The Effects of Pick Density on Order Picking Areas With Narrow Aisles Kevin R. Gue Department of Industrial & Systems EngineeringAuburn UniversityAuburn, AL 36849Russell D. Meller Department of Industrial EngineeringUniversity of Arkansas Fayetteville, AR 72701 Joseph D. Skufca Department of Mathematics Clarkson UniversityPotsdam, NY 13699January 23, 2006 Abstract The cost and service performa nce of an order fulfi llme nt cente r are determined par tly by ho w wo rkers are org ani zed into an ord er pic kin g sys tem. One common approach is batch picking, in which workers circumnavigate a picking area with other wo rkers, gather ing items on a pic k list. In some systems with high spac e util ization, narrow aisles prohibit workers from passing one another when in the same aisle, and this leads to cong estion. We buil d anal ytic al and simula tion models of these systems to investi gate their b ehavio r under different level s of activit y . Among other things, our results suggest that when the system is busier and pick density is high — that is, when workers stop often to make picks — congestion is less of a problem and workers are more productive. 1
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The Effects of Pick Density on Order Picking Areas
With Narrow Aisles
Kevin R. Gue
Department of Industrial & Systems Engineering
Auburn University
Auburn, AL 36849
Russell D. Meller
Department of Industrial Engineering
University of ArkansasFayetteville, AR 72701
Joseph D. Skufca
Department of Mathematics
Clarkson University Potsdam, NY 13699
January 23, 2006
Abstract
The cost and service performance of an order fulfillment center are determined
partly by how workers are organized into an order picking system. One common
approach is batch picking, in which workers circumnavigate a picking area with other
workers, gathering items on a pick list. In some systems with high space utilization,narrow aisles prohibit workers from passing one another when in the same aisle, and
this leads to congestion. We build analytical and simulation models of these systems
to investigate their behavior under different levels of activity. Among other things, our
results suggest that when the system is busier and pick density is high — that is, when
workers stop often to make picks — congestion is less of a problem and workers are
configuration determines space utilization by specifying the type of storage racks (single-
deep, double-deep, flow-rack, etc.) and the width of aisles. Narrow aisles result in higher
space utilization, but can lead to increased travel and congestion associated with one-way
travel.
The order picking policy specifies how workers are organized to retrieve orders. Tompkins
et al. (2003) identify three major order picking policies: (1) discrete order picking , in which
a worker picks all the items for a single order on each tour, (2) batch picking , in which a
worker collects items for several orders on each tour, and (3) zone picking , in which each
worker is assigned to a specific area of the warehouse and portions of orders are assigned to
appropriate zones. (Here, we consider discrete order picking to be a form of batch picking,
and therefore use the term batch picking to refer to either method.) Naturally, each methodhas advantages and disadvantages: discrete order picking is simple to implement and not
prone to mispicks, but is labor-intensive; batch picking has higher productivity due to less
worker travel per item picked, but can result in congestion and mispicks; zone picking has
high productivity (if there is sufficient picking activity to keep workers busy), but requires
downstream sortation, which can be costly. In an attempt to garner the advantages from
multiple methods, some warehouses use hybrid policies. We also note that multiple workers
are allowed in a zone in some zone picking systems, but this is rare in our experience.Notice that the physical configuration and the order picking policy might interact. If,
in an attempt to increase space utilization, the designer specifies aisles too narrow to allow
passing (which is not uncommon in practice), then having multiple workers in the same aisle
— as in batch picking — could lead to congestion. This is the situation we consider in our
work. Specifically, we are interested in narrow aisle picking systems (hereafter we mean this
to imply no passing within the aisles) when batch picking is the order picking policy; that
is, when there can be congestion among workers. We have visited narrow aisle systems withbatch picking that were designed this way and one, which we describe below, that was forced
into batch picking by a need for more throughput.
But we believe our work is relevant for another reason. Our experience suggests that batch
picking is not very common in narrow-aisle systems because managers believe that if required
to produce high throughput, congestion would be a major problem. Therefore, managers
often choose zone picking when narrow aisles prevent workers from passing, without (in our
opinion) carefully weighing the disadvantages of zone picking, such as the cost of downstream
sortation, the difficulty of balancing zones, which leads to the possibility of idle workers due
to zone imbalances, and so on.
The models we present suggest that the effect of congestion in narrow aisle systems —
particularly busy ones — is misunderstood. The idea for our work came after discussions with
a distribution center manager who told us he used zone picking rather than batch picking
in a narrow aisle picking area because the pick density (the probability that a worker will
pick from any given location during his tour) was so low (corresponding to low throughput).Several months later, when we visited again, he had converted the area to batch picking,
citing a sharp increase in requests from this area and a need to increase the throughput; that
is, pick density was high . This was not in keeping with our observation of industry practice,
which seems to use zone picking to avoid congestion in busy picking areas with narrow aisles.
His statement led us to pose the following questions:
•Does lower pick density lead to more congestion in narrow-aisle systems? Why? What
is the relationship between pick density and congestion, and how should this influence
the design of an order picking system?
