Explainable product backorder prediction exploiting CNN: Introducing explainable models in businesses

Shajalal, Md; Boden, Alexander; Stevens, Gunnar Article — Published Version Explainable product backorder prediction exploiting CNN: Introducing explainable models in businesses Electronic Markets Provided in Cooperation with: Springer Nature Suggested Citation: Shajalal, Md; Boden, Alexander; Stevens, Gunnar (2022) : Explainable product backorder prediction exploiting CNN: Introducing explainable models in businesses, Electronic Markets, ISSN 1422-8890, Springer, Berlin, Heidelberg, Vol. 32, Iss. 4, pp. 2107-2122, https://doi.org/10.1007/s12525-022-00599-z This Version is available at: https://hdl.handle.net/10419/312222 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) 1 3 Electronic Markets (2022) 32:2107–2122 https://doi.org/10.1007/s12525-022-00599-z RESEARCH PAPER Explainable product backorder prediction exploiting CNN: Introducing explainable models inbusinesses MdShajalal1,2 · AlexanderBoden1,3 · GunnarStevens2,3 Received: 8 June 2022 / Accepted: 27 September 2022 / Published online: 9 November 2022 © The Author(s) 2022 Abstract Due to expected positive impacts on business, the application of artificial intelligence has been widely increased. The decisionmaking procedures of those models are often complex and not easily understandable to the company’s stakeholders, i.e. the people having to follow up on recommendations or try to understand automated decisions of a system. This opaqueness and black-box nature might hinder adoption, as users struggle to make sense and trust the predictions of AI models. Recent research on eXplainable Artificial Intelligence (XAI) focused mainly on explaining the models to AI experts with the purpose of debugging and improving the performance of the models. In this article, we explore how such systems could be made explainable to the stakeholders. For doing so, we propose a new convolutional neural network (CNN)-based explainable predictive model for product backorder prediction in inventory management. Backorders are orders that customers place for products that are currently not in stock. The company now takes the risk to produce or acquire the backordered products while in the meantime, customers can cancel their orders if that takes too long, leaving the company with unsold items in their inventory. Hence, for their strategic inventory management, companies need to make decisions based on assumptions. Our argument is that these tasks can be improved by offering explanations for AI recommendations. Hence, our research investigates how such explanations could be provided, employing Shapley additive explanations to explain the overall models’ priority in decision-making. Besides that, we introduce locally interpretable surrogate models that can explain any individual prediction of a model. The experimental results demonstrate effectiveness in predicting backorders in terms of standard evaluation metrics and outperform known related works with AUC 0.9489. Our approach demonstrates how current limitations of predictive technologies can be addressed in the business domain. Keywords eXplainable artificial intelligence (XAI)· Backorder prediction· CNN· Local explanation· Global explanation JEL Classification M1· M15· O33· C80 Introduction Due to their superior predictive performance, complex machine learning and deep neural network-based models have received high attention and are widely exploited in the business domain (Bawack etal., 2022; Janiesch etal., 2021; Cliff etal., 2011) along with other fields including image processing (Jiao and Zhao, 2019), health (Panesar, 2019; Bartoletti, 2019) and bioinformatics (Cao etal., 2020; Li etal., 2019). The tasks of those technologies range across different application areas including supply chain management, credit risk prediction (Moscato etal., 2021; Bussmann etal., 2021), detection of fraud credit card transaction (Carcillo etal., 2021; Randhawa etal., 2018) and marketing campaigns in retail banking (Ładyyżyński etal., 2019). Generally, artificial intelligence (AI) techniques employ a huge size of training data for making predictions. While there is a huge interest in such predictions in various business domains Responsible Editor: Fethi Abderrahmane Rabhi * Md Shajalal [email protected]er.de * Alexander Boden alexander[email protected]er.de Gunnar Stevens gunnar.stev[email protected] 1 Fraunhofer-Institute forApplied Information Technology FIT, Schloss Birlinghoven, 53757SanktAugustin, Germany 2 University ofSiegen, Siegen57072, Germany 3 Bonn-Rhein-Sieg University ofApplied Science, 53757Bonn, Germany 2108 M.Shajalal et al. 1 3 (Ribeiro etal., 2016), one of the major problems of complex machine learning