Green Supply Chain Performance Prediction Using a Bayesian Belief Network

Green supply chain management (GSCM) has emerged as an important issue to lessen the impact of supply chain activities on the natural environment, as well as reduce waste and achieve sustainable growth of a company. To understand the effectiveness of GSCM, performance measurement of GSCM is a must. Monitoring and predicting green supply chain performance can result in improved decision-making capability for managers and decision-makers to achieve sustainable competitive advantage. This paper identifies and analyzes various green supply chain performance measures and indicators. A probabilistic model is proposed based on a Bayesian belief network (BBN) for predicting green supply chain performance. Eleven green supply chain performance indicators and two green supply chain performance measures are identified through an extensive literature review. Using a real-world case study of a manufacturing industry, the methodology of this model is illustrated. Sensitivity analysis is also performed to examine the relative sensitivity of green supply chain performance to each of the performance indicators. The outcome of this research is expected to help managers and practitioners of GSCM improve their decision-making capability, which ultimately results in improved overall organizational performance.


Introduction
Recently, supply chain performance prediction has received increased attention from academics and practitioners [1]. To predict the supply chain performance, the development of supply chain performance metrics is crucial. Developing a performance measurement system to empower the coordination mechanism for mutual decision-making has become a vital issue in supply chain management [2]. This mutual decision-making process can be used to combine the goals of independent participants and integrate their individual activities so as to optimize the performance of the whole supply chain [3]. Hoole [4] discussed that the performance measurement of a supply chain enables a company to employ more mature supply chain practices and, consequently, enables them to reduce cost faster than their less mature competitors. More accurately, there can be a variation of 5% to 6% of annual revenue in supply chain costs among competitor companies of the same industry. Therefore, it is important for a company to develop a performance measurement model to improve its operation [5,6].
Companies are presently trying to include environmental performance in the evaluation of the overall supply chain performance because of increased competitive, regulatory, and community (a) What are the performance metrics of a green supply chain? (b) How do the performance metrics affect the supply chain performance? (c) Which metrics have the most impact on GSCM performance? (d) How can a manager achieve a specified level of GSCM performance?
This study attempts to answer the above research questions by identifying the GSCM performance measures by reviewing the existing literature and taking expert opinion, developing a quantitative and probabilistic model using a Bayesian belief network (BBN). The effectiveness of the model is demonstrated using a real-world case study, as well as performing sensitivity and diagnostic analyses to determine the impact of various metrics on overall performance. The BBN-based green supply chain performance prediction model can consider the cause-effect relationships between different performance indicators and provide informed decisions effectively in cases of incomplete, imprecise and ambiguous information. The proposed BBN model is flexible enough to perform both diagnostic analysis or bottom-up inference, and predictive analysis or top-down inference.
The rest of the paper is organized as follows. Section 2 presents a review of the existing literature on traditional supply chain management performance measurement and GSCM performance measurement. Section 3 gives a brief overview of BBN. Section 4 presents the proposed research framework. Section 5 includes a BBN-based performance prediction model. Data collection and analysis, results, discussion of the findings and sensitivity analysis are also included in this section. Finally, Section 6 includes conclusions, managerial implications and recommendations.

Literature Review
In this section, a brief overview of GSCM and review of the related literature is provided. The literature review is divided into two parts. In the first section, the traditional supply chain performance measurement is discussed. In the second section, literature focusing on GSCM is discussed.

Green Supply Chain Management (GSCM)
GSCM is defined by incorporating the environmental aspect into the supply chain management that considers the effect and association of supply chain management to the surrounding environment [14,19,22,23]. The traditional supply chain focuses on the economic aspect of the supply chain, ignoring the environmental impact of the activities, whereas the green supply chain focuses on and tries to minimize the adverse impact of the supply chain activities on the environment. A green supply chain, however, must not just be environment friendly, it also must be economically viable [14]. According to Wilkreson [24], GSCM is not a cost center. Instead, it is an important business driver.
The rising scarcity of raw materials, environmental pollution and ever-increasing world population have placed utmost importance on GSCM [14,25]. It encompasses two major areas, green design and green operations [25]. Mishra et al. [19] expanded the repertoire of GSCM by adding green distribution and marketing to the definition. Green design is the incorporation of the environmental effect of a product throughout its life cycle in the design and development process [26]. Several tools exist that can help designers understand the impact of their product. Life-cycle assessment, design for environment principles and product stewardship are some of the tools [27]. Green operations include green manufacturing or remanufacturing, reverse logistics and waste management [28][29][30]. Reverse logistics is a crucial part of GSCM. Reverse logistics is a method of increasing environmental performance of a company by using the concept of the 3Re's (recycle, reuse and reduce the use of material) [10,19,29]. Swami and Shah [31] included the coordination of functional areas to share the responsibility for environmental performance as an important element of GSCM.

