A robust optimization approach to address correlation uncertainty in stock keeping unit assignment in warehouses

In this study, we address the problem of assigning correlated Stock Keeping Units (SKUs) to storage locations under uncertain SKUs correlation conditions. The objective is to allocate SKUs within the forward picking area of a warehouse to minimize the total picking distance. To quantify the correlation between SKUs, we employ the joint distribution concept, enabling a more systematic representation of their correlations. The problem is formulated as a Quadratic Assignment Problem (QAP), which becomes computationally intractable at large scales due to its complexity. To mitigate this challenge, the QAP model is linearized, and a robust counterpart is developed to effectively handle uncertainty. The robust model was evaluated through various small-scale scenarios. While it yielded optimal results within an efficient time frame for small-scale problems, the solution time increased significantly as the problem size expanded.