2.1. Predictive ML approach in supply chains

Predictive modelling in supply networks is an important analytical strategy that utilizes ML and sophisticated mathematical methods to forecast future supply chain behaviors, optimize resource allocation, and reduce risks associated with unpredictable demand and logistical uncertainty.

[14] adopted deep learning algorithms in macroeconomic statistics to predict late deliveries in the automobile industry, emphasizing the importance of external economic problems on supply chain efficiency. Additionally, in a predictive study by [4] that evaluated the efficacy of ML techniques for forecasting customer backorders to enhance the efficiency in supply chain. The study focusses on the difficulty of balancing accurate models and computational effectiveness in complicated supply chain contexts. By comparing the approaches generated with 22 variables to only the best five, the authors showed that simplified ML algorithms can dramatically cut computational expenses by 30% to 98%, while maintaining good accuracy with 0.6% to 4.2% decrease in F1-score. Applying accessible datasets, the study demonstrates the practical benefit of simplified prediction algorithms for real-time inventory and backorder management, indicating their suitability for wider industrial deployment.

In a similar study, [15] employed ML and AI approaches to forecast delays in truck delivery operations. Their research tackles transportation management issues by predicting delays, allowing management to more accurately plan and deploy resources. Practical logistical data was analyzed using a variety of ML algorithms, such as decision trees, random forests, Artificial Neural Networks (ANN), and support vector machines. The study revealed that each of these algorithms predicted delays with up to 97.6% accuracy, with the Adaboost classifier beating all of them in both accuracy and precision. This study illustrates the possibility of ML to improve logistics efficiency and reduce supply chain delays [2,15] examined the application of ML approaches to prediction in supply chain networks. The study addresses the constraints of traditional maintenance techniques by using ML methods to detect equipment failures, reduce unexpected downtime, and improve supply chain efficiency. By analyzing external variables, sensor inputs, and historical data, the research reveals how predictive analysis may detect possible issues before they cause disruptions. The study compares multiple ML models designed for maintenance prediction, providing useful insights into how ML may optimize supply chain operations and increase efficiency through proactive maintenance tactics [15].

A comprehensive study by [16] reported the development of a ML-based predictive and alerting system to improve practical decision-making system in a computerized warehouse setting. Their algorithm forecasts identification of late order using information gathered by Warehouse Management Systems (WMS), allowing for action through the designed alerting setting. Similarly, a tyre distribution company adopted this technology to validate a Shuttle-Based Storing and Recovery system. The approach successfully adopted some approaches by evaluating several ML models and customizing predictions for warehouse-specific factors. Their study focuses on the practical advantages of ML for improving short-term operational effectiveness in logistics [16].

In a recent study by [17] shows how hybridization and improved integration of models could enhance prediction. The study presented a priority-based architecture integrating space-time analysis and also a crash severity technique to assess pedestrian and bicyclist safety. Their results show the imperativeness of hybridization in prediction and how it influences outcome.

2.2. Causal inference and causal ML in supply chains

Causal inference methods have advanced beyond just understanding the relationships between variables to identify causal frameworks, but estimate treatment effects, forecast counterfactual events, and guide decision-making procedures in complicated real-world systems. Studies by [3] made a proposal for the implementation of causal ML to create intervention techniques, emphasizing the importance of understanding relationships between variables in order to improve decision-making. Similarly, [18] presented a novel method integrating causal discoveries with reinforcement learning to ascribe the fundamental causes of supply risks, tackling the complications of interdependence in supply chains. In the medical supply chains sector, [19] also reported two-stage methodologies integrating both ML and a Unified Robust Stochastic Programming (URSP) architecture to improve the survivability of medical supply chains (MSCs) during disease outbreaks globally. The first phase employs an ML algorithm to forecast infection levels and change demand projections accurately. To handle constraints under unpredictability, on the other hand, the second stage employs URSP, which combines stochastic programming and robust optimization with a configurable strength level, as well as Conditional Value-at-Risk (CVaR). This case study in Turkey showed that the integrative strategy outperformed previous methods by providing more cost-effective and robust allocation options. The study emphasizes the significance of combining predictive modelling and robust decision-making techniques to overcome substantial ambiguity within the healthcare supply chain [19].

