A mathematical model for the optimal configuration of automated storage systems with sliding trays

This work aims at contributing to the advancement of Logistics 4.0, focusing on the management of the storage of goods. The goal is to solve the complex problem of efficiently and rapidly configuring Vertical Lift Modules (VLMs) with sliding trays in automated warehouses. This problem is still barely discussed in the related literature and most contributions mainly focus on the optimization of the VLM throughput instead of trays allocation and respective items configuration. To fill this gap, this work proposes a novel mathematical model that allows to properly represent and solve this complex problem, taking into account practical logistic constraints. The problem is defined as a mixed integer non-linear programming model, which is validated on realistic scenarios. Further, a scalability analysis is performed to evaluate its performance even in complex scenarios. The obtained results demonstrate the effectiveness of the model in defining space efficient configurations in short computation time.