models is that they are very difficult to understand (Abedin etal., 2022; Adadi etal., 2018; Thiebes etal., 2021). Several Methods using induced ordered weighted averaging (IOWA) adaptive neuro-fuzzy inference system (ANFIS) can deal with multidimensional data to predict the quality of service and hence it help stakeholders in the decision-making process (Hussain etal., 2022a, b, 2021). As decisions often depend on a huge number of model parameters (Alvarez-Melis and Jaakkola, 2017), machine learning and deep learning techniques are like black-boxes or magic boxes to the general users (and often even for developers). The higher the accuracy of a complex machine learning model, the more opaque the models tend to become (Ribeiro etal., 2016). This opaqueness leads to a situation where users might question the predictions, because they are unable to understand the underlying decision making processes (i.e. the reasons for why a maybe counter-intuitive recommendation has been given) (Arya etal., 2019). User acceptance is generally one of the main barriers for the success of technologies in companies. As AI-based recommendations can potentially have a huge impact on operational as well as strategic decisions in companies, it seems to be beneficial if users or consumers of AI models could better understand why those recommendations have been made (Meske etal., 2022). Apart from increasing trust in AI-recommendations, having factual explanations of a certain decision would also help users to learn about the field of application (for instance gaining a better understanding in the importance or non-importance of certain factors for business decisions) (Förster etal., 2020). In addition, according to the general data protection regulation (GDPR) by the European Union, EU citizens have the right to receive explanations about AI-based decisions, for instance if an AI recommendation affects credit worthiness or insurance rates (Meske etal., 2022; Došilović etal., 2018). In this research, we propose a novel explainable predictive model for product backorder prediction. A backorder is a situation where customers can order a product even though that particular product is out of stock at the time when the order is placed (Hajek and Abedin, 2020; Ntakolia etal., 2021). Basically, its an order to a future inventory, going along with contingencies as time of delivery can vary and is not definitely known. Backorders are especially common for items that are highly popular. While for some items such as the latest flagship Apple iPhone, such events are quite common, it can be very unpredictable for other types of products. When retail companies order high amounts of products based on backorders, they risk their reputation if they are unable to keep the expected delivery dates. Another risk is that customers can cancel their orders because they don’t want to wait any longer or found another retailer where the product is in stock, leaving the company with excess products in their inventory. Here, predictive models can help to tackle these challenge by predicting the probability whether a certain product will be backordered or not, giving companies more time to plan and supporting them in their inventory management. In related works, researchers have proposed complex machine learning based methods to predict future product backorders. The predictive models include the application of support vector machine, XBoost, ensemble classifier and deep neural networks (Islam and Amin, 2020; Hajek and Abedin, 2020; Li, 2017; Shajalal etal., 2021). However, the mere prediction of future backorders only solves part of the problem. Suppose you are responsible for a particular inventory management system at a retail company. When you are notified that the AI model decided that a particular product is going to be backordered in the near future, what will you do? Would you increase the inventory level (i.e. obtaining more products in advance)? Would you change any policy (negotiating with suppliers about faster transit times, lead times etc)? If you increase the inventory level, how many products would you order, assuming that some would surely be cancelled? For taking these decisions, you would need to understand the reasons for the prediction. Hence, our approach tries to provide insights into the factors that contribute to a certain prediction, helping users to adapt their strategies accordingly. Our paper contributes in the following ways: • We proposed a new CNN-based model for backorder prediction. Since backorders are rare events in inventory management systems, it is a challenging task to identify them. Their rarity leads to an extremely imbalanced distribution within datasets. Often, the percentage of the backodered samples