库伦吧-新学期打算作文

附录
英文原文
Ling-feng Hsieh · Lihui Tsai

The optimum design of a warehouse system on order picking
efficiency
Received: 11 June 2004 Accepted: 6 September 2004 Published online: 4 May
2005 Springer-Verlag London Limited 2005

Abstract From literature review and deep understanding on the
practical industry, it is understood that the proper use of storage
assignment policies can use minimum storage space to reach the
purpose of minimum total traveling distance, and this has a direct
impact on enhancing the order picking performance. At the same
time, proper routing planning can minimize overall order picking
cost, and finally reach the goal of picking performance
enhancement in unit time. Therefore, this paper considers the
effects on the order picking system performance for factors such as
quantity and layout type of cross aisles in a warehouse system,
storage assignment policy, picking route, average picking density
inside an aisle, and order combination type, etc. A software,
eM-plant, will be used as a simulation and analysis tool, a
warehouse design database will be developed, which is based on
the minimum overall traveling distance as the optimum
performance index, the cross aisle quantity, warehouse layout,
storage assignment, picking route planning, picking density and
order combination type will be optimally integrated and planned in
the warehouse system. Finally, we provide this database to the
industry as a reference in the warehouse planning or warehouse
design improvement in the future.
Keywords Averaged picking density inside an aisle · Cross
aisle · Order picking performance · Picking route · Storage
assignment policy
1 Introduction

Among the internal operations in the distribution center, order
picking operation is an important and yet tedious task. From the
labor requirement point of view, currently, most of the distribu
L.-F.
Hsieh (~) · L. Tsai
Department
Chung Hua University,
of Industrial Management,
No. 707 Sec. 2 WuFu Road, Hsin-chu, Taiwan 300, R.O.C.
lfhsieh@
E-mail:
tion center still belongs to labor-intensive industry, and the labor
cost directly related to the order picking operation occupies even
above 50% of the overall cost. Many complicated merchandise
types are its characteristic, and some internal operation modifi-
cation can reduce the company’s cost easily. It is an urgent topic that
needs to be taken care of. Therefore, order picking operation
performance has an overwhelming effect on the warehouse’s
operating cost. Thus, warehouse design plus storage assignment
and picking routing planning will undoubtedly enhance the op-
erating efficiency and the space utilization, and reduce the order
picking cost.
This paper is based on the model provided by Vaughan and
Petersen [1], adding to it three factors: storage assignment policies,
order picking strategies and order combination type. Because all
three factors will affect the order picking efficiency, we take them
into account in the model, and add also different ways of storage
location planning, different picking density inside an aisle, different
picking strategies and single order picking or picking by combining
similar order plus recombining later. We hope that by doing
simulations on different combinations, we can produce an
optimum design for the warehouse system in order to enhance the
order picking operation efficiency.
A good warehouse system should ensure easy and efficient
access of merchandise, properly use the storage location to find the
shortest path, and finally to deliver the merchandise in a rea-
sonable time. This paper is focusing on the factors such as cross
aisle quantity, storage assignment, picker route, picking density
inside an aisle, and different ways of combination of order in the
picking operation storage area of the distribution center. We hope
to perform a systematic analysis and research on the factors in
order to obtain shortest travel distance.
Finally, verified by simulation result, a database for warehouse
system design will be developed, and we provide this database to
the warehouse industry as a reference in the warehouse system
planning. Good picking operation is expected to enhance the
production efficiency, and accompanied with perfect warehouse
system planning and picking policy decision will surely help the
company to reduce cost effectively.

2 Literature review
Take into account factors that affect order picking system per-
formance, this paper will aim at solving the problems of warehouse
system design in four directions of research such as “warehouse
layout”, “storage assignment policy”, “picker routing policy” and
“combination of order”.

