Garvey and Carnovale [31] | 2020 | yes | | ✔ | Low | Bayesian network |
Li and Zobel [6] | 2020 | yes | | ✔ | High | Topological analysis |
Gholami-Zanjani et al. [35] | 2020 | yes | | ✔ | High | Monte Carlo/entire mixed programming |
Kinra et al. [8] | 2019 | no | | ✔ | Low | Indexes |
Pavlov et al. [38] | 2019 | yes | | ✔ | High | Genome method |
Hosseini et al. [36] | 2019 | yes | | ✔ | High | Bayesian network/Markov chains |
Ojha et al. [11] | 2018 | yes | | ✔ | High | Bayesian network/indexes |
Chang and Li [39] | 2018 | yes | ✔ | | High | Model APIOBPCS (Adjusted Production Inventory Order Based on Production) Capacity System) |
Pavlov et al [32] | 2017 | yes | | ✔ | High | Hybrid fuzzy–probabilistic approach |
Sokolov et al. [10] | 2015 | yes | | ✔ | High | Method AHP (Analytic Hierarchy Process) |
While the linear/nonlinear and resilience-focused classifications are conceptually distinct, they intersect in important ways. Some studies employ advanced modeling techniques yet offer limited insights into resilience mechanisms, while others prioritize resilience but use basic linear tools. To address this overlap, a combined classification matrix was created to map how methodological complexity aligns with resilience depth across the literature. This structure helps clarify where the field is concentrated—and where future integration is needed. To address the reviewer’s concern regarding potential overlap between resilience focus and modeling type,
Table 3 presents a simplified cross-classification to visualize this relationship more clearly.
Beyond descriptive classification, the reviewed literature reveals several important analytical insights regarding the methodological landscape of Bullwhip and Ripple Effects in the context of supply chain resilience. First, the clear prevalence of nonlinear approaches (88.23%)—notably simulation, system dynamics, Bayesian networks, and network theory—highlights the consensus that supply chain disruptions are inherently complex and path-dependent. However, this methodological preference also exposes a bias toward computational sophistication, which, while capturing systemic interdependencies, often lacks practical translatability for decision-makers. For instance, studies like Park et al. [
9] and Pavlov et al. [
32] demonstrate advanced network-based or genome-based modeling yet offer limited operational strategies or policy-level applications.
In contrast, linear models such as those by Thomas et al. [
30] or Kinra et al. [
8], despite their simplicity, offer more direct implications for managerial control systems (e.g., inventory tuning and exposure assessment), particularly in environments with limited data or operational constraints. This dichotomy suggests a methodological gap in hybrid modeling, where analytical tractability and practical relevance are balanced—an opportunity scarcely addressed in the reviewed literature. Moreover, from the disciplinary perspective, the methodological choices seem to correlate with the originating academic fields: Engineering and Decision Sciences, which dominate the sample, tend to favor nonlinear, simulation-based, or control-theoretic methods. Meanwhile, contributions from Economics or Business lean more toward index-based or optimization-driven frameworks. This points to an opportunity for the cross-pollination of methodological paradigms, as few studies attempt to integrate, for example, econometric and system-dynamic approaches into a unified resilience framework.
Lastly, the bibliometric data show that while 64.7% of studies address resilience with a high conceptual focus, the Bullwhip Effect appears underexplored in this domain, comprising only 11.7% of the resilience-oriented studies. This is especially surprising considering the Bullwhip Effect’s foundational role in supply chain instability. The disproportionate focus on the Ripple Effect may reflect its more visible propagation dynamics, but it also suggests a need to reframe the Bullwhip Effect not just as a demand distortion but as a structural vulnerability within resilience strategies. In sum, this classification exercise not only organizes methodological choices but surfaces critical gaps and disciplinary silos that constrain the advancement of integrative, actionable resilience modeling.
4.2. Analysis of Quantitative Results
Figure 7a,b illustrate the trends in the volume of research conducted on the Bullwhip and Ripple Effects (in general scope, first exercise) from 2000 to 2023, along with the extent of its connections to various fields of study, based on the filtered results from the selected databases [
24]. Similarly,
Figure 7a,b depict the trends for research specifically focusing on the relationship between the Bullwhip Effect, Ripple Effect, and the Resilience Effect in supply chains.
