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04-11
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Duki} G., Olui} ^.: Zaporedje prevzema naro~il - Order-Picking Routing Policies
Prevzem naroèila je postopek zbiranja in priprave izdelkov v skladièu, glede na doloèeno naroèilo
kupca. Je najbolj teavna in draga dejavnost v skladièu. Za prevoz porabimo 50 odstotkov celotnega èasa
prevzema naroèila. Zmanjanje prevoznih poti je eden glavnih ciljev naèrtovalca skladièa.V prispevku smo
predstavili obirne simulacijske analize naèrtovanja poti in razporeditve polic s primerjavami hevristiènih
metod naèrtovanja poti in optimalnim algoritmom
© 2004 Strojniki vestnik. Vse pravice pridrane.
(Kljuène besede: skladièa, prevzemi naroèil, naèrtovanja poti, skladièenje)
Order-picking, the process of retrieving items from storage locations in response to a specific customer
request, is the most laborious and the most costly activity in a typical warehouse. As 50% of the total order-
picking time is spent on traveling, reducing travel distances is one of a warehouse designers objectives. In
this paper an extensive simulation analysis of routing and storage policies in order-picking systems is
presented. The best combinations of routing and storage policies are defined with a comparison between
routing heuristics and an optimal algorithm.
© 2004 Journal of Mechanical Engineering. All rights reserved.
(Keywords: warehouses, order-picking, routing policies, storage policies)
Order-Picking Routing Policies: Simple Heuristics, Advanced
Heuristics or Optimal Algorithm
Goran Duki} - ^edomir Olui}
© Strojni{ki vestnik 50(2004)11,530-535
ISSN 0039-2480
UDK 658.78
Pregledni znanstveni ~lanek (1.02)
© Journal of Mechanical Engineering 50(2004)11,530-535
ISSN 0039-2480
UDC 658.78
Review scientific paper (1.02)
Zaporedje prevzema naro~il: navadna
hevristika, izbolj{ana hevristika in optimalni
algoritem
0 INTRODUCTION
It is well known that logistic costs have an
important influence on the overall success of any
company. In western countries these costs are
estimated to be about 10 to 15% of GDP. Mostly they
are the result of the two main logistics activities:
transportation and warehousing. The order-picking
process, defined as the process of retrieving items
from storage locations in response to a specific
customer request, is the most laborious and the most
costly activity in a typical warehouse, consisting of
up to 55% of the warehouses total operating costs
[11]. The fact that about 50% of the total order-
picking time is spent on traveling gives the potential
to improve order-picking efficiency by reducing
traveling distances. One way to reduce traveling times
is an entirely new design (new equipment, new layout,
automation of processes). Hopefully, there are also
some less radical methods, that do not require large
investment costs.
Using a specific routing policy in
determining the sequences and routes of traveling is
one way to reduce traveling distances. Assigning
items to storage locations based on some rule, i.e., a
storage policy, can also reduce traveling distances
compared to a random assignment. Both have been
proven, used separately or in combination, to improve
the efficiency of the order-picking process. However,
the performances of existing methods depend greatly
on the layout and size of the warehouse, the size of
orders and the picking volume of items. Additionally,
the performance of a particular routing method
depends on the chosen storage policy, and vice versa,
the potential travelling- time savings using a particular
storage policy are not the same for all routing policies.
The purpose of this paper is to identify the
performances of routing policies, depending on the
given situation and the implemented storage policy.
The analysis is restricted to conventional
warehouses with the so-called basic warehouse
layout. These are rectangular warehouses with
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Duki} G., Olui} ^.: Zaporedje prevzema naro~il - Order-Picking Routing Policies
parallel aisles, a central depot (pick up/delivery point),
and two possibilities for changing aisles, at the front
and at the rear of the warehouse. The picking aisles
(the main aisles) are wide enough to allow two-way
travel, but picking can be done from both sides of the
aisle without a significant change in position. The
location of a depot (pick-up/delivery point) is at the
front corner of the warehouse. This is consistent with
observations of several similar studies presented in
the literature [2], [7] and [10].