While causal techniques can help with hypothetical intervention planning and identifying supply chain risk factors, new research shows that these methods are not enough to back up operational decision support in its entirety, since they cannot reliably predict the short term or analyze temporal patterns. In their discussion of the shortcomings of models that attempt to infer causation alone, [20] highlight the necessity for hybrid analytical techniques that also incorporate predictive performance and planning skills.

2.3. Hybridization of intelligent computational systems

The adoption of multiple intelligent mathematical models in supply chains as an advanced approach that integrates various computational frameworks to address various supply chains decision problems resulting in significantly robust and responsive supply chain systems. Many research studies have reported the hybridization [21] of these multiple models in addressing supply chains, such as [5] who assessed the application of intelligent computational methods such as IoT, ML, AI, and blockchain to improve accuracy and openness in smart manufacturing supply chains. The study focusses on two application cases, demand-side forecasting and buyer.

Furthermore, the increasing complexities in supply chain networks have resulted to better reliance on predictive models and causal inferences to minimize stockout risk. Recent studies have shown a various way to improve risk management, known causal ML, reinforcement learning and Bayesian networks [22]. Causal inference has grown increasingly significant in supply chain management because it allows organizations to go over correlation-based observations and discover actual cause-and-effect linkages. Unlike conventional predictive analysis, which focusses on projecting future trends, causal inference approaches can assess the direct influence of variables such as lead time, supplier disruptions, price strategies, and demand changes on stockout risk and final supply chain performance [23]. Table 1 shows the summary of some related studies that adopted various ML techniques.

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Table 1. Summary of some related studies.

https://doi.org/10.1371/journal.pone.0350429.t001

Despite these advances in the various studies reported, a significant gap remains in merging causal inference approaches with predictive modelling to thoroughly assess and predict stockout risks. While ML algorithms have showed promise for detecting possible disruptions, they frequently fail to identify a causal relationship between significant factors like lead time and stockout risk. This constraint impedes the creation of efficient intervention techniques for reducing stockout incidents.

Our study addresses a research gap by combining causal inference and predictive modelling to understand and forecast stockout threats. While previous research focusses on either ML for forecasting or optimization approaches within certain contexts, it falls short of identifying the causal associations between major risks in the supply chain, like lead time consequences on stockouts.

2.4. Methodological contribution and framework synthesis

While many articles have applied numerous methodological frameworks such as, ML, econometric or time series techniques to supply chain risk issues, these approaches are consistently adopted in isolation and target a single analytical objective. Predictive models focus mainly on forecasting accuracy, time series approaches are focused on analyzing temporal behavior and causal inference focuses on intervention effects. However, the operational decision-making necessitates the coherent knowledge on potential outcomes such as, when risk is likely to occur, what drives disruptions and how risk evolves with time. Therefore, lack of structured integration of these factors draw the practical value of current analytical techniques.

This study, contributes methodologically by proposing a simulation-Based Hybrid causal-predictive framework that establishes the integrated functionality of predictive modeling, causal inference and temporal analysis into a single decision-oriented architecture. Hence, the contribution does not involve proposing new estimators, but in defining a structured synthesis that includes each analytical process serving a distinct and adjunct decision role.

3.1. Research methodology

The study utilizes a simulation-based methodological analysis design to evaluate a hybrid decision-layered framework for stockout risk analysis. The methodological framework integrates causal inference, predictive modeling and temporal analysis within a structured architecture to intervene on relevance, operational forecasting and temporal monitoring.

Furthermore, the methodological objective focuses mainly on the validation of the proposed hybrid framework under controlled and structured conditions. Therefore, a synthetic dataset representing various supply chain operations based on similar studies, was generated to mimic realistic relationships within standard supply chains criteria such as, inventory levels, logistic factors, demand, stockout risk and supplier reliability. The simulation environment allows evaluation of analytical components characterized by well-defined dependencies and reproducibility. Data preprocessing steps such as Data cleaning, Data splitting and feature Engineering similar to [24] were adopted. Traditional ML models, causal inference techniques and time series were evaluated based on their evaluation metrics as shown in Fig 2.

