Order batching and sequencing for minimising the total order completion time in pick-and-sort warehouses

Under the pick-and-sort order batch processing strategy, orders successively go through an order picking process, a buffer area, and an order sorting process in the form of batches. Owing to the difference in order batches and the limitation of the buffer capacity, blocking in the picking and starving in the sorting often occurs. This leads to a longer order completion time. Therefore, to minimise the total order completion time, this study investigates the order batching and sequencing problem under this strategy to reduce or even eliminate the blocking and starving phenomena. We formulate this problem as a mathematical model. By analysing the model, two useful properties and a lower bound are obtained. Based on these properties, we propose a situation-based seed (SBS) algorithm to solve the problem, which provides the intelligence of coordination for the classical seed algorithm. Numerical experiments demonstrate the superiority, effectiveness and optimality of the proposed algorithm. The proposed algorithm can save 8.359% of the total order completion time compared with the real-life algorithm applied in pick-and-sort warehouses, and its performance is close to the lower bound (only 1.105% gap). In addition, we also provide some management insights on how to coordinate the picking and sorting processes in practical pick-and-sort warehouses.