1 ROUTING POLICIES IN ORDER-PICKING
There are several routing policies developed
and used in practice. They range from the very sim-
ple to the slightly more complex. The performance of
these heuristics depends on the particular operating
conditions of the system under study, as a result of
their definitions. The simplest routing heuristic is the
S-shape policy. When this policy is used, the order-
picker enters every aisle where an item has to be
picked and traverses the entire aisle. Aisles where
nothing has to be picked are skipped. An exception
is made for the last aisle visited in the case that the
number of aisles to be visited is odd. In this case a
return travel is performed in the last aisle visited.
Another very simple routing heuristic is the Return
policy. The order-picker enters and leaves aisles con-
taining item(s) to be picked from the front aisle. The
midpoint routing policy, also one simple heuristics,
looks like the return method on two halves of a ware-
house. Only the first and the last aisle visited are
traversed entirely. Similar to the last heuristic, with
the Largest Gap policy all the aisles that contain even
one item to be picked are also left at the same side as
they were entered, except the first and the last vis-
ited, which are traversed entirely. The gap represents
the separation between any two adjacent picks, be-
tween the first pick in the aisle and the front aisle, or
between the last pick in the aisle and the back aisle. If
the largest gap is between two adjacent picks, the
picker performs a return route from both ends of the
aisle. Otherwise, a return route from either the front
or back aisle is used. The largest gap is therefore the
portion of the aisle that the order-picker does not
traverse. This policy is a slightly more complex rout-
ing heuristic than the first three mentioned. The re-
sulting route is somehow similar, but definitely at
least equal or better than the route defined by the
Midpoint policy in all possible situations. Two rela-
tively new policies developed are the Composite
policy and the Combined policy. The Composite rout-
ing heuristic combines features of the S-shape and
Return heuristics, minimizing the travel distance be-
tween the farthest picks in two adjacent aisles for each
aisle individually. Combined heuristics is also a combi-
nation of S-shape and Return policies, but a small com-
ponent of dynamic programming gives it a possibility
to look one aisle ahead. The decision about the return
or the traversal route in the aisle depend not only on
minimized travel in that aisle, but also on a better start-
ing point for the next aisle. This in turn leads to a better
overall result than the Composite heuristic. All the rout-
ing policies described above by their definitions have
some restrictions when if comes to creating a route.
An optimal algorithm [9], combining a graph theory
and dynamic programming, results in the shortest pos-
sible, i.e., the optimal, route. Examples of routes cre-
ated by these routing heuristics and an optimal algo-
rithm are given in Figure 1.
Fig. 1. Examples of routes using routing heuristics and the optimal algorithm
S-shape Return Midpoint
Largest Gap Composite/Combined Optimal
Depot Depot Depot
Depot
DepotDepot
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Duki} G., Olui} ^.: Zaporedje prevzema naro~il - Order-Picking Routing Policies
Even with the optimal algorithm developed,
the majority of order-picking operations use heuristic
routing policies [7]. The reason for this is that
heuristic policies can provide near-optimal solutions
and avoid the confusion inherent in optimal solutions
[5]. It is true that a specific heuristic policy could in
some situations result in a near-optimal route, but in
some other situations it could perform badly.
Therefore, it is important to know in which situations
some heuristics are good or bad. Even more, which
are better than others, and how much better in
particular situations.
2 STORAGE POLICIES IN ORDER-PICKING
Storage policies assign items to warehouse
storage locations, based on popularity, demand, size,
hazard etc. In order-picking systems, storage policies
are solely based on the rule of assigning the
frequently accessed items to the locations near the
depot [3]. With a volume-based storage policy items
are assigned to storage locations based on the
expected volume. Large savings in travel distances
are possible with volume-based storage when
compared to random storage [8]. The most effective
storage policy in reducing the picking travel distance
seems to be the cube-per-order-index-based storage
policy [4]. The COI-based storage policy means
assigning items with a low ratio of the required
storage space to the order frequency to the locations
nearest to the p/d point. With the assumption that
each type of item is dedicated to only one location,
volume-based storage and COI-based storage are the
same. When warehouses are divided into forward
and reserve areas (picking operations are in the
forward area, items are replenished from the reserve
area), such a situation is likely to occur. One can also
use different types (patterns) of storage, as shown in
Figure 2. Items with a higher volume (or smaller COI)
are stored in the darker locations.