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Fig 2. Experimental framework.

https://doi.org/10.1371/journal.pone.0350429.g002

The analytical elements that comprise the framework are assessed using different criteria since they perform diverse decision-making roles. The interpretability, strength across estimators, and conceptual validity of causal inference approaches are evaluated in relation to their ability to estimate intervention impact and their adherence to identification principles. When evaluating predictive models, statistical performance indicators such as MAE, MSE, RMSE, and R² are used to gauge the accuracy of the forecasts. How well time-series approaches reflect the time frame and align their forecasts are two key metrics for evaluating them.

3.2. Implementation and platform

The experiment was carried out on Python (v3.9) using scikit-learn, causal ML, and other additional libraries. The analysis was carried out using python programming language. The Exploratory Data Analysis technique was adopted using normalization approach similar to study [25] where the dataset was standardized using the Minmaxscaler approach. Additionally, categorical dataset “supplier_type” was converted to numerical dataset using the OneHotEncorder approach.

3.3. Data description

The study adopted a synthetically generated supply chain dataset, structured to approximate real-world distribution network dynamics [26]. The dataset was generated using a parameterized probabilistic distribution, that reflects operational ranges in supply chains studies. The dataset contains 19 essential variables with 20,000 instances, relevant to supply chain operations. The variables include, order processing, inventory management, supplier reliability, logistics, and stockout risk factors. It provides integer-type variables like order_id, lead_time, inventory_level, demand, order_size, and warehouse_capacity to measure supply chain activities. Float-type characteristics such as supplier_reliability, stockout_risk, seasonality_factor, economic_index, warehouse_utilization, and market_demand_trend reflect ongoing risks and economic impacts. Additionally, the supplier_type feature represents categorical data. These characteristics together form a solid foundation for analyzing stockout risk and optimizing supply chain robustness through causal inference, machine learning, and time series forecasting. The data is briefly summarized on Table 2.

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Table 2. Data description.

https://doi.org/10.1371/journal.pone.0350429.t002

3.4. Causal inference

In the causal analysis executed in the study, the treatment variable was clearly stated as prolonged lead time, operated as a binary indicator. For every observation i∊ {1,2, …..,N} the treatment assignment T_i is specified as;

(1)

Where;

represents the lead time for observation while L symbolizes the collection of lead-time values in the dataset. The result variable signifies stockout risk, characterized as a normalized probability of stockout incidence under operational conditions.

Where; i∈ {1,2,…,N} indexes the observations, Tᵢ ∈ {0,1} represents treatment indicator, and Xᵢ ∈ ℝᵖ is the vector of observed covariates.

Causal inference methods are necessary to go beyond relationships and comprehend the actual impact of lead time on stockout risk. In contrast to conventional ML algorithms that only concentrate on prediction, causal inference approaches assist supply chain managers adopt data-driven policy decisions to lower stockout risk by identifying cause-and-effect linkages [23].

The relationships between numerous supply chain elements and two crucial variables, lead time and stockout risk, are shown in Fig 3. Numerous predictors, including inventory level, demand, supplier dependability, logistics costs, shipment delays, and warehouse capacity, are shown on the left side. These elements affect the likelihood of a stockout and the operational effectiveness of the supply chain. Thus, the pointed arrows indicate these independent parameters possible impact on lead time and stockout risk by illuminating the causal and predictive connections between them and the dependent parameters. Similar to research by [27], this visualization helps the study achieve its objective of better explaining and forecasting stockout difficulties in supply chains through the use of causal inference, ML, and time series forecast.

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Fig 3. Causal graph.

https://doi.org/10.1371/journal.pone.0350429.g003

The causal graph in Fig 3 shows how 17 important supply chain factors, including demand, inventory level, logistics cost, and supplier dependability, directly affect two important outcomes: lead time and stock out risk. A putative causal relationship is represented by each arrow, emphasizing the ways in which operational, logistical, and economic variables influence these targets’ variability. In order to maximize supply chain performance, this framework facilitates intervention planning and predictive modelling.