Traditional Supply Chain Management Performance Measurement
Though much work on performance measurement and management of internal organizational activities has been done, only a handful have focused on supply chain performance measurement [18]. Multiple echelon inventory-based supply chain models have generally considered various performance measures like cost, quality, delivery time, inventory levels, and environmental costs [32,33].
Comprehensive supply chain performance measurement has been the focus of some of the existing literature. Supplier performance evaluation and study of appropriate performance measures have received special attention from some researchers [34,35]. Most of these studies have focused on measuring supplier performance, and also focused on their roles in the supply chain. Beamon [36] observed the impact of the various elements on supply chain performance and recognized the inherent association between these elements and supply chain performance. Inventory system stock-out risk, the probability distribution of demand and transportation time are some of the major elements identified by the authors.
A. Gunasekaran et al. [20] described various supply chain performance metrics. Using these performance metrics, they also described sources. Though they did not include environmental performance metrics, they emphasized a comprehensive study of these general measures. As existing literature on traditional supply chain measurement fails to include environmental performance, several researchers have tried to incorporate environmental performance in their different studies. These studies will be reviewed in the next section.

GSCM Performance Measurement
The perception of ecological sustainability has been considered as a basis for studying management practices by several researchers [37][38][39]. They have acknowledged its applicability in both operational and strategic contexts. Greening of supply chains within various contexts has been studied and these contexts include product design [26], process design [25], manufacturing practices [40][41][42], purchasing [43,44], and a comprehensive combination of these factors [25,45].
Several researchers [10,25,46,47] emphasized that GSCM has emerged as an approach to build a competitive advantage and to fulfill the environmental requirements that are set by various regulatory bodies. Ahi and Searcy [48] proposed various metrics to measure environmental performance. Reducing the negative environmental impact (different types of pollution) and reducing the waste of resources (energy, materials, goods) were considered as overall objectives of a green supply chain by Hervani et al. [21]. The authors also noted that this reduction process should start from the extraction of raw material and should continue up to the consumption and shipment of products. Green supplier selection has attracted quite a bit of attention from researchers [49][50][51]. Several metrics for assessing supplier performance were identified by Kuo, Wang, and Tien [52]. These metrics include "green competencies", "current environment efficiency", "supplier's green image" and "net life-cycle cost". Actually, this supplier performance assessment procedure is a part of the green purchasing process. Yazdani, Chatterjee, Zavadskas, and Zolfani [53] used a Quality Function Development (QFD)-based multi-criteria decision-making approach for green supplier selection. Tang, Wei, and Gao [54] used the Muirhead Mean operator and dual Muirhead Mean (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs), which they then used to solve a supplier selection problem. Jenssen and de Boer [55] incorporated life-cycle assessment in the green supplier selection problem. Xu, Shi, Cui, and Quan [56] used interval 2-tuple linguistic hybrid aggregation operators to select green suppliers.
Researchers have introduced tools such as the analytical hierarchy process (AHP), activity-based costing and design for environmental analysis; life-cycle analysis and balanced scorecard for Green Supply Chain Performance Measurement. Although a few tools can be directly implemented for evaluating the performance, the remaining others need to be modified. For example, a management tool known as ecological supply chain analysis (ECOSCAN) was developed by Faruk et al. [45] to observe the effect of environmental management across the supply chain. The life cycle analysis model is the basis of the ECOSCAN tool, which emphasizes the connection between life-cycle analysis and GSCM methods.
Handfield, Walton, Sroufe, and Melnyk [57] combined AHP with an extensive information system. This information system enables environmentally conscious purchasing. Pineda-Henson, Culaba, and Mendoza [58] used AHP to analyze the impact of environment by following the life-cycle assessment approach, which mainly considers the manufacturing operations. Handfield et al. considered only green purchasing and Pineda-Henson et al. considered a particular case study of pulp and paper manufacturing; however, none of them considered the overall green supply chain performance.
By reviewing the existing literature, eleven corresponding green supply chain performance indicators were identified. These eleven indicators were then classified into a hierarchy model which was inspired by the works of Maleki and Machado [33]. The indicators were first clustered into small groups, e.g., indicators related to water and energy consumption were put into the group 'consumption'. These groups were then classified into performance measures. Two performance measures were considered: business wastage, and emission and consumption. Business wastage, in the context of this paper, is defined as waste materials produced as a result of various business processes. On the other hand, emissions and consumption includes all those indicators related to various solid, liquid emission and different resource consumptions. It is to be noted that two indicators, i.e., 'Output amount of hazardous and toxic material' and 'Percentage of energy obtained from renewable sources' were not clustered into any group as there no performance indicators similar to them. These performance measures and indicators were used for developing a BBN model. Using these performance measures and indicators, the green supply chain performance in different scenarios can be predicted. These performance measures and indicators are presented in Table 1 along with corresponding references and notations that will be used throughout the paper.