With diagonal storage, the highest volume
item is stored in the location closest to the depot,
while the lowest volume item is stored in the farthest
location from the depot. Tompkins et al., 1996, states
that this type of storage is optimal. Within-aisle
storage means that high-volume items are stored in
the aisle closest to the depot and the low-volume
items are stored in the aisle farthest from the depot.
Jarvis & McDowell [6] proposed this type of storage
for an S-shape routing policy, which was confirmed
by Petersen & Schmenner [8]. In along-front-aisle
(across-aisle) storage, the high-volume items are
stored along the front aisle and the low-volume items
along the rear aisle. Caron et al. [1] used this type of
storage with a Return routing policy. As the Midpoint
and Largest Gap routing policies are characterized
by return traveling from both the front and rear aisles,
a potentially good type of storage for these routing
policies could be along-front and rear-aisle storage.
3 THE COMPARISON OF ROUTING POLICIES
The comparison of routing policies and their
interactions with storage policies is based on an
extensive analysis made by simulation. The pick size
varied from 5, 10, 15, 20, 30 and 40 picks per route.
Two different warehouses, with respect to their size
(small and large), with four different layouts, with
respect to the shape (the ratio of width and depth
were 2:1, 1:1, 1:2 and 3:1, for more explanation readers
are referred to [7]) were analysed. This gives 48
different situations examined for each combination
of routing and storage policy. In order to explain the
potential savings using the storage policies, we first
present an analysis of the routing policies with
random storage. The results are partly illustrated in
Figure 3.
The graph shows the performances of rout-
ing policies depending on the pick-list size for one
examined layout. Two routing policies, Midpoint heu-
ristic and Composite heuristic, are excluded from the
presentation because they are very similar, but
slightly worse, than two other analysed policies, Larg-
est Gap and Combined heuristic, respectively. Note
that despite the fact that the Composite heuristic is
outperformed by the Combined heuristics, it is still
generally better than simple heuristics. The Return
routing policy was outperformed by all the other rout-
ing policies in all the simulated situations, while the
difference increases as the pick-list size increases
Fig. 2. The types of volume-based storage
a) diagonal type b) within aisle type c) along front aisle type d) along front and rear
aisle type
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Duki} G., Olui} ^.: Zaporedje prevzema naro~il - Order-Picking Routing Policies
(but note that this policy could be beneficial in terms
of some other aspects, for instance, the total space
required, as there is no need for a rear aisle). The S-
shape routing policy is just a few percent over the
optimal in the case of a large number of picks, but
does not perform well with small pick-list sizes. In
contrast, the Largest Gap policy performs well with
small pick sizes (about 5% over the optimal policy),
while it is not so good in the case of a large number of
picks. The Combined policy is, in general, the best
heuristic policy. It is slightly outperformed only by
Largest Gap policy in situations with a very small
number of picks in a large warehouse (long aisles).
For a small number of picks per tour, the best heuris-
tic policy for a given situation is only 510% over the
optimal policy, depending on the shape of the ware-
house. The difference between the optimal and the
best heuristics in the case of a large number of picks
per tour is neglected.
To compare the routing policies with
volume-based storage, the best type of storage for a
particular routing policy should be determined. The
simulation analysis included four different volume-
based ABC curves, denoted as 50/20, 60/20, 70/20,
80/20 (the first number indicates the percentage of
the total activity corresponding to items indicated in
the percentage by the second number). Caron et al.
[1] presented a simple function that describes well
the COI-based ABC curve
(1)
where x indicates the ratio of the required storage
space to total storage space, corresponding to the
items whose order frequency represents a fraction
F(x) of the total warehouse activity. The function
above depends on a single parameter the shape
factor s. Note that with each type of items stored in
only one location, the COI-based ABC curve is
identical to the volume-based ABC curve.
For an S-shape routing policy, where the
order-picker entirely traverses each aisle containing
a pick location(s), it is obvious that within-aisle
storage will minimize the travel distance minimizing
both the within-aisles travel component (minimizing
the visited number of aisles) and the across-aisle
component (minimizing the furthest aisle visited).
With Return policy, to minimize the within-aisle
travel component an across-aisle storage is used.
