The picker routing problem in mixed-shelves, multi-block warehouses

Unlike conventional warehouses, where the inventory of an item is concentrated on a single shelf, the inventory in mixed-shelves warehouses is broken down into units and dispersed throughout the warehouse. As a result, the locations from where items are to be retrieved must be chosen when designing the picker tour. The rare research on the picker routing problem (PRP) in mixed-shelves warehouses focuses on (and heavily exploits the properties of) 1-block warehouses, which are warehouses with only two cross aisles. Here, we tackle the more general PRP in mixed-shelves, multi-block warehouses. To solve the problem, we propose a logic-based Benders decomposition method whereby the master problem selects the locations from where each item is retrieved and the subproblem designs the associated picker tour. We introduce tailored optimality cuts and prove their validity. In addition, we propose a set of various techniques to enhance the performance of the logic-based Benders decomposition, including a lower bounding function and valid inequalities. We show the efficiency and effectiveness of the proposed method through extensive computational experiments carried out on both standard instances from the literature (for the 1-block setting) and newly generated instances (for our case). We also leverage our algorithms to generate managerial insights into the benefits of multi-block layouts and mixed-shelves policies in warehousing.