is less than 0.01% (specifically 0.007%, de Santis etal. (2017)). To address this data imbalance, we incorporated an adaptive synthetic oversampling (ADASYN) technique that generates synthetic samples for a minority class. The results, based on diverse experimental settings and comparison with existing known related works, illustrated that our method achieved better prediction performance achieving a new state-of-the-art methods performance in terms of standard evaluation metrics. • To provide an overall insight of the predictive model’s decision-making priorities, we investigate the impact of different attributes of an order in the predictive models. We introduce an XAI technique, namely SHAP (Shapely additive explanations), that can interpret and/ or explain the predictive model to identify the most important attributes of the decision making. Hence the stakeholders are enabled to better understand the model’s decision-making priorities and consider that when they have to work with such technologies. • By explaining specific predictions, our method can answer why a particular product will be backordered or not. Every order has different feature’s values which are 2109 Explainable product backorder prediction exploiting CNN: Introducing explainable models… 1 3 considered to make predictions. Therefore, we trained a local interpretable surrogate model employing LIME (local interpretable model-agnostic explanations), and present explanations for an individual prediction to answer the question “why has this specific decision been made?” Hence, stakeholders can not only assess the models’ priorities in general, but also analyse singular decisions to better understand them. The organization of the rest of this paper is as follows: Section2 summarises related works on predicting product backorders. We present a brief discussion about different XAI terminologies in Section3. In Section4, we present our method for predicting future product backorders and the explanation generation techniques. The predictive performance of our proposed CNN-based method and performance comparison with classical machine learning classifiers and known related works are presented in detail in Section5. The decisions of complex machine learning and deep learning models are explained through different types of explanations both for models’ priorities as well as specific predictions in Section6. Finally, Section7 concludes our proposed methods and findings of this study by discussing the prospects of introducing XAI technology in the business domain. Related work This section presents the discussion of related research on backorder prediction and explainable artificial intelligence in supply chain management. Existing works proposed different models to predict plausible future backorders in inventory management systems. Based on the types of techniques used, the predictive models can broadly be classified into two categories: i) Classical machine learning classifiers and ii) Deep learning-based predictive models. In the former category, the classifiers include support vector machine (Hajek and Abedin, 2020), gradient boosting (Ntakolia etal., 2021; de Santis etal., 2017), decision trees, and random forests (Islam and Amin, 2020). The deep learning-based models employed recurrent neural networks (RNN) (Li, 2017), deep auto-encoders (Saraogi etal., 2021), as well as deep neural networks (DNN) (Shajalal etal., 2021). Islam and Amin (2020) proposed a method to predict future backorders by applying distributed random forest and gradient boosting classifiers. They introduced a ranged-based approach to cope with the numerous types of real-time data. However, they did not include some features of the samples such as features related to inventory level, previous sales, future sale forecasting, and lead time. A profit-maximizing function based approach is introduced by Hajek and Abedin (2020). They aligned their profit maximization function with classical machine learning classifiers. The performance of their methods demonstrated how much profit can be increased by predicting future backorders. An explainable classical machine learning-based method is proposed by Ntakolia etal. (2021). Their method applied several classifiers such as random forest, XGBoost, SVM, etc. They also applied shapely additive values to present the global explanations to interpret the models. Similarly, de Santis etal. (2017) also used different classical classifiers. The performance of deep learning approaches is comparatively better than the classical classifiers. Shajalal etal. (2021) proposed a deep neural network (DNN) based backorder prediction model. Inspired by the success of deep learning classifiers, Li (2017), Saraogi etal. (2021) and Lawal and