2.1 Warehouse layout design
One of the very important factors affecting the order picking system
is the storage area planning. Ashayeri [2] suggests a solution for the
warehouse layout problem, targeting a goal of minimum building
cost or material handling cost. Generally speaking, the warehouse
layout is based on a rectangular shape. Caron et al. [3] propose that
the warehouse layout can be divided into three types. The first is
parallel storage aisle with IO station that is located in the middle of
the head or end of the aisle; the second and third are vertical aisle,
but the IO station is located in the middle and lower left,
respectively.
According to the research from Roodbergen and Koster [4], they
consider to put cross aisle between the originally parallel aisles, and
compare the result with that without cross aisle. They found a
distinguished difference of average picking distance between the
two cases. Ratliff and Rosenthal [5] study the picking problem in
rectangular warehouse, where there are only pathways at the two
ends of an aisle. They use graph theory to find the shortest picking
time, and find that the picking time is independent of the
merchandise items quantity but linearly dependent on the quantity
of the pathways. Vaughan and Petersen [1] study the effect of order
combination type in the cross aisle layout on the picking distance.
They found that when the cross aisle is in the optimum condition, a
most beneficial effect will be generated. Roodbergen and Koster [6]
find an optimum combination of multiple cross aisles and picking
path.
Caron et al. [7] find that the warehouse layout has a distin-
guished effect on picking travel distance. They prove that the layout
design has an effect of more than 60% on the total travel distance,
and also find the relationship between warehouse layout and
picking travel distance. Vaughan and Petersen [1] develop a
heuristic algorithm to obtain an optimum quantity on cross aisles in
order to generate an optimal performance, whereas Roodbergen
and Koster [4] compare the average travel time between normal
layout and a cross aisle layout and prove that the warehouse with
cross aisle will have a shorter average travel time. Therefore, one of
their research highlights is to build an optimum aisle design of a
warehouse system.

2.2 Storage assignment policy
Generally, the storage assignment policies are as follows: random
storage, classified storage, fixed storage, volume-based storage, etc.
Rosenblatt and Eynan [8] suggest that the assignment basis of
classified storage methods is mainly on turn over rate. Their
conclusion suggests that as the classified items increase,
the travel time is expected to be reduced, and a better improve-
ment is found when the classified items are below ten.
Jarvis and McDowell [9] focus on rectangular warehouses,
627
which include cross aisle in the end position and assume every item
has the same picking time. The picking time is proportional to
picking distance, so they use fixed storage method to calculate the
expected picking time. Rosenblatt and Eynan [8] divide the
warehouse into some smaller zones and use classified storage
assignment policy to reduce the total picking time, and finally derive
an optimum automatic warehouse system. Guenov and Raeside [10]
study the optimum aisle width under band heuristic layout and
automatic storageretrieval system (ASRS). They suggest that using
the ABC storage principle will effectively increase the capacity of
the ASRS machine. Jeroen and Gademann [11] explain that
classified storage policy is based on the customer requirement
proportion, and give ways to classify storage location and product
effectively. Petersen and Schmenner [12] investigate the heuristic
picking path, and the storage assignment policy that is based on
picking quantity. They point out that among all the storage methods
based on picking quantity, storing between aisle saves about 10 to
20% picking than that of other storage methods. Jarvis and
McDowell [9] develop a random model that when under transversal
policy, their assignment can obtain minimum average
storageretrieval time.
2.3 Picker routing policy
The purpose of picker routing planning is to reduce the unnecessary
picking distance that in turn results in the shortest and the most
efficient picking. Ratliff and Rosenthal [5] propose a new solution to
the picker routing problem: first to find out individually the picking
distance of each path, then find out the distance connecting to next
path, and repeat in this manner until finish picking all merchandise
items.
Goetschalckx and Ratliff [13] develop an efficient optimal al-
gorithm and show to yield policies with up to 30% savings in travel
time over commonly used policies. It is also shown that, for most
practical aisle widths, it is significantly more efficient to pick both
sides of the aisle in the same pass rather than pick one side and then
pick the other side, unless the pick densities are greater than 50%.
Most warehouses that employ manual order picking are composed
of one or more sections of parallel aisles similar to those illustrated
in Fig. 1 (circles indicate locations of items in the order). There are
four possible policies for picking within an aisle: traversal, split
traversal, return and split return. A traversal policy enters at one end
of an aisle and exits at the other end. A return policy enters and exits
at the same end of the aisle. A split policy is a traversal policy from
both ends or a return policy from both ends. In Fig. 1, aisle 1B rep-
resents a traversal policy, aisle 4A a split traversal policy, aisle 2A a
return policy, and aisle 3A a split return policy. Jeroen and
Gademann [14] consider the picking sequence between zones under
fixed storage policy of an automatic warehouse system, which in
turn result in the shortest travel time during access. Caron et al. [3]
compare the effect of different aisle types on the travel distance and
aisle quantity. The results show that the pick-

