Timing Picking Waves in a Warehouse

Abstract
To facilitate eÆcient picking tours and worker supervision, warehouses often release
orders to workers in picking waves. The timing of these waves determines how long
orders sit in the queue waiting to be processed, and so provides some control over
average order cycle time. We show how to time picking waves in a warehouse to
minimize average order cycle time. We report on results at a warehouse in California,
which reduced average order cycle time by more than 25% after restructuring its picking
waves. We also argue that cycle time may not be the best metric for many distributors,
and propose a di_erent one based on the practices of a leading e-commerce distributor.
Keywords Warehousing, Distribution, Measurement and methodology, Personnel and shift scheduling

Background
Reducing cycle time in the supply chain means lower inventories and better response to
customers. As distribution _rms wring the last drops of ineÆciency out of their distribution channels, warehouses have focused on tightening up processes and reducing costs. Moreover, the need to satisfy increasingly demanding customers has led to new performance measures that will require even more emphasis on process optimization and cost cutting.
In the future, _rms will have to adapt to the world of e-commerce distribution: direct
customer orders via the Internet, precise order tracking, stringent performance measurement and even auction-based services. As many e-commerce retailers have found, customer satisfaction goes beyond the web experience to e_ective distribution and order delivery. The Internet has also bred the impatient customer, who expects delivery of products ordered on the web almost as quickly as the clicks it took to place the order. Firms are responding by
restructuring processes to reduce order cycle time in the warehouse. The thought is that
reduced order cycle time will improve customer service.
In the warehouse, one component of order cycle time is the time an order spends waiting
to be downloaded, or pulled, from the information system. Waiting time occurs because
work is not released to workers continuously, but rather in batches called picking waves.
Warehouses routinely use picking waves to improve the eÆciency of picking tours. When orders are batched, the _xed time that it takes to circumnavigate a picking area is amortized over more orders, thus reducing average cycle time; but if the batches are too large, cycletime goes up because orders wait excessively in the queue.
We investigate the e_ects of the number and timing of picking waves on average order
cycle time at a warehouse. We describe a simple model, which we solve with a genetic
algorithm, that _nds the optimal times to release work to the warehouse, given its speci_c
order arrival distribution. We report the use of the model at a large warehouse in California,which reduced average order cycle time by more than 25% after restructuring its pickingwaves. After presenting the results, we argue that minimizing cycle time in most cases is not the right objective. We present a superior objective and show how to modify our model to accommodate it.

Choosing picking waves
The test site for our study is a large, multi-warehouse complex (hereafter, \the warehouse")located in California, which supports customers throughout the United States and Asia.The warehouse handles all types of material, from pallet loads to individual piece parts, and employs several methods of storage and material handling, including block stacking, palletrack, man-aboard picking cranes, and mini-stackers.
Because the warehouse supports customers from such a geographically diverse region,
orders arrive throughout the 24-hour day. Customers order via an information system that
holds orders in a queue until the warehouse downloads, or pulls, them from the system. Oncethe orders are in the warehouse system, they are transmitted to handheld or mounted RFdevices maintained by the workers, creating a wave of orders. Workers then traverse their areas, picking orders into totes or onto pallets as appropriate. From the picking area, ordersmove to packing, then on to the shipping area, where workers sort them by customer andtransportation mode.
The number and timing of picking waves determine to some degree the cycle time for
orders, because they determine how long orders spend in the queue. The size of the wave
also determines how long a picking tour will be, which also a_ects cycle time.

Theory and practice
Why not release the work continuously? In theory, releasing the work in a continuous streamminimizes average order cycle time. Imagine that a new order arrives and is transmitted toa worker in an aisle at the moment he is about to pass the item's location.
Proposition 1 Passing over a pick always increases average order cycle time.
Proof Assume total travel in the aisle takes non-zero time s and there are n + 1 picks
remaining in an aisle, each of which takes time t. Assume, without loss of generality, that
we are considering whether or not to pick the next item in the aisle. Consider the average
cycle time delay experienced by all n + 1 items: if we pick the next item, then total delay ist for each of n items, and average delay is ntn+1; if we pass the next item and pick it on the3next tour, then total delay is at least s + nt for that item, and average cycle time delay is s+nt n+1 > nt n+1; therefore, average cycle time is greater if the pick is passed over. 2
Proposition 1 suggests that the optimal order picking strategy is to have workers circum-
navigate the warehouse continuously, picking orders as they appear on their handheld RF
devices. In practice, this is infeasible for a number of reasons. First, order pickers typically have other duties involving paperwork, cleaning, and stowing that are normally done be-tween picking waves. The wave structure allows supervisors to assign workers to other tasksbefore the next wave begins. Second, the warehouse management system must support thecontinuous feed, inserting and sorting orders appropriately as they arrive. (The warehouse management system at our test site was not con_gured to do this.) Third, workers could spend much more time traveling, especially during slow periods, thus wasting labor; that is, continuous picking minimizes cycle time, but at the expense of higher labor costs.What is the minimum time between waves? The answer depends on a number of things:the time required to circumnavigate each picking area, the time to pick an individual order, the order arrival pattern, and the amount of slack time needed by supervisors to accomplish other things with the workers. At the warehouse, managers suggested that picking waves separated by 2 hours were possible, but waves in consecutive hours were not.

The model
Consider a warehouse that receives orders continuously, but not necessarily uniformly, through-out every 24-hour cycle. Every hour the warehouse has an opportunity to release all orders in the queue to the warehouse, or it may delay until a future hour.
Assume that orders arrive to the warehouse every hour according to some distribution.
We seek a set of n picking waves that minimizes average order cycle time. Because total system throughput (orders/day) is _xed, we know by Little's Law that minimizing the average work in process inventory also minimizes the average cycle time.
Planning picking waves is similar to the well-studied production lot-sizing problem with
time-varying demand (see Nahmias, 1997, for a discussion of di_erent solution methodologies). In our case, inventory holding cost is simply one hour per unit per time period, but the notion of setup cost is di_erent. In the lot-sizing problem, one incurs a monetary setup cost each time a new lot is ordered. In our problem the warehouse incurs a _xed time penalty for each wave (in the form of a picking tour) that could prevent scheduling a wave in the next hour. We work around this issue by specifying the number of waves a priori. ( to be continued……………. )

Source : Kevin R. Gue Department of Systems Management
Naval Postgraduate School Monterey.