Akintola (2021) applied deep auto-encoder, a recurrent neural network-based classification models. Backorders are not a common scenario in inventory management systems. In turn, the number of non-back- ordered items is much larger than the backordered ones. Hence, real-time data collected from any inventory system will be strongly imbalanced, leading to challenges in predicting future backorders on that basis. In this particular task (Li, 2017), the ratio between majority (non-backor- dered) and minority (backordered) samples is 100:0.007. In the case of an imbalanced dataset, the classifiers might learn the pattern with potential bias. That is why different under-sampling, oversampling, and class weight-based approaches are common to balance the dataset and bias (Hajek and Abedin, 2020). Randomly duplicating the minority samples or randomly discarding the majority samples has also been applied to balance the dataset (Chawla etal., 2002). But randomly duplicating the minority samples will increase redundant samples and hence the model might be biased. Therefore, generating synthetic minority samples based on the Euclidean distance is a popular approach to balance the dataset. This method is called SMOTE (Synthetic Minority Over-sampling Technique) (Chawla etal., 2002). The combination of SMOTE and random under-sampling has been applied by Hajek and Abedin (2020) and Shajalal etal. (n.d., 2021). Li (2017) applied different balancing techniques including SMOTE, ADASYN (Adaptive Synthetic Sampling) (He etal., 2008) and random under-sampling. Bagging (Błaszczyński and Stefanowski, 2015) is also applied for the same purpose by (de Santis etal., 2017). Table1 summarises the existing methods for predicting product backorders. However, to the best of our knowledge, none of the studies applied XAI to interpret their machine learning model except Ntakolia etal. (2021). In our paper, we propose a convolutional neural network framework-based model that outperformed different classifiers including classical and deep learning-based models in backorder prediction. Ntakolia etal. (2021) interpreted only classical models mainly with global explanations. Our method integrated explainable artificial intelligence that generates global explanations for the classical and deep learning-based prediction 2110 M.Shajalal et al. 1 3 model. Though the global interpretation is useful to illustrate the general mechanisms and behavior of the model, it can not explain a particular prediction. We introduced a model applying shapely additive explanation (Lundberg and Lee, 2017) and local interpretable model-agnostic explanation (Ribeiro etal., 2016) to interpret the overall model and local specific decisions. To clearly illustrate the research gap in the existing literature and our research focus, we present a comparative analysis in Table2. XAI terminology In this paper, we employed two XAI techniques, namely shapely additive explanations (SHAP) and local interpretable model-agnostic explanations (LIME). Here, we present the background and working principle of these two techniques. SHapely Additive exPlanation (SHAP) Lundberg and Lee Lundberg and Lee (2017) first proposed a unified approach to explain and interpret the prediction of machine learning models. The explanations basically illustrate the contributions (positive and negative importance or influence) of different features for the predicted decision of a particular sample x. The overall feature importance of different features of the whole model can also be interpreted as global explanations. In that case, the importance score resembles the weight of features as in the linear model. The SHAP values represent the importance of the features. The explanation of every single prediction can be seen as a vector of shap values. The same representation is used to interpret the overall model. For a given instance x, the explanation using SHAP can be defined as Table 1 The summary of existing study on product backorder prediction Research paper Contributions Explainabaility Islam and Amin (2020) • Applied Distributed Random Forest (DRF) and Gradient Boosting Machine • Inherent (Global feature importance) • Incorporating SMOTE oversampling • No local explanation to understand particular decision Hajek and Abedin (2020) • A genetic algorithm-based profit maximizing prediction system • Not Explainable • Applied classical ML classifiers Shajalal etal. (2021) • Proposed a deep neural network-based prediction model • Not Explainable • Combined random undersampling and synthetic oversampling to overcome class imbalance problem Li (2017) • Applied recurrent neural network (RNN) based predictive model • Not Explainable • Exploited SMOTE, ADASYN, and random undersampling for balancing