This scientific attempt is dedicated to model and solve the production inventory system (PIS) in supply chain (SC). The original problem is modelled by an Optimal Control Problem (OCP) with disturbance term and stochastic deterioration in two levels SC that it is possible to return the goods. As we know, this research is the first attempt for modelling and resolving such a PIS in supply chain management (SCM) with stochastic deterioration. The SC model contains two-level; Each level consists of a firm and each firm has a manufacturing factory and a recycling. Also, items are broken down according to Weibull distribution and returned to the firm for recycling. The SC is modelled as a dynamic system and then is reformulated as an OCP. The OCP is changed to a system of equations so that an artificial neural network (ANN) is provided to solve it. For demonstrating the proposed scheme’s effectiveness, performance, and efficiency of the model a real-world problem and an example are given. The results of validation and sensitivity analysis show the convergence of the variables’ response to the target values and their logical behavior against the change of parameters.

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