Application of Neural Networks in Predicting the Level of Integration in Supply Chains

Purpose: This investigation is based on the theoretical analysis of the application of neural networks to the design and manage supply chains, along with an empirical approach, this investigation its developed with the prediction of the level of integration in the supply chain through neural networks. Design/methodology/approach: The methodology designed and used for the processing of data was the instruction of a neural network which is used to predict the level of integration in a supply chain. This type of predictive application appears in the literature reviewed on supply chains. This analysis was carried out in a comparative way with the heterogeneous and homogeneous weights of the neuron training. Findings: The main results of this research focus on predicting the level of integration in the supply chain from the neuronal network. This provides a coached neuron that can be applied in other studies and, therefore, predict the outcome. On the other hand, it is shown that if the weights of the integration level variables are not homogeneous, the procedure presents different results depending on the context in which it is developed. Research limitations/implications: Among the limitations of the implementation of neural networks it should be noted, the necessary adaptation to the characteristics of the supply chains and the areas of performance of the business organizations under study, in the framework of activities productive or service itself, in addition to analyzing its corporate purpose in relation to the satisfaction of certain needs of the target markets. Originality/value: The literature shows multiple theoretical sources that refer to studies of neural networks in supply chains, observing the opportunity to apply this technique to predict the level of integration due to its benefits for decision making. The originality of this scientific work lies in the possibility of comparing the historical data of the level of integration and those predicted as a result of the coaching of the neuron with the weights of the heterogeneous and homogeneous variables.


Introduction
The integration of supply chains (ISC) is a required element in the gates of Industry 4.0. These radicates from the interrelation of the processes and internal flows of each company, to the combination of the processes and flows of multiple performers; on the other hand, that these processes are aligned according to the chain's strategy, with the goal of satisfying the customer (Cooper, Lambert & Pagh, 1997;Al-Doori, 2019). Other performers classify the levels of integration in relation to their complexity (Pires & Carretero-Díaz, 2007;Sablón-Cossío, Pulido-Rujano, Orozco-Crespo & Ruíz-Cedeño, 2018): Assignment, Market Negotiations, Association, Cooperation, Coordination and Collaboration.
Based on this need, estimating ISC is a challenge. Where traditional approaches arise as descriptive and inferential analysis (Sablón-Cossío, Pulido-Rujano et al., 2018). Together with management philosophies that focus on collaboration between parts of the supply chain, for example: Supplier-managed inventory (VMI), Customer relationship management (CRM), Efficient consumer response (ECR), Provision and replenishment of collaborative planning (CPFR), (Kazemi & Zhang 2013).
Based on this neccesity, the ISC estimate is a challenge. Coming from traditional approaches such as descriptive and inferential analysis (Acevedo-Urquiaga, 2013;Sablón-Cossío, Pulido-Rujano et al., 2018). On the other hand, other studies with a renewal approach such as artificial intelligence. For example: the blurry logic for the selection of variables (Bautista-Santos, Martínez-Flores, Fernández-Lambert, Bernabé-Loranca, Sánchez & Sablón-Cossío, 2015) and qualify the solutions to face the risk in the supply chain networks (Jafarnejad, Momeni, Abdollahi, Safari & Nakhai-Kamalabadi, 2018), the genetic algorithms (Liu & Ran 2019), the structural equation modeling for (Sreedevi & Saranga, 2017) and the neural networks for variable forecasting (Baharmand, 2019). This last perspective is the subject of this article.
The goal of this article is to predict the level of integration in the supply chain through neural networks in two different contexts, the architecture algorithm and the supervised learning algorithm. The importance of this research lies in its methodological contribution, due to obtaining a trained neural network that can predict integration in order to make decisions in different contexts. In addition to the social contribution, which is framed in the possibilities of making early decisions to possible consumer needs.
The particular background of this research work in relation to the technique used is the procedure of training a neural network as defined in (Muñoz, Cedeño, Ruiz & Cruz, 2019). In this case, a prediction of success or failure of a purchase request from one financial institution to another was made.

Applications of Neural Networks in Supply Chains
The application of neural networks in supply chains has been diverse and towards different variables. Scientific texts related to the subject, are generally searched in three databases: Springer, Taylor and Francis and Elsevier. These identify 55 documents related to the particular issue between the period from 1995 to 2019.
From these studies, some uses were identified in the: optimization of processes and flows in the chain, the prediction of some of the variables, modeling and simulation, globalization (integration), decision support and risk management as the last characteristic of greater presence. Out of which 22% refers to the forecast, 20% to globalization, 16% model and simulation and support for decisions in equal amounts, 13% to optimization and risk management as detailed in Figure 1. Out of these, globalization is directly related to this research. Of this percentage (16%) refer to studies on how variables that favor integration are predicted or related (Leung, 1995;Chiu & Lin, 2004;Minis & Ampazis, 2006;Li, Lai & Nie, 2007;Lichun & Cai, 2008;Jeeva & Guo, 2010;Lee, Jung & Nie, 2010;Singh & Benyoucef, 2010;Bousqaoui, Said & Tikito, 2017;Yang, 2017;Kokkinos, Exadactylos, Vafidis & Hatziioannou, 2018;Liu & Ran, 2019). In the study by Chiu and Lin (2004), neural networks are used for the evaluation of collaborative planning in supply chains. The latter focuses on the modeling of the mitigation of errors between objectives and clients, as a mechanism for collaboration between the actors in the supply chain.