Groups Indicators Reference
Business Wastage related Materials related.

Bayesian Belief Network
As mentioned before, Bayesian Belief Network is the method of choice for predicting the performance of green supply chain in this study. A Bayesian Belief Network, or Bayes net in short form, is a probabilistic graphical model that presents knowledge about an uncertain domain. Bayes net is an effective method to represent causality and conditional probabilities among various factors [72,73]. Moreover, this method is suitable when the factors are probabilistic in nature. According to several authors, such as Langseth and Portinale; Mahadevan, Zhang, and Smith; Maleki and Machado [33,74,75], BBN shows high performance in handling uncertainty. As the factors and the relationships among them are represented using nodes and edges, any model represented using this method is easier to understand for practitioners than any other techniques [72]. As the performance indicators used in this study are probabilistic and the state of performance measures are conditionally dependent upon the states of performance indicators, Bayesian Network has been chosen to predict environmental performance.
BBN consists of two parts B = (G, θ). The first part, "G", is a directed acyclic graph (DAG) which includes nodes and arcs. DAG presents the network visually where variables of the data set X 1 , . . . . . . , X n represent nodes and arcs indicate dependencies among nodes [76]. The second part of BBN is the conditional dependency distribution of θ where θ xi|πxi = P B (x i |π xi ) is the set of direct parent variables of x i in G [77]. Using the joint probability distribution, the network B can be represented by: In a BBN, random variables are represented by nodes, and probabilistic dependencies among the corresponding random variables are represented by edges between the nodes. A BBN actually is a probabilistic model that can compute the posterior probability distribution of any unobserved stochastic variables, given the observation of complementary subset variables [78]. In a BBN, "backward" probability propagation is also possible and it is helpful to find the most probable scenario indicating the evidence set [79].
Inference in BBN is used to update the probability for a hypothesis as more evidence or information becomes available. Figure 1 illustrates a simple Bayesian network where "A" and "B" are parent nodes, "C" is a child node. There are two types of inference support: predictive and diagnostic support for a node X i . Predictive support for node X i is a top-down approach that considers evidence nodes connected to X i through its parent nodes. On the other hand, diagnostic support for node X i is a bottom-up approach that considers evidence nodes connected to X i through its child node [80].
Sustainability 2020, 12, x FOR PEER REVIEW 6 of 20 "backward" probability propagation is also possible and it is helpful to find the most probable scenario indicating the evidence set [79]. Inference in BBN is used to update the probability for a hypothesis as more evidence or information becomes available. Figure 1 illustrates a simple Bayesian network where "A" and "B" are parent nodes, "C" is a child node. There are two types of inference support: predictive and diagnostic support for a node Xi. Predictive support for node Xi is a top-down approach that considers evidence nodes connected to Xi through its parent nodes. On the other hand, diagnostic support for node Xi is a bottom-up approach that considers evidence nodes connected to Xi through its child node [80].

Framework Development
The aim of this research work is to find out the most significant quantitative green supply chain performance measures and predict green supply chain performance in different scenarios. Figure 2 illustrates the methodology of this research. The proposed research consists of five steps as described below.

