A Matheuristics for the Configuration of Automated Vertical Lift Modules Warehouses

Abstract

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 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. Note to Practitioners—VLMs are closed structures composed of columns that house a variable number of sliding trays and a lift-mounted module that handles the trays. Their operation revolves around the so-called “goods to the man” principle, where goods are automatically brought to the operator using a dedicated access bay. This design ensures that stored items are easily accessible to operators, reducing time for order picking and improving workplace safety and ergonomics. Designing a VLM for logistics companies is a complex and time-consuming task since it requires optimizing a target objective while satisfying a large set of constraints. The current manual approach lacks automated methods and relies on experienced operators and iterative improvement processes. Our two-phase matheuristic algorithm automates VLMs layout configuration, addressing tasks from item placement to tray allocation within columns. The algorithm is versatile, considering various practical and logistic constraints, making it applicable in warehouse design decision support systems or engineering software.