Preliminary Research Work Related to the Subject Under Study
The study of the level of integration in the supply chain has several approaches according to the specialized literature. Despite this, this article uses the methodology for evaluating the level of integration of Sablón-Cossío, Cárdenas-Uribe, Pérez-Quintana, Bravo-Sánchez and Manjarez-Fuente (2018). This algorithm has been used in supply chains of various countries, products and scopes as described in Table 1.
This methodology begins with the selection of the work group in each actor. These are based on the experience of the staff and the influence of their knowledge in decision making. The degree of importance is assigned to each variable by the working group, using the Hierarchical Analytical Method. The checklist of 91 items of Sablón-Cossío, Pulido Rujano et al. (2018) to each of the actors in the chain. It is analyzed through a descriptive statistical study, where the weight of each variable is multiplied by the results of the corresponding items.

No.
Objects of study Classification Application Developing A set of variables under study has been identified as detailed below: Strategy (D1), Information (D2), Planning (D3), Purchases (D4), Inventory (D5), Transportation (D6) and Collaborative Performance (D7). These are broken down into items that are evaluated with a Likert scale from 1 to 5 for items measured in ordinal scale, where the value 1 corresponded with the criterion of very low and 5 with that of very high. Finally, the level of integration of the chain was determined by the following expression: (1) Where: From the level of integration of the chain, the strategies and joint objectives of the supply chain in relation to the object of investigation are identified. Due to this, the need arises to identify a prospect of this level, in order to anticipate possible market changes for this purpose, the use of neural networks is proposed.

Materials and Methods
The training methodology of a neural network of Muñoz et. al (2019) to predict the level of integration in the supply chain. In these algorithms are used for the construction of a neural network: the architecture algorithm and the supervised learning algorithm.

Architecture, Multilayer Neural Network
• Number of neurons in the input layer: The number of neurons is determined by the number of independent variables.
• Number of hidden layer neurons: It is determined by the pyramidal formula, to approximate the number of neurons in the hidden layer. (2) Where: h ( To determine the initial number of neurons in the hidden layer, Equation (2) is used, which results in the value of three neurons. From this number, a series of tests were carried out establishing the value of ten neurons avoiding a mismatch or over-adjustment in the learning of the neural network. From the number of neurons in the output layer, whose role is to predict or estimate a numerical value, the last layer is made up of a neuron.

Supervised Learning Algorithm
Neural network learning takes place through the backpropagation learning algorithm, which consists of five steps:

a) Initialization
As there is no prior information, the weights and balances of each connection are initialized with random values between 0 and 1.
Formula for the net value of the output in each neuron. ( Where: v = Net worth. i i = Number of input neurons, of the input variables. ω i = Weights associated with each connection of the neural network. b = Neural netwok balance. Sigmoid function, establishes whether the output signal of each neuron is exciter or inhibitor. It is responsible for calculating the level of the activation state by generating an exciting signal (very high values) or inhibitory (very small values) from the net input of each neuron.
Activation function evaluated with the net value.
Where: a = Activation function.
To simplify calculations in the following applies the first derivative to the activation function:

b) Presentation of the training sample
Choose an input pattern of the data X (μ) to be analyzed. Each variable will enter a neuron in the input layer.

c) Forward phase
Propagate the signal forward through the network, calculating the net inputs and activation function of each perceptron in the neural network.
Calculate δ i L . The learning error in the resulting layer y i L , which is the difference between the observed and expected values. Where:

d) Backward phase
The learning error marks the most appropriate way to update the weights that will produce a satisfactory response at the end of the training. The deltas for the preceding layers are calculated by propagating the errors backwards.
= Total sum of the resulting error.
The modification of each weight is made using Function 8.
The learning method that is the descending gradient is the variation that occurs over time of the value of the weights, spreading the error from the final layer to the input layer. Where n is the learning factor, which determines the speed with which the neural network learns. The learning factor is the learning speed of the network, through trial and error it must always be between 0.4 and 1, because if it is very high the value will make the progress of the training faster and therefore may not produce a convergence.
Equation 10 calculates the new weight value by adding the increase Δw to the current weight value.

e) Iteration
Steps 3 and 4 are repeated with the training sample until the algorithm adjusts the weights of the network to minimize the mean square error of the learning error until a decrease of less than 10 -6 The application of this procedure is carried out in the Rstudio IDE (Integrated Development Environment) program of Neuralnet (2019).
Both methodologies are applied to a supply chain in the context of Ecuador. First the Integration Level (NI) is calculated by the traditional method and then this result is predicted through the neural networks. These two results are correlated and the prediction error is determined. This study is carried out both for different and equal levels of importance and these results are compared.

