Viable intertwined supply network: Modelling and dynamic analysis using artificial neural networks

The viability of intertwined supply networks (ISNs) has recently been studied as a critical topic in operations management. Modelling the viability of ISNs is considered a promising tool to meet the demands of extraordinary events, such as the Russo-Ukrainian War and the COVID-19 pandemic. To enhance the viability of ISNs, the structures of ISN must be modelled, and the behavioral dynamics of interactions between firms in a changing environment should be analyzed. In this study, a trophic chain-based dynamic formulation of ISN viability is presented, and a solution methodology for dynamic analysis of the ISN viability model is designed. The concept of artificial neural networks (ANNs) in ISN analysis is introduced to predict and analyze future behavioral strategies in buyer-supplier relations. The dynamic model of ISN is represented by a system of nonlinear differential equations and described in terms of three dynamic values: suppliers $X\left(\tau \right)$, focal firms $Y\left(\tau \right)$, and market demand $Z\left(\tau \right)$. The stochastic numerical simulations are performed for the dynamics of ISN model by employing ANNs with a scaled conjugate gradient neural network (SCGNN) in a more advanced and efficient manner. Two numerical cases are investigated to evaluate the performance of the proposed approach. The validation, correctness, and reliability of the proposed stochastic SCGNN technique are analyzed by selecting 78 % of the data for training, 12 % for validation, and 10 % for testing. The correctness of the scheme is authenticated through the overlapping of the proposed and state-of-the-art results. Moreover, the statistical analysis is presented graphically in terms of mean square error, state transitions, function fitness, error histograms. The regression coefficient values are calculated as 1 for each scenario presents the perfect model. Finally, a comparison of numerical results, which shows the overlapping is examined and the absolute error is performed between 10⁻⁰⁵ to 10⁻⁰⁷. The small mean square error performances enhance the correctness of the scheme. These results indicate that the dynamical model can effectively analyze the ISN structures and help researchers and practitioners ensure the survival of supply chains during extraordinary events.