Assigning products in a Vertical Lift Module supermarket to supply production lines

Abstract

This paper presents the development of a mathematical model for product assignment in a Vertical Lift Module (VLM), which are increasingly em-ployed in the industrial sector due to their advanced technology and efficient parts-to-picker process. Mathematical modelling plays a crucial role in address-ing the complexity of these problems and providing intelligent and innovative solutions. Despite being a tactical problem with medium-term implications, the competitive nature of the industrial environment demands quick adjustments driven by the mass customization paradigm. This requires continuous evaluations to reconfigure the supermarket accordingly, which can be efficiently accom-plished through the rapid application of artificial intelligence using advanced mathematical methods. The proposed integer linear programming, which is based on the well-known transportation problem, features a simple objective function aimed at minimizing the number of trays in the VLM. Additionally, five constraints are included to ensure the applicability of the model to real-world scenarios. The simplicity of the AMPL implementation of the mathematical model is emphasised. Experi-mental computation using real data validates the proof of concept and assesses the impact of introducing new rules for product assignment. This research also explores the potential for optimising warehouse operations and suggests avenues for further investigation.