ing distance of a warehouse with cross aisle is proportional to aisle
quantity, the picking travel distance increases rapidly as the cross
aisle quantity increases, and the picking travel distance of “Z” shape
aisle is independent of aisle quantity.
Hall [15] investigates three different picker routing policies in a
rectangular warehouse including transversal, mid-point return and
largest gap return. The simulation method is used to compare the
travel distance of different policies, and the result shows that the
largest gap return has better performance than others. Vaughan
and Petersen [1] investigate the warehouse layout that has cross
aisle, to find out a shortest order picking distance. They calculate
picking distance by different experimental combination designs
based on four factors and also by dynamic planning. The result
shows that when the aisle length increases relatively to the aisle
width, an optimal cross aisle quantity can be obtained. Roodbergen
and Koster [6] decide the average travel time of different
warehouse sizes and different picking lists by using dynamic
planning calculation method and find out that if the layout is a
middle aisle type (three cross aisles), the average travel time is
obviously lower. Seven methods of order picking path are
mentioned in that paper. Among them, combined method has the
best performance and the largest gap heuristic is better when
applied to the case with two cross aisles and low picking density.
2.4 Combination of order
Single order picking means that the picking is performed based on a
single order. Instead, the batching and zoning picking is a picking
method that combines different order and performs the picking in
different picking areas, respectively. Lin and Lu [16] propose five
kinds of order classification, accompanied with two policies and
verified by simulation results, they find that each order type has its
own appropriate policy. A consistent result
can be obtained in both minimum picking time and enhancement
of the labor utilization rate. Gademann et al. [17] use a variable
picking operation in parallel aisle warehouse, studying order
batching method in wave picking, give several batches to a set of
pickers, and solve the order batching problem by branch-andbound
method. They find that the major improvement is obtaining a very
simple and efficient process to improve the lower bound of batch
size. Chiang [18] proposes that when the order assignment cost is
high, one can divide the order into multipledelivery or two-delivery
mode. Then it is possible to study the order division method under
periodic review system to find out the optimum delivery number in
the order delivery time period, and finally reduce the overall
inventory cost effectively.
3 Model construction
This article will describe in detail the picking performance factors in
the distribution center warehouse system design such as quantity of
cross aisle, picking path, picking density and order combination. It
also describes how to use the minimum picking distance as a basis
to obtain a warehouse system design of optimum picking
performance combination under different warehouse environments.
Conventional warehouse layout has no cross aisle design.
Therefore, even if the first aisle need only to take a short course to a
certain storage location to pick up some merchandise, you still must
go from the first storage location to the last location or go back to
the first location and then to the second aisle. Therefore, a lot of
unnecessary overlapped distance is taken. To solve the
above-mentioned problem, Vaughan and Petersen [1] propose an
idea of cross aisle as shown in Fig. 2. After adding the




Fig. 2. Warehouse layout with one cross aisle

cross aisle, the total storage locations are not changed, but the main
aisle length has been increased, and therefore the necessary total
space has been increased and the space utilization rate has been
decreased. But adding the cross aisle in turn adds the picking path
flexibility and picking efficiency can be enhanced. This helps to
reduce the overall picking distance. But when excess quantity of
cross aisles are added, as shown in Fig. 3, the storage space is
increased too much, which in turn results in an increasing order
picking distance.
3.1 Warehouse system simulation structure
3.1.1 Warehouse layout consideration
and classification assumption
This article is based on cross aisle quantity (1 ~ 9) proposed by
Vaughan and Petersen [1], and extends further the cross aisle
quantity to 11 in the assumption, 0 to 10, respectively. This article
only considers the input and output points (IO points) located at
both lower left and lower right. In each picking, the picker starts
from the input point, and finishes it by walking to the output point to
finish the picking of an order. If the picking is based on order
combination, it is then to finish all orders in that picking mission,
considering the actual travel distance in the picking. In other words,
it is calculated based on rectilinear distance.

