Solving the joint order batching and picker routeing selection problem in warehouses

In this work, we address an extension of the order batching problem (OBP) called the joint order batching and routeing policy selection problem (JOBRPSP). It deals with determining batches of orders and selecting for each batch a route from three policies–return, traversal and largest gap–to minimise the total distance of the pickers under a given storage policy. To the best of our knowledge, this extension has not been addressed before in the literature. We propose two exact solution approaches for the optimal solution of the JOBRPSP: column-and-cut generation and branch-price-and-cut schemes. Both approaches make use of two different labelling algorithms and two valid cuts proposed in the literature for the OBP. Using two sets of problem instances–one with a single-block layout generated from the benchmark instances in Muter and Öncan [2015. “An Exact Solution Approach for the Order Batching Problem.” IIE Transactions 47 (7): 728–738], and another with a two-block layout taken from Van Gils et al. [2019. “Formulating and Solving the Integrated Batching, Routing, and Picker Scheduling Problem in a Real-Life Spare Parts Warehouse.” European Journal of Operational Research 277 (3): 814–830]–we measure the benefit of simultaneously considering multiple routeing policies compared to a single routeing policy. We find that the benefit of adopting multiple routeing policies varies depending on the routeing and storage location policies adopted, and can be as high as 37.63% and 29.27% in warehouses with single-block and two-block layouts, respectively.