The causal inference method for the suggested strategy assesses the impact of lead time on stockout risk based on a number of conventional identification assumptions. These assumptions describe the circumstances in which the predicted Average Treatment Effects (ATEs) may be evaluated logically instead of associatively. It is considered that all pertinent confounders influencing both lead time and stockout risk are accounted for conditional exchangeability, that units possess a non-zero likelihood of being assigned either of the treatment and control groups and that every single supply chain incident is distinct with no influence among observations. In the case of instrumental variable assessment, the instrument is presumed to be associated with lead time and to influence stockout risk solely through this mechanism. These hypotheses direct the assessment of causal estimates in the simulated framework.

3.4.1. Propensity Score Matching (PSM).

PSM is a technique that uses a quasi-randomized test to determine the causal relationship between lead time and stockout risk. It compares observations that have been treated and those that have not, according to the propensity score that indicates the probability of receiving the treatment.

(2)

where;

e(Xᵢ) shows the probability that observation i is assigned the treatment based on the observed covariates Xᵢ where i ∊ {1,2,…,N} indexes the data observations, Ti ∊ {0,1} signifies the treatment indicator, and Xi ∊ R^p signifies the vector of p observed covariates [28].

3.4.2. Doubly robust estimation.

Doubly robust approaches integrate IPW and regression modifications to produce consistent results regardless of whether one of the models is incorrectly defined [1].

The doubly robust estimator is defined as:

(3)

Where;

i ∊ {1, 2,…, N} indexes the observations, N is the total number of observations, Ti ∊ {0,1} is the treatment indicator, Yi denotes the stockout risk, Xi ∊ R^p represents the vector of observed covariates, e(Xi) represents the propensity score, and g₁(Xᵢ) and g₀(Xᵢ) are outcome models for treated and control categories [29].

3.4.3. Instrumental Variables (IV).

Instrumental Variables (IV) analysis is employed whenever the assignment of treatment is intrinsic, which means it is influenced by unobserved variables that impact the final result. Supplier distance is used as an instrumental variable for lead time, believing that it exclusively influences stockout risk by lead time.

(4)

Second-stage model:

(5)

Where;

i ∊ {1,2,…,N} represents the index observations, Ti denotes the treatment variable, which is the lead time, T_i is the predicted treatment from the first-stage model, Yi, denoting stockout risk, Zi represents supplier distance and Xi is the observed covariates [30].

3.4.4. Inverse Probability Weighting (IPW).

IPW weights observations depending on their propensity scores, resulting in a reweighted pseudo-population that simulates a randomized experiment.

(6)

Where;

i ∊ {1,2,…,N} indexes the observations, wi is the weight assigned to observation i, Ti ∊ {0,1} is the treatment indicator, and e(Xi) represents the propensity score, which is defined as the probability of receiving treatment given the observed covariates Xi [31].

3.5. Predictive modeling in supply chains

Predictive modelling is an essential framework in supply chain management that allows businesses to forecast stockouts, demand variations, and logistical problems. Predictive techniques employ ML techniques to analyze previous data, detecting trends and forecasting future events, resulting in enhanced decision-making and operational effectiveness [32].

3.5.1. Random Forest.

Random Forest (RF) is an ensembled ML technique that builds numerous decisions trees and then combines their predictions to increase accuracy and avoid overfitting. It is especially beneficial for supply chain risk modelling since it accommodates non-linear interactions, performs effectively with high-dimensional dataset, and delivers significant feature insights [33].

RF classifier is made up of several decision trees (T₁, T₂....., T_B), all are trained on a randomly chosen subset of attributes and a random portion of the data employing bootstrapping, also known as bagging. By combining each of the tree outputs, majority decision for categorization and average for regression, the ultimate prediction is produced [24].

Step 1: Bootstrapping and Feature Selection [34]

(7)

A randomly selected portion of the initial data (D_b) is selected with substitution from the entire dataset(D).

At every divided a randomized subset of 𝑚 variables is chosen from the entire 𝑝 features (𝑚 ≪ 𝑝).

(8)

Where;

f(x)=predicted stockout risk for x input

B = number of trees.

Tb(x)= predicted from the both tree [35].

3.5.2. Extreme gradient boosting for stockout risk prediction.

Extreme Gradient Boosting is a more advanced variant of gradient boosting which enhances accuracy of predictions, computing efficiency, and handling missing data. It is often employed in supply chain risk modelling because of its capacity to capture complicated interactions between variables while reducing overfitting through regularization.