The quantitative analysis in
Section 3.2 employs several statistical techniques to validate the robustness of time-series trends and to detect significant structural changes in research dynamics. One of the main tools used is the Wald-type test for structural breaks, implemented through the “Swald” procedure available in Stata. This test is designed to identify statistically significant shifts in the behavior of a time series (e.g., in publication volume) by evaluating changes in model coefficients at unknown breakpoints. The assumptions for this test include a minimum number of observations on either side of the potential break, the stationarity of residuals, and independence across time lags. Results are considered significant if the null hypothesis of no structural break is rejected at common significance levels (1%, 5%, 10%). In addition to the Swald test, the analysis includes the following: normality tests, Augmented Dickey–Fuller (ADF) tests to assess stationarity, Bartlett’s test to evaluate residual autocorrelation, and the Variance Inflation Factor (VIF) to test for multicollinearity. These were applied to ensure that the LSTM model was built on a statistically reliable time series. All variables were log-transformed and normalized before testing to meet the distributional assumptions.
The approach’s limitations include the relatively short time series in some disciplinary categories, the potential sensitivity of the Swald test to noise and sample size, and the lack of causal modeling due to the exploratory nature of the data. However, the combination of structural break detection and time-series diagnostics provides a strong foundation for interpreting trend discontinuities as meaningful shifts in research focus. Full model specifications and the Stata/Python code are available from the authors upon request.
Figure 7a highlights the significant growth in the production of scientific articles, using “Bullwhip Effect” and “Ripple Effect” as the keywords, over the past two decades. Notably, the year 2016 marked a pivotal point in this upward trend for the Bullwhip Effect, as confirmed by the Swald test, which showed high statistical significance; and the year 2019 for the Ripple Effect tipping point (critical values were determined based on the chi-square distribution at conventional significance levels (1%, 5%, and 10%); the reported
p-values indicate whether the null hypothesis of no structural break can be rejected). This suggests that the interest in studying the Bullwhip Effect has remained consistently strong, particularly considering its initial discovery in the 1960s [
3]. In 2016, some momentous global events helped to shape the Economic and Business landscape: the UK leaving the European Union (Brexit) in June created market uncertainty and raised fears about future trade relationships; the election of Donald Trump as President of the United States shifted global trade and regulatory policies, notably leading to the abandonment of the Trans-Pacific Partnership; in its transition to a consumption-driven economy, China’s economic slowdown sharpened global commodity markets; the crude oil prices engendered timid recoveries after their previous turmoil, an event impacting equally on exporters and importers; at last, in the crevice of the refugee crisis in Europe, ignited by the conflicts in the Middle East, the wheels of the smoke and labor systems in the region were further clogged. These events seem to have greatly influenced the explosion of Bullwhip Effect studies, as indicated by the structural break identified in the Swald test.
Similarly,
Figure 8a illustrates the production volume of scientific articles where “Bullwhip Effect”, “Ripple Effect”, “resilience”, and “supply chain” are used as keywords, showing remarkable exponential growth in this interdisciplinary area. As indicated by the Swald test, which found a structural break in 2019, which served as a major catalyst for this surge in research output for Bullwhip and Ripple Effects: the year 2019 witnessed several significant economic and logistical events globally (critical values were determined based on the chi-square distribution at conventional significance levels (1%, 5%, and 10%); the reported
p-values indicate whether the null hypothesis of no structural break can be rejected). The U.S.–China trade war intensified, imposed tariffs, and disrupted supply chains all over the world, particularly for industries that rely heavily on Chinese manufacturing. Brexit in the United Kingdom created a cloud of uncertainty over Europe’s trade and logistics landscape due to companies rushing to prepare for possible border delays and regulatory changes. A slowdown of the global economy with a waning growth of major regions in Europe and Asia. The technological revolution continued its onslaught in transforming logistics, with automation and AI increasingly embraced in warehouses and the growth of e-commerce fueling demand for efficient last-mile delivery solutions. Additionally, sustainability became a focal point, with businesses implementing greener supply chain practices to address environmental concerns.
A notable finding from the results is the strong connection of this interdisciplinary field not only with economic sciences, typically associated with the Bullwhip and Ripple Effects, but also with Engineering and Decision Sciences.
