At the operational level, warehouse management mainly focuses on the efficient execution of the picking process. In this work, we investigate the picking activities, that consist in collecting all the products of a given set of customer orders. Products are located into a warehouse in a set of parallel vertical aisles. To collect them, human operators push a trolley with a fixed capacity. As a consequence of the trolley capacity, orders must be grouped into batches. Each batch is collected separately by a single picker. To retrieve all the products of the orders in a batch, each picker as to be routed in the warehouse in order to minimize the total distance or time. Usually, the works in the literature assume that no congestion exist in the warehouse, so given a set of batches, the route for each batch can be optimized independently. However, such a situation is far from reality.

In this work we propose to model the delay produced by picker congestion, and provide a Mixed Integer Linear Program (MIP) formulation for the joint order batching and picker routing problem with picker congestion. Due to the characteristics of the human behavior, we propose a rough estimation of the level of congestion instead of an exact coordination of the pickers. Given the complexity of the model due to the introduction of a timing aspect, a two-steps solving procedure is described. Computational results are presented and discussed.