A Linear Formulation and an Exact Algorithm for the Optimal Order Selection Problem

In this work, we propose a solution pipeline for the Optimal Order Selection Problem (OOS). This pipeline consists of an iterative reduction step of the search space, through two parallel routines that solve subproblems of the OOS with a fixed number of aisles, followed by a linear reformulation for modeling the problem, which can be efficiently solved using modern solvers. The results showed that this exact approach is capable of solving considerably large instances to optimality in a timely manner, finding optimal solutions in 27 out of 35 public instances.