Figure 8b highlights that the highest-ranked academic areas in the collected data include Engineering and Decision Science alongside Business, Mathematics, Economics, Social Sciences, Environmental, Computer, Energy, and others. This suggests that applied Engineering Sciences play a critical role in the study of the Bullwhip Effect in its general scope. For the quantitative analysis, a series of tests were conducted on the collected time series to ensure their statistical robustness, checking for probabilistic distribution, multicollinearity, autocorrelation, and stationarity. High multicollinearity was found in the variables, as confirmed by the Variance Inflation Factor test (
Figure 9c). The Augmented Dickey–Fuller unit root test (
Table 4) confirmed non-stationarity only in one variable. To address these problems, the neural network model was chosen, which effectively handles both multicollinearity and non-stationary series. Preliminary results showed a Gaussian distribution of residuals, supported by normality tests (Swilk and Sktest in Stata 15.0 [
40]), and acceptable results in Bartlett’s autocorrelation test, remaining within the 95% confidence range as lags increased (
Figure 9b).
Thus, after implementing the adjustments suggested by the preliminary statistical tests, the final reduction in the model for the first exercise is ((2) and (3)):
Figure 10a shows the loss during both training and validation across 100 epochs, with Mean Squared Error (MSE) as the metric. We observe that both curves decrease rapidly in the first 20 epochs, indicating effective learning during this initial phase. However, after epoch 20, the MSE stabilizes and exhibits a slight increase in fluctuation. The validation curve closely follows the training curve, which suggests that the model generalizes well and that there is minimal overfitting. Model performance was assessed using standard metrics. For the Bullwhip Effect model, the final Mean Squared Error (MSE) on the validation set was 7.59 × 10
−7, while the Ripple Effect model achieved an MSE of 1.009 × 10
−4 (see
Figure 10a). Both models converged after approximately 30–40 epochs, and validation loss remained stable across the training window, indicating strong generalization. While LSTM models do not rely on R
2 in the same way as traditional regression models, supplementary estimation yielded approximate R
2 values above 0.85 for both cases, suggesting solid predictive accuracy. In addition, the 80/20 time-based train–validation split, combined with early stopping and low learning rate tuning, helped prevent overfitting, as reflected in the close alignment of training and validation error curves.
Figure 10b is a SHAP (Shapley Additive Explanations) force plot, which reveals the individual feature contributions to a particular average output. SHAP (Shapley Additive Explanations) was applied to interpret variable importance in the LSTM neural network model used for bibliometric trend analysis. This approach was chosen due to its ability to provide transparent, feature-level contributions in complex, nonlinear models. To ensure robustness, SHAP results were compared with alternative feature importance methods (e.g., permutation importance) and exhibited consistent patterns, reinforcing its validity for this context. Given SHAP’s widespread use in deep learning explainability, its application here is methodologically justified. Here, for the Bullwhip Effect, study fields like Economics and Social are pushing the prediction value higher (shown in red), while variables such as Mathematics and Computation are pushing it lower (shown in blue). This demonstrates that certain variables like Economics and Social Sciences have a more significant positive effect, indicating a strong correlation with the target of the Bullwhip Effect. Conversely, the technical fields such as Mathematics, Computation, Decision, and Energy Sciences contribute less, or even negatively, suggesting that their influence on the model is less direct in this scenario. For the case of the Ripple Effect,
Figure 10c shows that Computation and Engineering Science are the strongest contributors to the predicted value in the model.
Figure 10d,e present a SHAP summary plot, which ranks the features by their impact on the model output across all observations. The top features, such as Energy, Environment, and Business, show the highest influence on the Bullwhip Effect in its general scope and Business, Environment, and Energy, for the Ripple Effect scope. Interestingly, the presence of multiple time-lagged features from the same categories suggests that Energy has a temporal and cumulative impact on the prediction. Moreover, features with higher SHAP values (closer to the right) have a more substantial positive effect on the model outcome, while those on the left may contribute less or negatively.
In
Figure 10f, the SHAP dependency plot shows how the Energy interacts with the model’s predictions and with the rest of the Bullwhip Effect’s most important variables (Social, Business, Environment, Computation Sciences), and
Figure 10g shows the Ripple Effect’s ones (Business, Energy, Environment). For the Bullwhip Effect results, the Energy variable demonstrates a nonlinear relationship with SHAP values; additionally, the variable Energy has an important influence from the Business and Environment variables on its higher values. For the case of the Ripple Effect,
Figure 10g shows that its most important variable (Business) has a higher influence than the Energy and Environment variables, implying that sustainability plays an important role in this Ripple phenomenon.
