Joint order batching and picker Manhattan routing problem

•We jointly consider order batching and order routing, measured precisely by Manhattan distance.•We develop particle swarm optimization (PSO) with bad experiences for this problem.•We propose a solution representation to handle batching and routing simultaneously.•We theoretically analyze stability and convergence of the proposed PSO heuristic.•We evaluate performance of the proposed PSO heuristic for a real-world PC company. In picking product items in a warehouse to fulfill customer orders, a practical way is to classify similar orders as the same batch and then to plan the optimal picker routing when picking each batch of items. Different from the previous problems, this work investigates the joint order batching and picker Manhattan routing problem, which simultaneously determines the optimal order batching allocation and the shortest picker Manhattan routing that cannot pass through storage shelves in the warehouse, under some practical constraints. This work further addresses this problem by particle swarm optimization with bad experience to avoid bad solutions, in which a novel solution representation is designed for simultaneously handling both order batching and picker routing. The idea of the design is to transform the warehouse floorplan into a grid, in which virtual order center and batch center are defined to represent symbolic positions of orders and batches of the solution, respectively. By calculating the distance between the two centers, similar orders are categorized as the same batch. Additionally, theoretical analysis of convergence and stability of the proposed approach is also derived. Performance of this approach is evaluated via comprehensive experimental analysis and a case study.