the dataset Saraogi etal. (2021) • Proposed deep autoencoder based model for backorder prediction • Not Explainable • Used unsupervised approach rather than supervised one Ntakolia etal. (2021, 2021) • Introduced classical machine learning model to predict backorder • Interpreted the global feature importance to explain the model • Incorporated interpretability to understand decision making • No local explanation for particular decisions de Santis etal. (2017) • Exploited classical machine learning classifier including gradient boosting and ensemble model • Not Explainable • Used bagging to overcome data imbalance problem LAWAL and AKINTOLA (2021) • Applied recurrent neural network (RNN) based predictive model • Not Explainable • Exploited SMOTE, ADASYN, and random undersampling for balancing the dataset 2111 Explainable product backorder prediction exploiting CNN: Introducing explainable models… 1 3 where g is denoted as the explanation model. The vector for simplified features, known as the coalition vector is represented by z′ ( z�∈{0, 1}M ). The 1 represents that features’ values are the same as the original instances and vice-versa. The attribution of particular features j of the instance x is denoted by 𝜙j which is a real number. The higher the value of 𝜙j , the more important the feature j. The 𝜙j is computed based on Shapely values (Nowak and Radzik, 1994), a gametheoretic approach that identifies and detects the contribution of all players in a collaborative game. The collaborative game with multiple players is analogue to the prediction of the instance having multiple features. In turn, applying this game-theoretic approach we can examine the contribution of each feature to a particular decision. For a given feature vector x′ and a predictive model f, the computation is done as follows: The subset of the features employed by the model is denoted as z′ . x′ is the vector with features values to be explained and can be defined as [ f(z � ∪x � i )−f(z �)] and M is the number of features. The prediction by the model f is denoted by f(z�) . (1) g (z�)=𝜙0+ M ∑ i=1 𝜙jz� j , (2) 𝜙 i(f,x�)= ∑ z�⊆{x� 1 ,x� 2 ,...,x� n }⧵{x� i } (|z � |)! (M−|z � |−1)! M! ⋅[f(z�∪x� i)−f(z�)] , Moreover, SHAP values are computed by a standard gametheoretical approach and utilized Shapely values to have a unified interpretable model with fast computation. More mathematical and technical details for SHAP can be found in the study published by Lundberg and Lee (2017) as well as in Nowak and Radzik (1994). Local interpretable model‑agnostic explanation (LIME) LIME mainly provides model-agnostic explanations based on local surrogate models. Ribeiro etal. (2016) first introduced this approach for training a local surrogate model instead of a global model for providing explanations for a particular prediction. LIME employed a new local dataset containing the permuted samples with corresponding predictions to train the local interpretable surrogate model. This surrogate model is then used to explain individual predictions. The model is considered as an approximation of the original complex, black-box predictive model. The computation of the surrogate model can be defined as follows: The explanation model for a particular instance x and the explanation family are represented by g and G, respectively. The original model is denoted by f and L is the loss function. (3) 𝜉 (x)=arg min g∈ 𝐆 L(f , g , 𝜋x�) + Ω(g ) Table 2 Existing research gaps in explainable product backorder prediction and our steps to fulfil the research gaps Issue Research gaps in literature Our contributions Performance Most existing methods suffer from low We proposed a novel CNN-based prediction performance in modelling product backorder model with the ADASYN technique prediction due to extreme data that achieved new state-of-the-art imbalance problem. The majority of performance. prior studies applied classical ML methods. Model’s Interpretability Lack of interest in applying XAI to We introduced shapely additive explanation explain the predictive model’s decision- (SHAP), one of the most successful making priorities. Hence the existing XAI techniques to explain the models’ models can be seen by the stakeholders global priorities that help stakeholders as black-box. in sense-making about the working strategy of the predictive models. Local Explaiability No existing works explain the specific We exploit LIME and SHAP to explain prediction to answer specific predictions about why a particular “why has this specific decision been made?” product is assumed to be on (i.e., why a certain product is going to be backordered?) backordered or not. These techniques can explain which features/attributes are responsible for a particular decision. Hence the