For the second exercise, assessing the interdisciplinary relationship between the Bullwhip and Resilience Effects in supply chains, the same model was applied, with research volume as the dependent variable. Statistical reliability tests included a multicollinearity check (VIF,
Figure 11c), revealing high multicollinearity, and an Augmented Dickey–Fuller test (
Table 5), which identified one irreversibly non-stationary variable. Various linear and nonlinear models were tested but proved insignificant, leading to the adoption of a neural network to handle non-stationary time series and multicollinearity. Residual tests confirmed a non-Gaussian distribution (
Figure 11a), and an autocorrelation test via Bartlett’s procedure showed good results within the 95% confidence level for several lags (
Figure 11b).
Finally, after implementing the adjustments suggested by the preliminary statistical tests, the final reduction in the model for the first exercise is ultimately as follows ((4) and (5)):
Figure 12a illustrates the loss for both training and validation over 100 epochs, using Mean Squared Error (MSE) as the evaluation metric. Notably, both curves decline rapidly within the first 20 epochs, indicating efficient learning during this early phase. After epoch 20, however, the MSE levels off and shows minor fluctuations. The validation curve closely follows the training curve, indicating that the model has generalized well and has undergone insignificant overfit. This close alignment also implies that the model has detected a steady trend in the data. Model performance was assessed using standard metrics. For the Bullwhip Effect model, the final Mean Squared Error (MSE) on the validation set was 1.94 × 10
−5, while the Ripple Effect model achieved an MSE of 8.83 × 10
−4 (see
Figure 12a). Both models converged after approximately 30–40 epochs, and validation loss remained stable, indicating good generalization. While LSTM models do not require R
2 in the same way as regression models, supplementary estimation yielded approximate R
2 values above 0.85 for both cases, suggesting strong predictive power. Additionally, the train–validation split (80/20) and the use of early stopping helped prevent overfitting, as reflected in the alignment between the training and validation loss curves.
Figure 12b presents a SHAP (Shapley Additive Explanations) force plot, which highlights the individual feature contributions to a specific model output (average value of 0.05). In this plot, fields such as Social, Engineering, and Business Sciences are principally driving the prediction value upward (represented in red) for the Bullwhip Effect, while variables like others are pulling it downward (represented in blue). In the same way, fields such as Economics, Computation, and Social Sciences are the principal positive drivers for the Ripple Effect, without any field working against its positive behavior (
Figure 12c).
Figure 12c displays a SHAP summary plot, ranking the features based on their overall impact on the model output across all observations. The most influential features, such as Social and Computational, exhibit the strongest effects on the model’s performance in the general scope. Notably, the appearance of several time-lagged features from the same categories suggests that Computational has both a temporal and cumulative influence on the prediction. Additionally, features with higher SHAP values (closer to the right) contribute more positively to the model’s outcome, whereas those positioned on the left tend to have lesser or even negative contributions. For the case of the Ripple Effect, the most influential fields seem to be the Social, Business, and Energy fields (
Figure 12e).
In
Figure 12f, the SHAP dependency plot illustrates how the Social variable interacts with the model’s predictions and the other key variables (Mathematics, Environment, Computation Sciences). The Social variable shows a nonlinear relationship with the SHAP values, indicating that its influence on the outcome changes as its values rise.
Figure 12g reveals that the Business and Energy fields are the most influential drivers for the principal pivot of the Ripple Effect within the supply chains, the Social field.
Interdisciplinary Influence and SHAP Interpretability
Beyond static importance, SHAP also revealed temporal and relational patterns, offering further insights into the evolving disciplinary structure of resilience research.
To enhance the transparency and explainability of the LSTM predictions, SHAP (Shapley Additive Explanations) was applied as a post hoc interpretability method. SHAP is particularly suitable for this context as it provides individualized, model-agnostic attributions of feature contributions, even in highly nonlinear and temporally sensitive models such as LSTM [
27,
28]. This allows not only a clearer understanding of which disciplinary variables influenced predictions at different time steps but also deeper insights into the interdisciplinary structure of resilience-focused research on the Bullwhip and Ripple Effects.
The SHAP force plots (
Figure 12b,c) revealed that the Bullwhip model was most influenced by contributions from Social Sciences, Engineering, and Business, whereas categories grouped as other (including niche disciplines or uncategorized fields) had a dampening effect on the predicted publication volume. This is consistent with how the Bullwhip Effect is typically explored—as an operational issue tied to process efficiency, organizational routines, and demand fluctuations [
8,
30]. By comparison, the Ripple model revealed a distinctly different disciplinary emphasis.