• Could we develop insights that would help designers know if congestion would be a
problem in narrow-aisle, batch picking areas?
Here, we present analytical and simulation models of narrow-aisle batch picking systems
and show that our DC manager was mostly correct: as throughput increases to high levels
in a narrow-aisle system, congestion among workers does (according to our models) tend to
Figure 1: A graphical representation of a batch picking system with narrow aisles. Workers
travel one-way within aisles gathering items (indicated by black dots) as required.
and customers can be blocked by a customer receiving service ahead. Unlike our model,
customers receive service at only a single station before exiting the system. Eisenstein
(2001) examines the design of picking lines in a zone picking system. Il-Choe et al. (1992)
discuss the tradeoffs between zone picking and batch picking, but do not examine in-the-aisle
blocking. Rouwenhorst et al. (2000) raise, but do not address, the question of batch versus
zone picking in discussing a preliminary model of how to design a warehouse.
3 Analytical models
In the system we model (see Figure 1) workers circumnavigate unidirectional aisles making
picks where required, and there is no passing. If a worker’s next pick is beyond the location
of a downstream worker, the upstream worker is blocked until the downstream worker moves
beyond the upstream worker’s next pick. We assume that the workers in the batch pickingsystem travel in an aisle-by-aisle fashion due to the one-way aisle structure (i.e., to skip an
aisle, the worker would have to look ahead and see that he does not have any picks in the
next two aisles — an event that rarely occurs). We address other limitations of the model
the next picking point in this epoch, unless that point is occupied by another worker making
a pick. In that case he is blocked for that epoch. Since the picking area is circular, either
worker can block the other. We assume that once a pick is made at a point, the worker will
move past the current point in the next epoch with probability 1. Assume that workers have
the same picking time, walking speed, and probability of stopping at any picking point.
Consider the distance Dt between Worker 1 and Worker 2 at epoch t, where worker
numbers are assigned arbitrarily, a priori , and never change. The distance is always equal to
(n + (Worker 1 position) − (Worker 2 position)) mod n. Since the workers are not allowed
to be at the same picking point, 1 ≤ Dt ≤ n − 1. For example, in a picking area with n = 6
picking points, the workers could be as close as points 2 and 1 ( Dt = 1) or as far away as
points 6 and 1 (Dt = 5).The sequence {Dt} is not a Markov chain because if a worker picked during the last
epoch he must move during this epoch; therefore, Dt+1 depends on Dt and on the action
of the workers in the previous step. To establish the Markov property we must include the
history of the previous step in the state. We label states as rxy, where x and y represent the
previous action of Workers 1 and 2, respectively. For example, state 3 pw says that workers
are 3 picking points apart, Worker 1 just picked, and Worker 2 just walked. The state 1wp
is not achievable because it indicates that workers are adjacent immediately after Worker1 walked and Worker 2 picked, which could only happen if the workers occupied the same
picking point in the previous epoch. We called this the blocked state instead. All other states
are achievable except state (n − 1) pw, which we also label as blocked.
We order the states {1 pp, 1 pw, blocked , 1ww, 2 pp, 2 pw, 2wp, 2ww, . . . , (n − 1) pp, blocked , (n −1)wp, (n − 1)ww}. Figure 3 illustrates the transitions. The resulting transition matrix is
manager stated that zone picking was used because of the low pick density. During our
second visit, about 2 years later, the same picking area had shifted to a form of batch
picking. Managers said the shift was due to a significant increase in business and the need
to increase throughput. The requirement for increased throughput translated into a higher
pick density. The shift to batch picking meant having to have multiple workers per aisle,
and this did lead to some congestion. At the time of our second visit, there were 13 workers
in the 8 aisles, which contained a total of 144 picking points.
Workers dealt with congestion in a different way than we have modeled, loosely following
this protocol: when one worker is blocked by another, they quickly confer to decide if a pass is
appropriate based on the number of picks each has remaining in the aisle. If appropriate, the
downstream worker drives through the aisle and circles back behind the blocked worker, thusallowing him to pass. The interesting part of this protocol is that there is still a productivity
penalty for blocking, but some of it is shifted to the blocking worker.
While the Lathrop DC case does not validate our models, it does provide anecdotal evi-
dence that increasing pick density in a narrow-aisle system should lead managers to consider
batch picking.
6 Conclusions
Our work is an effort to gain insights into the effects of pick density on operator blocking
in systems with high space utilization. These systems typically disallow passing due to the
limited width of aisles, and so are susceptible to worker congestion when firms use batch
picking.
In general, we find that congestion among workers can be a significant issue in batch
picking areas with high space utilization. Blocking was between 2–11% for systems withpassing allowed (at the end of the aisles) and reasonable numbers of workers, picking points,
and pick density (see Figure 10). As expected, we also find that increasing the number of
workers in a batch picking area tends to reduce productivity for all workers in that area. As
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