Order Picking Problem: A Model for the Joint Optimisation of Order Batching, Batch Assignment Sequencing, and Picking Routing

Background: Order picking is a critical activity in end-product warehouses, particularly using the picker-to-part system, entail substantial manual labor, representing approximately 60% of warehouse work. Methods: This study develops a new linear model to perform batching, which allows for defining, assigning, and sequencing batches and determining the best routing strategy. Its goal is to minimise the completion time and the weighted sum of tardiness and earliness of orders. We developed a second linear model without the constraints related to the picking routing to reduce complexity. This model searches for the best routing using the closest neighbour approach. As both models were too complex to test, the earliest due date constructive heuristic algorithm was developed. To improve the solution, we implemented various algorithms, from multi-start with random ordering to more complex like iterated local search. Results: The proposed models were tested on a real case study where the picking time was reduced by 57% compared to single-order strategy. Conclusions: The results showed that the iterated local search multiple perturbation algorithms could successfully identify the minimum solution and significantly improve the solution initially obtained with the heuristic earliest due date algorithm.