stakeholders are enabled to take steps to overcome future backorder and reduce the company’s loss. 2112 M.Shajalal et al. 1 3 The complexity of the model can be defined by Ω(g) . LIME is useful to explain specific decision predicted by the model (i.e., local prediction). Explainable product backorder prediction The overview of our proposed explainable product backorder prediction framework is depicted in Fig.1. We first apply preprocessing step to handle the missing values, converting qualitative variables into quantitative ones and normalizing the values in a similar range. Next, we apply our proposed convolutional neural network-based backorder prediction model to classify the product. Finally, we introduce explainable AI techniques to explain both global, model agnostic aspects as well as individual decisions with the intent to make the inventory manager understand better why his or her backorder prediction system acts as it does. Preprocessing andfeature analysis In our dataset, each particular sample has 21 different features/attributes including current inventory, lead time, forecasting for a different time, sales performance, different risk flags. The details of the dataset are presented in Section5.1.1. The value of different features is varied widely among binary, quantitative, qualitative, and categorical. In this step, all the feature values are transformed into a real number. The missing values are handled by filling them in with the median of other samples’ values. A normalization technique is then applied to convert each feature value into a certain range [0,1]. Here, we applied the most widely recognized MinMax normalization technique. However, a dataset having highly correlated features is not suitable for applying classification methods. We investigate to see whether any high correlated features are available, exploiting the Pearson correlation coefficient measure for this purpose. According to the findings, we observe that there are no features with a high correlation ( 𝜌>.80 ). Hence, the dataset should now be suitable for our purpose of backorder predictions. Handling class imbalance withADASYN As we noted earlier, a product backorder scenario is a rare event that leads the dataset to be extremely imbalanced. Therefore, we employed one of the efficient synthetic oversampling methods, ADASYN (Adaptive Synthetic Oversampling) (He etal., 2008) to balance the dataset. Considering the difficulty level of learning, ADASYN generates synthetic minority class examples utilizing the weighted distribution. ADASYN focused on generating more synthetic minority class examples for those minority samples that are harder to classify. Given a training dataset, Dtrain with N number of samples where each sample is denoted as x,y, the vector x is represented by a K dimensional vector containing different attributes of an ordered product and y is the binary value that indicates the label (0 for non-backordered and 1 for backordered one). Let mmin and mmaj be the number of examples of minority class and majority class, respectively such that mmin +mmaj =N , and in this backorder prediction task m min << mmaj . ADASYN oversampling techniques generate synthetic minority class examples to balance the dataset according the algorithm illustrated in Algorithm1. It first calculates the degree of imbalance d and then, depending on the tolerated imbalance ratio, computes the number G that denotes the number of synthetic minority class examples needed to be generated. Here 𝛽∈[0, 1] indicates the desired bleaching ratio, 𝛽=1 Fig. 1 Proposed explainable backorder prediction approach Training Data Preprocessing Handling Class Imbalance Trained Predictive Model [CNN, Classical ML] Predicted Class Explanation Generator Explanations product Inventor y Mana g er 2113 Explainable product backorder prediction exploiting CNN: Introducing explainable models… 1 3 indicated that the dataset will be fully balanced. For each minority example xi , ADASYN then calculate the ratio ri applying K-nearest neighbors with Euclidean distance, where Δi is the number of nearest neighbors of xi . Using the normalized ratio ri , then it computes the number of synthetic examples for each minority examples xi . Finally it generates the synthetic minority class examples applying the distance vector and the random number 𝜆 . Convolutional neural network‑based prediction model Inspired by the success of the convolutional neural network (CNN)-based models in computer vision, natural language processing and other classification tasks, we proposed a 1-dimensional CNN classifier to predict product backorder in advance. The structure of our proposed CNN-based predictive model is illustrated in Fig.2. Our CNN-based predictive model has two