This article presents a deterministic mathematical model for a closed circuit of reverse internal logistics, with application in the automotive assembly sector, which allowed data collection, respecting the confidentiality of the information collected, to improve empty returnable container collection processes. In addition, the object-oriented simulation of the current and proposed situation was carried out, using the FlexSim Problem Solved® simulation software, allowing real-time visualization of the present scenario in the automotive plant and the improvement alternative, achieving in turn with the mathematical model calculate output and preparation of returnable empty containers. First-order differential equations of separable variables were used in the model to find an approximate solution, and with additional design adjustments in the layout of the facilities. Keywords: deterministic, flow racks, inverse, layout, lean, model, objects, process, simulation, tokens, tuggers.