MIP Modeling for Order Picking: A Comparative Approach Between Exact and Approximate Optimization with Item Groupings and Aisles

We developed and compared two formulations of Mixed Integer Programming for the Optimal Order Picking Problem, the theme of the SBPO 2025 Challenge. The exact formulation fully linearizes the rational goal-function. The approximate formulation, based on the discretization of the number of active corridors and the total number of items, reduces the number of variables and, consequently, the processing time. The models were implemented in Java and their performance was evaluated considering CPLEX 22.11 and 20 public instances. With the exact model, in 55% of the cases optimal solutions were obtained within the time limit defined for the challenge. The approximate model obtained viable solutions for all instances, with an average deviation of 24% in relation to the known optimal value. The results show the compromise between solution quality and scalability, as well as the potential of the approximate version for applications that require quick responses, such as e-commerce.