A Matheuristics for the Configuration of Automated Vertical Lift Modules Warehouses

The design of the layout of Vertical Lift Module (VLM) warehouses is a non-trivial process that involves selecting dimensions, internal configuration, and allocation of each tray to avoid space loss while satisfying logistic constraints. Our contribution in this context is a two-phase \textit{matheuristics} --an algorithm that combines exact mathematical methods and heuristics-- to simplify the design of VLMs layout. The proposed matheuristics relies on three Mixed-Integer Linear Programming models, addressing the internal configuration of trays and the allocation of trays into columns based on industrial logistic constraints. This approach requires as input parameters the items features, predetermined tray types with different dimensions, matheuristic settings, and a priority rule for tray allocation. The algorithm outputs to the logistics operator types and quantities of trays needed, internal partitioning, item positions in each tray, and tray positions in each column. Extensive testing demonstrates the effectiveness of our approach under realistic scenarios. Additionally, we introduce a comprehensive set of priority rules for allocating trays into columns, providing a comparison to assist logistics operators in selecting the most suitable for specific scenarios.