Mathematical programming modeling for joint order batching, sequencing and picker routing problems in manual order picking systems

This article aims to introduce mathematical programming models for the joint order batching and picker routing problem (JOBPRP) and the joint order batching, sequencing and routing problem (JOBSPRP). For this purpose, we present formulations for the traveled distance and travel time between picking positions in low-level and high-level picker-to-part systems (2D and 3D warehouses) and single-block and multiple-block warehouses. Likewise, we formulate Steiner traveling salesman problem (STSP) models considering multiple pickers, heterogeneous picking vehicles, multiple objectives and due windows. We calculate the number of binary variables, continuous variables and constraints for the proposed models, in order to show the complexity of solving these order picking problems using exact solution methods. As a result, we introduce several mathematical models for manual order picking systems, which could serve as references for researchers interested in finding optimal or high-quality solutions to joint order picking problems, considering realistic warehouse and distribution center environments.