convolutional hidden layers with batch normalization, max-pooling, and dropout layers. To extract unique and low-level features, the max-pooling layers are exploited. In addition, max-pooling makes the computation faster by reducing the dimension and parameters (Wu and Gu, 2015). Moreover, it reduces the variance. Then we utilized one flattened layer followed by three dense layers with dropout layers. To overcome the over-fitting problem, dropout layers are applied to randomly drop some neurons in the training process for regularization (Kingma etal., 2015; Srivastava, 2013). The parameters and activation functions in different layers of convolutional neural networks are summarized in Table3. In the convolutional layers and all hidden dense layers, we employed the Relu (Ramachandran etal., 2017) activation function. Finally, Sigmoid (Ramachandran etal., 2017) activation function is applied in the output layer. Experiments andevaluation Dataset collection andevaluation metrics This section presents the details of dataset that is leveraged to conduct experiments using our proposed method. We also present a brief discussion about the evaluation metrics considered to measure and validate the performance. Dataset We carried out a wide range of experiments to validate the performance of our methods on a publicly available benchmark dataset called “Can you Predict Product Backorder1”The dataset has an 8 weeks inventory of historical data. The brief statistical summary of the dataset is depicted in Table4. The numerical figures in Table4 illustrate that the number of backordered (positive) samples is much lower than the number of non-backordered (negative) samples. Hence, the ratio (1:137) indicates that this dataset is an extremely imbalanced one. For a better understanding of why this is a challenging problem, we illustrated the distribution of backordered (positive) and non-backordered (negative) samples using a doughnut chart in Fig.3. There are 22 features for each sample and the attributes/features include current inventory, transit time, quantity, forecasting, and different Algorithm1 ADASYN: Adaptive Synthetic Oversampling 1 https:// github. com/ rodri gosan tis1/ backo rder_ predi ction. 2114 M.Shajalal et al. 1 3 risk flag. The list of features with a brief description is depicted in Table5. Evaluation metrics Generally, the performance of any classification method is measured based on the common evaluation metrics including accuracy, precision, recall and f 1 -score. The confusion metrix is used to compute those metrics. However, the backorder prediction dataset is extremely class imbalanced, and the above mentioned evaluation metrics are not enough to validate the performance of any classifier on a imbalanced dataset. Therefore, we employed accuracy, AUC (Area Under the Curve) and ROC (Receiver Operating Characteristics) curves to measure and visualize the performance of our proposed backorder prediction method. The accuracy score is calculated by using the measures from confusion metrics as follows: where tp, fp, fn and tn denote the number of classified samples as true positive, false positive, false negative and true negative, respectively. AUC is one of the most efficient metrics to measure the performance of any classification model on imbalanced data. The AUC is calculated as follows: (4) Acc = tp +tn tp +fp +fn +tn, Fig. 2 Structure of our proposed convolutional neural networkbased backorder prediction model reyaLD1vnoC noitazilamroNhctaB MaxPooling Dropout COnv1 Layer Batch Normalization MaxPooling Dropout Flatten Dense Dropout Dense Dropout Dense output reyaltupnI Table 3 The summary of different layers with parameters and activation functions SL Layer Input/Output Activation 1. Conv1D (20,32) Relu 2. Batch Normalization (20,32) − 3. Max Pooling (10,32), stride=2 − 4. Dropout (10,32) − 5. Cov1D (9,64) Relu 6. Batch Normalization (9,64) − 7. Max Pooling (4,64), strid=2 − 8. Dropout (4,64) − 9. Flatten − − 10. Dense 64 Relu 11. Dropout 64 − 12. Dense 32 Relu 13. Dropout 32 − 14. Dense 1 Sigmoid Table 4 Brief statistical summary of the dataset No of samples No of positive samples No negative samples Imbalance ratio 1,929,936 13,981 1,915,954 1:137 Fig. 3 Distribution of backordered and non-backordered samples Backordered 13981 Non-Backordered 1915954 2121 Explainable product backorder prediction exploiting CNN: Introducing explainable models… 1 3 References Abedin, B., Klier, M., Meske, C., & Rabhi, F. (2022) Introduction to the minitrack on explainable artificial intelligence (XAI). Proceedings of the 55th Hawaii International Conference on System Sciences, 1–2. http:// hdl. handle. net/ 10125/ 70765 Adadi, A., & Berrada, M. (2018). 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