Framework Development
The aim of this research work is to find out the most significant quantitative green supply chain performance measures and predict green supply chain performance in different scenarios. Figure 2 illustrates the methodology of this research. The proposed research consists of five steps as described below.
Sustainability 2020, 12, x FOR PEER REVIEW 6 of 20 "backward" probability propagation is also possible and it is helpful to find the most probable scenario indicating the evidence set [79]. Inference in BBN is used to update the probability for a hypothesis as more evidence or information becomes available. Figure 1 illustrates a simple Bayesian network where "A" and "B" are parent nodes, "C" is a child node. There are two types of inference support: predictive and diagnostic support for a node Xi. Predictive support for node Xi is a top-down approach that considers evidence nodes connected to Xi through its parent nodes. On the other hand, diagnostic support for node Xi is a bottom-up approach that considers evidence nodes connected to Xi through its child node [80].

Framework Development
The aim of this research work is to find out the most significant quantitative green supply chain performance measures and predict green supply chain performance in different scenarios. Figure 2 illustrates the methodology of this research. The proposed research consists of five steps as described below. Step 1: Identification of performance measures and their corresponding indicators Step 1: Identification of performance measures and their corresponding indicators In the first step, an extensive list of green supply chain performance measures (GSC-PM) is generated based on the factors that have a significant influence on green supply chain performance. The most significant GSC-PM are identified through a literature review. For the literature review, papers published from 1995 to present day were chosen for the review timeline. Literature about green supply chain was searched for factors that the authors believe can significantly affect the environmental performance of a company. Papers about green purchasing, green consumption, green marketing, green manufacturing, green 3R (reduce, reuse, recycle) and supply chain performance measurement were also studied for green performance indicators. A total of 11 performance indicators were identified, which represent two major performance measures. These indicators and measures were identified by reviewing the existing literature.
Step 2: Collection of data about performance indicators In this step, data about performance indicators were collected. These data were used for calculating the prior probability of each performance indicator in the BBN model and for learning in the BBN model. Step 4: Using a learning algorithm to draw an inference from data sets In this step, a learning algorithm is used to draw an inference from data which are collected during step 3. The inference is used to update the probability for a hypothesis (here, the hypothesis is whether the performance indicator will be in a satisfactory state or in an unsatisfactory state) as more evidence or information becomes available.
Step 5: Monitoring performance measures and predicting green supply chain performance by applying evidence to specific nodes in the BBN model In this step, performance measures are monitored and green supply chain performance is predicted by applying evidence to specific nodes which represent performance indicators in the BBN model. Evidence will be different for different scenarios and, as a result, green supply chain performance will be different for different scenarios. The methodology of this research is illustrated in Figure 2.

Identification of Performance Measures and Their Corresponding Indicators
Using a thorough literature review, eleven performance indicators have been identified which will be used to build the model.

Data Collection
The developed methodology has been applied to a real-world case study and used to predict the green supply chain performance of this case company. Necessary data about performance indicators have been collected from this company. These data and information will help to determine the prior probability of the performance indicators being in the satisfactory state, and also the prior probability of performance indicators being in the unsatisfactory state. The data of "Amount of Solid Wastes" performance indicator are highlighted in Table 2 as an example. Using a histogram, collected data about performance indicators and their corresponding recommended levels are presented in Figure 3.  Using a histogram, collected data about performance indicators and their corresponding recommended levels are presented in Figure 3.  According to Table 2, the company has met the recommended level 13 out of 20 times. For this, the probability that performance indicator "Amount of Solid Wastes" will be in the Satisfactory state = ((13/20) × 100) % = 65% and Unsatisfactory state = ((7/20) × 100) % = 35%. Similarly, prior probabilities for other performance indicators have been calculated and are listed in Table 3. Table 3. Prior probabilities for green supply chain performance indicators. According to Table 2, the company has met the recommended level 13 out of 20 times. For this, the probability that performance indicator "Amount of Solid Wastes" will be in the Satisfactory state = ((13/20) × 100) % = 65% and Unsatisfactory state = ((7/20) × 100) % = 35%. Similarly, prior probabilities for other performance indicators have been calculated and are listed in Table 3.

BBN Model Development
The BBN model was developed using commercially available software Netica [81] and prior probabilities of performance indicators listed in Table 3 are presented in Figure 4. To learn the conditional probabilities in the network, Netica has counting algorithms, expectation-maximization (EM) and gradient descent [79]. As there are no hidden variables or incomplete data, Netica used counting algorithms for the model development.