Results
The procedure for forecasting neural networks is applied, with two specifications when the weight is homogeneous and heterogeneous, based on the established process of the algorithm making the comparisons of the errors.

Case study 1: Textile supply chain in Northern Ecuador
The chain under study has five links and 109 actors, is classified as: suppliers of inputs, suppliers of raw materials, processing center, clothing, distribution and customers. Within the marketing there are two classifications: that of wholesalers who sell their products in large volumes and supply to other actors, on the other hand, we find retailers (which are those that come directly to the customer and are dedicated to selling in small quantities). This may be at the national level and also at the international level, but there are few international sales due to the low collaboration between the actors in the chain.
Input suppliers supply machinery and raw materials, there is only one actor within the area under study. The fabric is the main raw material that is used for the manufacture of shirts, quality and easy access depend on the success of the actors who are dedicated to the transformation of this. These can be industrial fabrics or knitted fabrics. Within this link there are also the manufacture and threads, these are used by manufacturers for clothing.
From the identification of the actors, the checklist for the evaluation of the level of integration was applied to them. On the other hand, the values of the application of the checklist and the analysis of the seven dimensions with the heterogeneous and homogeneous weights are described respectively, as detailed in Table 2 and 3. Both with seven input variables and one output variable.
The architecture of the network, an input layer is identified is composed of seven neurons for each covariate, the hidden layer has ten neurons, and the output layer, one because it is predictable.
A random sample of 70% of the database is taken, thereby performing the neuron training. From the data of each of the variables pass to each input neuron. Weights and balances of each connection are made plus a balance (Equation 3). With the characteristic that weights and balances are used between 0 and 1. The activation function is continued (Equation 4). This calculation is performed on each neuron in the neural network. In the case, that the values as a result of the activation function generates signals of very high or very low levels. This encourages the definition of the importance of each neuron. With the goal of simplifying the calculations, the first derivative of the function used is applied, and together to promote the propagation of the signal forward (importance of the variable). This is applied progressively until the last network layer, resulting layer.
The learning error of the neural network that establishes the difference between the real value of the variable and the estimated one is calculated. If that square error is different from 0, or 10-6, the backprogapation process begins, which is backward learning. Continue to update the weights of the connections back until you reach the input layer, and start again with the fordward process. As a result of the processing of the starting information, trained models are shown in Figures 2 and 3.  Actual and estimated values, corresponding to 30% of the data used to test the model, there are negative estimators, these are preliminary results, the ranges must be adjusted. The execution time of the learning algorithm of neurons with heterogeneous weights is 6.31 seconds and with homogeneous weights is 0.75 seconds. This demonstrates the performance of the second in relation to the predetermined time. The estimated results of the resulting variable with heterogeneous and homogeneous weights (Table 4), demonstrates the use of the neural network model makes better estimates with the homogeneous weights of the input variables in the initial layer.
With the objective of evaluating the model of the neural network, 30% of the data are used, which were not part of the training of the network, on the other hand, the model is applied and the real and estimated values are estimated with the process explained previously. These estimators are compared with the real values and the Spearman correlation coefficient is calculated, in order to establish that the data have similar values and closest to 1 or -1. In relation to the correlation, the results of the chain with heterogeneous weights are low with a value of 0.2251772. On the other hand, the correlation factor of the variables with homogeneous weights is high 0.9754289 as shown in Figure 4.  It is concluded that the application of neural networks can be used with homogeneous weights to estimate the level of integration in the supply chain. This encourages decision-making only with the input variables of the integration level. This analysis is convergent based on the variables and their weights respectively.

Discussion
The study of the integration in the supply chains presents different perspectives: from the management of the flow and the processes from the supplier to the final customer, the integration variables and their optimization (customer service, costs, cycles, demand, inventory) , the collaboration between the actors and their processes, information management and support media (internet and applications), risk prevention (ISO 31000), sustainability and sustainability, agility and traceability over the chain. Despite this variety, there are gaps aimed at the application of technologies and tools that allow the foundation of decision-making, as is the case of the textile supply chain in Northern Ecuador. The incorporation of neural networks allows the identification based on a prospective analysis of possible market changes, and adopting the action plan required to mitigate the effects of the behavior of exogenous variables in relation to the problem under study.

Conclusions
At present, the use of a technique for forecasting the integration of the supply chain is essential when anticipating market changes. It is an indispensable element to minimize the risks and the achievement of the principles of Industry 4.0. In this research, the application of neural networks in the prediction of the level of integration in the chains of the textile industry in northern Ecuador was presented. The study concluded that the use of neural networks is evident for the problem of forecasting integration in the study supply chain with homogeneous weights, which makes it possible to make decisions on equal terms. In addition, a set of techniques that shaped the neural network methodology were used, which demonstrates the robustness of the algorithm and its possible application to different problems. The results obtained show the application in the textile sector in Ecuador. In future research, it is proposed to compare the results of neural networks in different supply chains of study interest.