(9)

XGBoost creates an ensemble of additives decision trees, with each tree correcting its predecessor’s flaws by utilizing gradient descent to minimize a loss function [36].

3.5.3. Light gradient boosting machine for stockout risk prediction.

LightGBM (LGBM) is a gradient boosting system that focusses on speed and efficiency in huge datasets. It varies from typical gradient boost approaches like XGBoost in that it employs statistical illustration-based learning and leaf-wise tree development, which makes it computationally efficient and scalable.

Similar to XGBoost, LightGBM iteratively optimizes the loss function by constructing an ensemble of decision trees. Nonetheless, it brings about significant advancements in data processing and tree growth.

(10)

Where; [37], L (yi, yi) is the loss function, Ω(fk) is used to prevent overfitting.

3.6. Time series forecasting

Time series forecasting is an important part of supply chain management because it allows firms to forecast prospective stockout risks using past trends. In contrast to traditional predictive modelling, time series approaches expressly consider variations in time in data, allowing organizations to foresee and manage risks. In this work, we adopted the Moving Average (MA) technique to evaluate and anticipate stockout risks [38].

3.6.1. Moving average (MA) model.

The Moving Average (MA) approach is a basic time series method that smoothers variations in stockout risk by combining previous observations across a defined window. This strategy aids in the identification of patterns and seasonality, allowing for more informed inventory management decisions.

(11)

Where; q represents the order of the moving average process, ∊ t is the white noise error, μ represents the mean of the series, Yt is the stockout risk [39].

3.7. Model evaluation

Performance metrics or model evaluation are quantitative evaluations of a model’s efficiency, particularly in mathematical modelling, ML, and prediction analysis. In regard to the task for which a model is intended, they assist both scholars and practitioners in evaluating the model’s general efficacy, precision, accuracy, and resilience [33]. In this study, the prediction algorithms’ accuracy and reliability were assessed using conventional performance indicators such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and Coefficient of Determination (R²) as shown in Table 3.

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Table 3. Performance Evaluation.

https://doi.org/10.1371/journal.pone.0350429.t003

4.1. Exploratory and dependency

The datasets were analyzed to find relationships between confounders and lead time as treatment variables to explore the interactions within the dataset.

The scatterplots demonstrate an association between lead time and numerous supply chain variables. The data indicates extremely crowded and consistently distributed, indicating little relationship between lead time and the independent parameters. Additionally, client priority has a discontinuous distribution, which indicates categorical data. The visualizations point to the necessity for additional statistical evaluation, such as coefficients of correlation or a regression simulation, to evaluate potential correlations s shown in Fig 4.

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Fig 4. Correlation Scatter plots.

https://doi.org/10.1371/journal.pone.0350429.g004

Furthermore, the scatter plots in Fig 5 demonstrate the interactions among numerous supply chain variables and supplier type on lead times. The visualizations indicate modest variations in lead time behavior depending on whether the provider is local or not.

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Fig 5. Scatter plots of interaction amongst the variables on lead time.

https://doi.org/10.1371/journal.pone.0350429.g005

The distribution plots in Fig 6 demonstrate variations in and distribution trends among major supply chain elements. Most numerical characters, including lead time, inventory level, demand, logistics cost, and supplier reliability, have a very equal distribution, signifying a harmonious dataset. However, stockout risk looks heavily skewed, implying that extreme outcomes (high stockout risk) are uncommon. Customer preference is bimodal, meaning two separate types of clients. Managing time and shipment delays exhibit different periodic patterns, which could imply systematic programming or regular influences. These findings inform feature selection and modification for predictive modelling and causal inference.

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Fig 6. Distribution Plot.

https://doi.org/10.1371/journal.pone.0350429.g006

The correlation matrix represents the interactions among different supply chain parameters, emphasizing the pairwise dependencies. Lead time and stockout risk have a moderate positive connection (~0.48), suggesting that longer lead periods may increase stockout risks. Shipment delay has a smaller connection (~0.17) with stockout risk, indicating a possible but indirect influence. The majority of other features have low correlations, indicating that there are few direct linkages. This insight improves feature selection for predictive modelling and causal inference by focusing on the most pertinent factors influencing stockout risk as shown in Fig 7.