Economics, Computer Science, and Social Sciences emerged as the most influential drivers, indicating a stronger theoretical and systems-oriented foundation. This reflects how the Ripple Effect, as a cascading and network-based disruption phenomenon, attracts attention from fields concerned with macro-level modeling, risk propagation, and the simulation of interdependencies [
9,
36].
Figure 12d,e display the SHAP summary plots, which aggregate feature importance over time. They show that Business, Energy, and Environmental Sciences consistently contributed to model output across both the Bullwhip and Ripple analyses. This convergence suggests that, regardless of effect type, resilience-oriented research is increasingly framed through the lens of sustainability and strategic resource management [
6,
35,
39]. The prominence of Computational Sciences—especially in the Ripple model—reveals that data-intensive methods and dynamic system modeling are becoming central to resilience analysis. Interestingly, SHAP scores changed over time, showing that disciplines like Engineering and Energy did not always play the same role—they gained or lost influence depending on the decade. This shifting relevance underscores how resilience has grown into a dynamic, evolving research theme across domains [
1,
10,
33].
The SHAP dependence plots (
Figure 12f,g) build on this by capturing how disciplines do not just matter in isolation—it is their interactions that reveal deeper, nonlinear relationships, shaping how the Bullwhip and Ripple effects are modeled.
The SHAP dependence plots (
Figure 12f,g) further illustrate this complexity by revealing nonlinear interactions between disciplines, showing how their combined influence shapes the way Bullwhip and Ripple effects are studied. In the Bullwhip model, the effect of Energy on publication trends intensified when coupled with high levels of Business and Environmental Science, reflecting system-level concerns such as energy logistics and carbon-sensitive supply chains. In the Ripple model, Business and Energy acted as moderators of the influence of Social Sciences, indicating that the modeling of Ripple propagation often draws on organizational dynamics and policy frameworks embedded in socio-economic systems [
9,
11,
38]. These complex interdependencies reinforce one of the central conclusions of this review: supply chain resilience research is no longer confined to isolated fields but instead emerges from the dynamic interaction between technical, economic, and social-scientific knowledge systems.
4.3. Practical Implications for Supply Chain Decision-Makers
- (a)
Adopt Simulation and Network-Based Risk Tools
Given that over 88% of the reviewed studies rely on nonlinear modeling approaches, managers are encouraged to move beyond traditional linear tools and static risk matrices. Instead, they should adopt simulation-based platforms such as system dynamics, agent-based models, or Bayesian networks to visualize how disruptions propagate and interact across multi-tier supply chains. Tools like these are crucial for identifying hidden fragilities and preparing adaptive responses under uncertainty.
- (b)
Establish Resilience Intelligence Units
Cross-functional teams should be formalized into what we call Resilience Intelligence Units. These should integrate operations managers, data scientists, engineers, and sustainability officers who can co-develop strategies for supplier diversification, scenario-based planning, and recovery pathways. This reflects our SHAP analysis, which identifies Business, Engineering, and Environmental Science as the most impactful domains influencing resilience knowledge production.
- (c)
Use Leading Indicators for Disruption Anticipation
Managers should implement internal–external dashboards that combine KPIs (e.g., order fill rate and lead time variability) with macro-level foresight indicators like climate risk alerts, political instability indices, or global commodity trends. Our LSTM-based trend detection shows that the academic focus on Ripple and Bullwhip Effects often aligns with external shocks like trade wars or pandemics, underlining their anticipatory relevance for strategic planning.
- (d)
Reframe the Bullwhip Effect as a Proactive Resilience Metric
Rather than viewing the Bullwhip Effect as an inefficiency problem, it should be leveraged as a resilience proxy. Tracking demand amplification and response lag can help firms sense early-stage stress across the supply chain. Reassessing policies on order batching, pricing, and replenishment could mitigate amplification and improve coordination even under disruption.
- (e)
Prioritize Hybrid Modeling for Tactical Decision Support
Managers would benefit from using hybrid strategies that mix straightforward, easy-to-understand models for everyday decisions—like setting reorder points—with more advanced tools like neural networks to spot long-term trends or unexpected changes. This combination helps managers find the right balance between transparency and advanced forecasting, making it easier to take informed actions based on real-time data while still keeping sight of how supply chains evolve and respond to disruptions over time.