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 consists 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 has 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 exists 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 an exponential Mixed Integer Linear Program (MIP) formulation for the joint order batching and picker routing problem with picker congestion. To solve the model a heuristic column generation approach is proposed, solving the pricing problem with a dedicated dynamic programming algorithm. Computational results will be presented and discussed.