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Fig 7. Correlation Matrix.

https://doi.org/10.1371/journal.pone.0350429.g007

4.2. Experimental results

Table 4 shows how the study analyses stockout risk thoroughly by combining causal inference approaches, ML techniques, and time series forecasting. Amongst the causal inference approaches, PSM and IPW showed substantial ATE, demonstrating a strong causative association between lead time and stockout risk. The IV technique however, had a lower ATE of 0.5535, with a P-value of 0.3148 and a R²f 0.2435. This suggests a weaker causal effect, possibly due to poor instrument selection or unknown confounders.

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Table 4. Comparative results.

https://doi.org/10.1371/journal.pone.0350429.t004

RF and LGBM generated a R² of 0.25, but XGBM had a lesser R² of 0.153 but an increased MSE of 0.835, indicating differences in predicting accuracy. The Moving Average technique excelled other approaches with the greatest R²f 0.883 and the lowest MAE of 0.675, suggesting its strong ability to identify patterns in stockout trends over the years. This multi-method technique, summarized in Table 4, provides a solid foundation for identifying causal relationships and improving predictability in supply chain stockout risk management. Furthermore, to construct a baseline, we employed a typical Linear Regression approach to stockout risk prediction. The regression model recorded a low R² of 0.00063, meaning it describes almost no variation in the dependent variable, and an extremely high Mean Squared Error (MSE) of 18.89. Our ensemble approach, Random Forest and LightGBM, attained R² values of 0.25 and lower MSEs of 0.736–0.741, indicating significant increase in predicting ability. This contrast demonstrates that the proposed ensemble paradigm outperforms simple linear methods for modelling complex supply chain behaviors.

In addition, IV causal inference approach, yielded an Average Treatment Effect (ATE) of 0.5535 having a p-value of 0.3148, suggesting the impact assessment wasn’t statistically noteworthy at standard thresholds. The approach’s R² score of 0.2435 indicates moderate explanation power. In comparison with other simulations, the IV algorithm’s R² is slightly lesser compared to the RF and LGBM approaches, which both attained R² scores of 0.25, and significantly lower than the time series approach Moving Average, that attained the highest R² of 0.883. The high R² reveals the robustness of the persistence and autocorrelation in the simulated stockout process, instead of the model complexity, reflecting the controlled simulation setup.

An ATE of 0.882 shows that persistent lead time increases the stockout risk index by approximately 0.882 units on a 0–1 scale proportional to shorter lead times, under the assumed conditions.

Fig 8 compares the expected stockout risk to the actual values over an extended period. The dark blue line indicates the projections, whereas the less colored area shows the actual stockout risk levels. The plot shows that the moving average approach covers overall stockout risk patterns, but there are considerable variances, particularly during strong oscillations. The model accurately predicts stockout risk over the years, as evidenced by the high R² of 0.883 and low MAE of 0.675 based on experimental data.

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Fig 8. Moving average forecast.

https://doi.org/10.1371/journal.pone.0350429.g008

To prevent data leakage and to maintain temporal validity, the MA technique was evaluated using a rolling origin forecasting procedure. During each predictions step, the MA window integrated only historical observations based exclusively on information available prior to the forecast horizon. No information from future time points was used in model development or evaluation.

This research identifies practical factors for supply chain risk management, which enables it to provide practical consequences at both the operational and policy levels. Thus, due to the fact that the outcomes of the causative investigation establish lead time as an intervening variable, it is recommended that organizations increase their supplier procurement guidelines, logistics organization, and lead-time reserve contracts as architectural risk control process. Therefore, in order to facilitate flexible procurement and performance-driven supplier management, predictive modelling provides the capability to foresee risks in the short term. On the other hand, temporal analysis suggests that safety stock programs should reflect periodic and lasting risk trends rather than depending on fixed reserve levels. As a whole, these realizations lend support to the creation of unified risk monitoring systems and situational planning techniques. They also demonstrate how linked management, forecasting, and monitoring can improve the robustness of supply chain operations.