Within-aisle storage minimizes the across aisle
travel component and the expected number of visited
aisles, but due to the increased number of picks per
visited aisle (increased travel per visited aisle) the
total amount of travel distance reduction with the
Return policy is questionable. Finally, somewhere
between is diagonal storage, decreasing to the some
degree the across-aisle component, expected travel
within the visited aisles and the number of visited
aisles. Petersen & Schmenner [8] proposed this type
of storage for the Return policy. To determine the
best type of storage for Return routing policy all three
mentioned types were analyzed. The results showed
that the within-aisle type of storage is outperformed
either by diagonal or across-aisle storage, depending
on the pick-list size, the skewness of the ABC curve
and the size of the warehouse. With a large number
of picks and a less-skewed ABC curve one should
prefer across-aisle storage, while for smaller orders
and a more-skewed ABC curve the diagonal storage
is preferable. As the size of a warehouse increases,
the preference region for across-aisle storage
increases. With the Largest Gap routing policy, within-
aisle storage also minimizes the across-aisle travel
component and the expected number of visited aisles.
Like the Return policy, an increased number of picks
per visited aisle leads to a reduced largest gap in the
aisle, and therefore increased travel within such aisles.
Travel within aisles could be reduced using an across
aisle type of storage. As the order-picker enters the
aisles from the front and rear aisles, depending on
Fig. 3. Comparison of routing policies and the interaction with pick-list size for random storage
70
110
150
190
0 10203040
Pick list size
Travel distance, m
S-shape
Return
Largest Gap
Combined
Optimal
Number of aisles: 6
Length of an aisle: 12 m
Width of front and
rear aisle: 3 m
Distance between two
adjascent aisles: 4 m
(1 )
() sx
Fx sx
+×
=
+
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Duki} G., Olui} ^.: Zaporedje prevzema naro~il - Order-Picking Routing Policies
the position of the largest gap, it is logical to expect
that along the front and rear aisle type of storage will
result in better performance. However, these two
types of storage have no influence on the number of
visited aisles and the across-aisle travel component.
Diagonal storage is again a good candidate,
influencing both the across-aisle travel and travel
within the visited aisle. The simulation results have
confirmed that storing fast movers along front and
rear aisles is better than storing them along just the
front aisle. However, the diagonal storage policy
generally performed better. The best type was, in any
case, within-aisle storage, in all the examined
situations. The routes created by Combined and
Optimal routing policies are a mix of traversal and
return travel (from one or both ends, respectively).
Therefore, the within-aisle type seems to be the best
storage type for those routing policies [8].
Additionally, diagonal storage was analyzed too. With
the Combined routing policy, within-aisle storage is
preferable in the case of a larger number of picks,
irrespective of the skewness of the ABC curve. With
just a few picks per tour, diagonal storage performs
better. For the optimal algorithm the best type of
storage is definetely within-aisle storage.
The simulation results, partly illustrated in
Figure 4., showed that all volume-based storage
methods provide travel savings over random storage.
Large savings (45 to 55%) are possible in
the case of a small number of picks and more-skewed
ABC curves, while for less-skewed curves and large
pick lists the advantage of using volume-based stor-
age is diminished (only a few to 15%, depending on
the routing policy). The Return routing policy is no
longer inferior to other heuristics in all situations.
With a small number of picks and more-skewed curves
it could outperform the S-shape and the Largest Gap
policies. Also, the decision factor between using the
S-shape or the Largest Gap routing policy is no longer
only the average number of picks per (visited) aisle,
but also the skewness of the ABC curve. For an 80/20
ABC curve, the Largest Gap routing performs as well
as the Combined heuristic, even for a very large
number of picks. Generally, the Combined policy is
still the best routing heuristic. The correctly selected
simple heuristic with an appropriate type of volume-
based storage results in travel distances that are only
48% over the optimal route. Combined heuristics is
even better, with only 15% over the optimal travel,
depending on the pick-list size and the skewness of
the ABC curve.