BBN Model Development
The BBN model was developed using commercially available software Netica [81] and prior probabilities of performance indicators listed in Table 3 are presented in Figure 4. To learn the conditional probabilities in the network, Netica has counting algorithms, expectation-maximization (EM) and gradient descent [79]. As there are no hidden variables or incomplete data, Netica used counting algorithms for the model development.
From Figure 4, it can be found that there is a 52.4% probability that performance measure "Business Wastage" will be in a satisfactory state and 53.6% probability that performance measure "Emissions" will be in a satisfactory state and, finally, there is a 57.6% probability that Environmental Performance or Green Supply Chain Performance will be in a satisfactory state. These results are based on current prior probabilities of performance indicators which were collected from the data.

Model Validation
Both qualitative (extreme-condition test and scenario analysis) and quantitative (sensitivity analysis) validation approaches were performed for validation of the proposed model [82]. From Figure 4, it can be found that there is a 52.4% probability that performance measure "Business Wastage" will be in a satisfactory state and 53.6% probability that performance measure "Emissions" will be in a satisfactory state and, finally, there is a 57.6% probability that Environmental Performance or Green Supply Chain Performance will be in a satisfactory state. These results are based on current prior probabilities of performance indicators which were collected from the data.

Model Validation
Both qualitative (extreme-condition test and scenario analysis) and quantitative (sensitivity analysis) validation approaches were performed for validation of the proposed model [82].

Extreme-Condition Test
To validate the model, two extreme conditions are considered in this paper. In extreme case 1, all the performance indicators are in a satisfactory condition. In extreme case 2, all the performance indicators are in an unsatisfactory condition. The results for extreme cases 1 and 2 are shown in Figures 5 and 6, respectively. From Figure 5, it can be found that, when all the performance indexes have a 100 percent probability of being satisfactory, the environmental performance has a 92.8 percent probability of being in a satisfactory condition. Similarly, according to Figure 6, when all the performance indicators have a 100 percent probability of being in an unsatisfactory condition, the environmental performance has only 4.15 percent probability of being in a satisfactory condition. So, the extreme-condition tests show that the proposed environmental performance model works according to expected model behavior.
Sustainability 2020, 12, x FOR PEER REVIEW 11 of 20 To validate the model, two extreme conditions are considered in this paper. In extreme case 1, all the performance indicators are in a satisfactory condition. In extreme case 2, all the performance indicators are in an unsatisfactory condition. The results for extreme cases 1 and 2 are shown in Figures 5 and 6, respectively. From Figure 5, it can be found that, when all the performance indexes have a 100 percent probability of being satisfactory, the environmental performance has a 92.8 percent probability of being in a satisfactory condition. Similarly, according to Figure 6, when all the performance indicators have a 100 percent probability of being in an unsatisfactory condition, the environmental performance has only 4.15 percent probability of being in a satisfactory condition. So, the extreme-condition tests show that the proposed environmental performance model works according to expected model behavior.

Scenario Analysis
In this analysis, different hypothetical scenarios are considered except the two extreme cases. Due to space limitations, only two performance factors, namely, Scrap_Flow_quantity and Hazardous_Toxic_Material have been considered here. Eight different scenarios are considered where the probability of a satisfactory state of these two performance factors is varied from 90 percent to 10 percent in increments of 10 percent. The results of the analysis are shown in Figure 7 and summarized in Table 4.
In scenario 1, where Scrap_Flow_quantity and Hazardous_Toxic_Material are at 90 percent, Environmental Performance is at 61.3 percent. In scenario 2, where the probability of satisfactory To validate the model, two extreme conditions are considered in this paper. In extreme case 1, all the performance indicators are in a satisfactory condition. In extreme case 2, all the performance indicators are in an unsatisfactory condition. The results for extreme cases 1 and 2 are shown in Figures 5 and 6, respectively. From Figure 5, it can be found that, when all the performance indexes have a 100 percent probability of being satisfactory, the environmental performance has a 92.8 percent probability of being in a satisfactory condition. Similarly, according to Figure 6, when all the performance indicators have a 100 percent probability of being in an unsatisfactory condition, the environmental performance has only 4.15 percent probability of being in a satisfactory condition. So, the extreme-condition tests show that the proposed environmental performance model works according to expected model behavior.

