Order fulfillment is the most expensive and critical operation for companies engaged in e-commerce. E-commerce distribution centers must rapidly organize the picking and sorting processes during and after the transaction has taken place, with the ongoing need to create greater responsiveness to customers. Sorting brings a relatively large setup time, which cannot be well admitted by existing polling models. We build a new stochastic polling model to describe and analyze such systems, and provide approximate explicit expressions for the complete distribution of order line waiting time for polling-based order picking systems and test their accuracy. These expressions lend themselves for operations and design operations, including deciding between “pick-and-sort” or “sort-while-pick” processes, and warehouse performance evaluation