4 CONCLUSIONS
Even with the optimal algorithm developed,
many manual warehouses apply very simple rules for
routing order-pickers [10]. The performance of such
methods heavily depends on the situation, regard-
ing the size and the shape of the warehouse and the
size of the pick lists. The correctly selected routing
heuristic could result in routes that are only a few
percents over the optimal route. On the other hand,
bad decisions regarding routing policy could lead to
very inefficient order-picking. With storage assign-
ment involved, the right selection is even more com-
plex. Even though all volume-based storage meth-
ods reduce the travel distances of order-pickers, each
routing policy has its own best type of storage for a
particular situation. Choosing the best combination
of routing and storage policies is therefore a crucial
task in improving order-picking efficiency. The opti-
mal algorithm with within-aisle storage is definitely
the best choice. However, it one seeks to avoid the
possible confusions of order-pickers following the
optimal routes, the near-optimal solutions are also
available. Even the simplest routing heuristics in com-
bination with a belonging type of storage could, in
some situations, result in routes that are not more
than a few percent over the optimal.
Finally, it should be noted that the analysis
was restricted to the manual, narrow-aisle warehouses
with only one block. Having one or more cross-aisles
Fig. 4. Comparison of routing policies with volume-based storage and the interaction with pick-list size
60
85
110
135
160
0 5 10 15 20 25 30 35 40 45
Pick list size
Travel distance, m
S-shape
Return
Largest Gap
Combined
Optimal
Number of aisles: 6
Length of an aisle: 12 m
Width of front and
rear aisle: 3 m
Distance between two
adjascent aisles: 4 m
ABC curve: 80/20
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Duki} G., Olui} ^.: Zaporedje prevzema naro~il - Order-Picking Routing Policies
(two or more blocks) in some situations could de-
crease travel distances. If the aisles are wide, the
traversal travel has to include crossovers from one
side of the aisle to the other. As a consequence, the
preferences of some routing policies (and combina-
tions with storage policies) could be changed with
respect to other. Also, the paper was focused on only
two order-picking methods: routing and storage.
Batching, grouping the customer orders into one pick-
ing order; and zoning, dividing the picking area into
zones, are also proven to improve the order-picking
efficiency. If used, one should be aware of the possi-
ble interactions of order-batching and zoning meth-
ods with routing and storage policies.
5 REFERENCES
[1] Caron, F., G. Marchet & A. Perego (1998, Routing policies and COI-based storage policies in picker-to part
systems. International Journal of Production Research, 36(3), 713-732.
[2] Chew, E.P. & L.C. Tang (1999) Travel time analysis for general item location assignment in a rectangular
warehouse. European Journal of Operational Research, 122, 582-597.
[3] Choe, K.I. & G.P. Sharp (1991) Small parts order picking: design and operation. Technical Report, Georgia
Tech Research Corporation, Atlanta, Georgia.
[4] Gibson, D.R. & G.P. Sharp (1992) Order batching procedures. European Journal of Operational Research,
58, 57-67.
[5] Hall, R.W. (1993) Distance approximations for routing manual pickers in a warehouse. IIE Transactions,
25(4), 76-87.
[6] Jarvis, J.M. & E.D. McDowell (1991) Optimal product layout in an order picking warehouse. IIE Transactions,
23(1), 93-102.
[7] Petersen, C.G. (1997) An evaluation of order picking routeing policies. International Journal of Operations
& Production Management, 17(1), 1098-1111.
[8] Petersen, C.G. & R.W. Schmenner (1999) An evaluation of routing and volume-based storage policies in an
order picking operations, Decision Sciences, 30(2), 481-501.
[9] Ratliff, H.D. & A.S. Rosenthal (1983) Order-picking in a rectangular warehouse: a solvable case of the
travelling salesman problem. Operations Research, 31(3), 507-521.
[10] Roodbergen, K.J. & C.G. Petersen (1999) How to improve order picking efficiency with routing and storage
policies. In: Forger, G.R. et al., Perspectives in Material Handling Practice (107-124), Charlotte, North
Carolina: Material Handling Institute.
[11] Tompkins, J.A., J.A. White., Y.A. Bozer, E.H. Frazelle, J.M.A. Tanchoco, & Trevino (1996) Facilities planning,
John Wiley & Sons, New York.
Authors Address:Dr. Goran Dukiæ
Prof.Dr. Èedomir Oluiæ
University of Zagreb
Faculty of Mechanical Eng.
and Naval Architecture
Ivana Luèiæa 1
10000 Zagreb, Croatia
goran.dukic@fsb.hr
Prejeto: 4.6.2004 Sprejeto: 30.9.2004 Odprto za diskusijo: 1 leto
Received: Accepted: Open for discussion: 1 year