Scenario Analysis
In this analysis, different hypothetical scenarios are considered except the two extreme cases. Due to space limitations, only two performance factors, namely, Scrap_Flow_quantity and Hazardous_Toxic_Material have been considered here. Eight different scenarios are considered where the probability of a satisfactory state of these two performance factors is varied from 90 percent to 10 percent in increments of 10 percent. The results of the analysis are shown in Figure 7 and summarized in Table 4.
In scenario 1, where Scrap_Flow_quantity and Hazardous_Toxic_Material are at 90 percent, Environmental Performance is at 61.3 percent. In scenario 2, where the probability of satisfactory

Scenario Analysis
In this analysis, different hypothetical scenarios are considered except the two extreme cases. Due to space limitations, only two performance factors, namely, Scrap_Flow_quantity and Hazardous_Toxic_Material have been considered here. Eight different scenarios are considered where the probability of a satisfactory state of these two performance factors is varied from 90 percent to 10 percent in increments of 10 percent. The results of the analysis are shown in Figure 7 and summarized in Table 4.
Environmental Performance decreases to 54 percent. Similarly, from scenarios 4-8, where the probability of a satisfactory state of Scrap_Flow_quantity and Hazardous_Toxic_Material decreases, the probability of Environmental Performance being in a satisfactory state also decreases. In scenario 8, where the performance indicators are at 10 percent of the probability of being in a satisfactory state, the Environmental Performance has only a 32 percent probability of being in a satisfactory state. Thus, the scenarios show the expected model behavior.   In scenario 1, where Scrap_Flow_quantity and Hazardous_Toxic_Material are at 90 percent, Environmental Performance is at 61.3 percent. In scenario 2, where the probability of satisfactory states of performance indicators decreases to 80 percent, the nvironmental performance decreases to 57.6 percent. Scenario 3 depicts 70 percent satisfactory probability of performance indicators where Environmental Performance decreases to 54 percent. Similarly, from scenarios 4-8, where the probability of a satisfactory state of Scrap_Flow_quantity and Hazardous_Toxic_Material decreases, the probability of Environmental Performance being in a satisfactory state also decreases. In scenario 8, where the performance indicators are at 10 percent of the probability of being in a satisfactory state, the Environmental Performance has only a 32 percent probability of being in a satisfactory state. Thus, the scenarios show the expected model behavior.
All these eight scenarios represent the anticipated model behavior. In a similar way, the different combinations of the performance indicators are considered to generate different scenarios and their Environmental Performance probability distribution is tested to perform model validation.

Sensitivity Analysis
To identify the contribution of each individual input in the model output, a sensitivity analysis was performed. This analysis provides information about how slight variations in input parameters like water consumption and solid wastes can affect the model output, which in this case is Environmental Performance. Because the input variables, in this case, are discretized continuous parent nodes, using a variance reduction method is recommended [82]. However, the results of an entropy reduction method are also provided.
The variance reduction method calculates the variance reduction of the expected real value of a query node E (e.g., Environmental_Performance) due to a finding in a varying variable node I (e.g., Recycled/re-used, Remanufactured, Renewable_Source). The variance of the real value of E given evidence I, V(e i) is computed using the following equation [82,83]: where e is the state of the query node E, i is the state of varying node I, p(e|i) is the conditional probability of e given i, Y e is the numeric value corresponding to state e and E(e i) is the expected value of E after the new finding i for node I. Entropy reduction calculates the expected reduction in mutual information of E from a finding for variable I (Kabir et al., 2019). The formula is given below: where H(E) and H(E|I) are the entropy before the new findings and after the new findings. The results of the sensitivity analysis are provided in Figure 8. The result of sensitivity analysis allows the decision-maker to identify the input parameters that affect the output most and prioritize them in the decision-making. In the case of Environmental Performance, the managers should first prioritize reducing toxic waste and focus on using renewable sources to improve environmental performance.

Diagnostic Analysis
Marginal probabilities of root or parent nodes can be determined by performing a diagnostic analysis [83]. The posterior probabilities conditioned to the aggregated risk can be identified using this analysis. The posterior probabilities of the parent nodes conditioned to aggregated risk are shown in Table 5. Table 5 shows the change in the probability of performance indicators in two extreme cases of Environmental Performance. All the probabilities for a satisfactory state decrease when Environmental Performance goes from a satisfactory state to an unsatisfactory state. On the other hand, the probabilities of an unsatisfactory state go up. This is in line with the expected model  For query node Environmental_Performance, Hazardous_Toxic_Material has the highest contribution (1.830% variance reduction and 5.354% entropy reduction, respectively) followed by Renewable_Source (0.386% and 1.141%), Solid_Wastes (0.223% and 0.645%), Scrap_Flow_quantity (0.195% and 0.564%), Remanufactured (0.133% and 0.385%), Liquid_Wastes (0.099% and 0.287%), Recycled/re-used (0.090% and 0.260%), Greenhouse Gas Emission (0.053% and 0.153%) have medium effects on Environmetal_Performance. Energy_Consumption and Air_Emission, Water_Consumption have very low contributions. The variance reduction and entropy reduction for both are below 0.05%. The total contribution of parent nodes in variance reduction is 3.039% and for entropy reduction is 8.856%.
The result of sensitivity analysis allows the decision-maker to identify the input parameters that affect the output most and prioritize them in the decision-making. In the case of Environmental Performance, the managers should first prioritize reducing toxic waste and focus on using renewable sources to improve environmental performance.

Diagnostic Analysis
Marginal probabilities of root or parent nodes can be determined by performing a diagnostic analysis [83]. The posterior probabilities conditioned to the aggregated risk can be identified using this analysis. The posterior probabilities of the parent nodes conditioned to aggregated risk are shown in Table 5. Table 5 shows the change in the probability of performance indicators in two extreme cases of Environmental Performance. All the probabilities for a satisfactory state decrease when Environmental Performance goes from a satisfactory state to an unsatisfactory state. On the other hand, the probabilities of an unsatisfactory state go up. This is in line with the expected model behavior.

Conclusions, Implications and Limitations to This Study
In this study, a BBN-based probabilistic model is proposed for predicting green supply chain performance. Eleven green supply chain performance indicators and two green supply chain performance measures were identified through a review of the existing literature, and then BBN was used to develop the model that would predict the overall environmental performance. Inputting the satisfactory/unsatisfactory states of the performance indicators in the model will provide the decision maker with the overall green supply chain environmental performance state. This will allow the manager to see how the performance metrics can affect the overall green supply chain performance. To validate the model, an extreme condition test was used. Furthermore, performing a sensitivity analysis reveals the most important performance indicators and provides the decision makers with a ranking of the indicators in the order of importance. For the case company in this study, output amount of hazardous toxic material was found to be the most important indicator having the highest variance reduction and entropy, followed by percentage of energy obtained from renewable sources. Amount of solid wastes, total flow quantity of scraps, and percentage of materials remanufactured are also some important indicators with relatively high sensitivity. On the other hand, amount of water consumption, quality of air emission and amount of energy consumption were found to be the least important indicators with low sensitivity. The manager of this company can give relatively less focus to these factors without worsening the environmental performance too much. This model can also help a manager to achieve a prespecified level of performance. The model allows a manager to input the required level of environmental performance, and the model will determine at what level each environmental indicator needs to be.
This study makes several theoretical contributions in the field of green supply chains. First, this study identified the key performance indicators that affect the overall environmental performance across the supply chain of an organization. Second, this study proposes a BBN-based framework for the green or environmental performance prediction of a supply chain. The final contribution of this paper is that it investigates how the individual key performance indicators affect the overall environmental performance of a supply chain.
Using this model, managers and executives will be able to understand which performance indicators most affect green supply chain performance of their company. They will also be able to understand which performance indicators to focus on first, and where the resource should be allocated first to achieve the optimum level of environmental performance. As managers usually have limited resources at their disposal, prioritizing and optimizing resource allocation can greatly help in achieving environmental objectives of a supply chain. Using the current performance level of each performance indicator, they will be able to monitor current environmental performance, which will help them to understand the company's current relative position in the industry. Using diagnostic analysis, managers can determine the target performance indicator levels required to achieve satisfactory overall performance. This study has some limitations. Due to limitations in collecting data, only one company's data has been used to test the model. Another limitation is that not all possible key environmental performance indicators were added to the proposed BBN model. This model only considered two states, namely satisfactory and unsatisfactory states for the BBN nodes.
There are several directions future researches on this topic can take. One direction can be adding more performance indicators. A more comprehensive model validation test can be performed by collecting data from multiple sources and performing multiple case studies. Another direction for future research can be incorporating multiple states instead of just satisfactory and unsatisfactory states, which can be an exciting direction for future research. IoT devices can be used to collect environmental data in real time which can be used as the input for an online algorithm. This algorithm can update the BBN model in real time for monitoring purposes. Other artificial intelligence-based tools such as knowledge systems, fuzzy AHP, or Bayesian Regression Trees can be developed for predicting green supply chain performance and the results can be compared.