3.1.2 Storage assignment planning
In the warehouse system storage assignment policies, two different
policies exist, namely, one that is based on the merchandise item
access frequency, another is based on merchandise item access
frequency plus merchandise item similarity. Previous study
has proved that the storage assignment policy based on considering
merchandise item similarity as well as access frequency, has helped
to improve the picking efficiency in the warehouse system. This
629
article focuses mainly on the effectiveness of the improvement.

3.1.3 Picker routing planning
For the picker routing planning, consider the two picking policies
proposed by Goetschalckx and Ratliff [13], namely, the modified
Z-pick policy, and the return policy. To deal with the actual situation
of modified Z-pick and return policies, the distance calculation of
return policy is based on rectilinear distance. The calculation is as
shown below:
1. The horizontal distance
M(i, m),
is the distance from the
i
th
aisle transfer to the
m
th aisle, where
a
is the width of each
storage location,
b
is the depth of each storage location, and
w
is the aisle width:
M(i, m)
= 2× |
m
-
i
|×
b
+ |
m

-i -
1|×
W;
for
i,
m
= 1, 2, . . .,
N .

2. The travel distance
Mw
inside an aisle is calculated as the
product of the location width and the actual locations passed,
that is:
Mw
=
a
× the actual storage locations passed
The formation of modified Z-pick picking policy is based on the
basic principles of Z-pick picking policy proposed by Goetschalckx
and Ratliff [13], where the aisle width should be greater than 2.1 m.
In the picking operation, the picker has to cross the aisles frequently.
The track of the paths passed by the picker is similar to a
Z
shape, so
it is named the Z-pick picking principle, as shown in Fig. 4. The
picking distance calculated

630
in Z-pick policy is based on Euclidean distance. For example, in Fig. 4,
the picking locations of a single order are storage location i, storage
location j, storage location k and storage location l, respectively.
Then, the total picking distance is the sum of the following five
distances (in the figure, x is the sum of the storage location number
at one side of an aisle):
1. The distance from point o to point
o~
is:

~ ________
Dist ~o,
o~~
=
a2
+
1
4

w
2
.
2. The linear distance from point
o~
to point

i is:
Dist ~o
~
,
i~
=

ax .

3. The distance from point i to point j is:
~ ____________
Dist (i, j) =
w2
+

(x - 1)
2

a2
.


4. The distance from point j to point kis: Dist
( j, k) = 2 (x - 1) a + a .

5. The distance from point k to point l is:
~ ____________
Dist (k, l) =
w2
+

(x - 1)
2

a2
.


This article proposes a policy to modify the Z-pick picking path,
its main purpose is to delete the conventional limit of Zpick, which
has to go back and forth the two sides of an aisle. The typical Z-pick
picking path planning is as shown in Fig. 5. Because Z-pick picking
principle has the limitation of having to go back and forth around
the two sides of the aisle, when the picking density inside the aisle
is too high, it will add unnecessary distance to cross the aisle.
Therefore, in this article we propose a policy of modified Z-pick
picking path, mainly to modify the picking order inside a single aisle,
hopefully to help the picking performance. The modified Z-pick
method is based on Z-pick basic principle and the most neighboring
method to decide the picking order inside an aisle. It uses further
2-opt to change the picking order, without the limitation of having
to go back and forth around the two sides of the aisle, to find a
picking order inside an aisle, which has minimum picking distance.
For example, at the entrance of each aisle, judge the picking order
inside an aisle as point 2, 3, 4 and 1, as shown in Fig. 6a, which is an
initial solution. Then, use the inner path exchange method to
enhance the picking path. The initial picking path of point 2, 3, 4,
and 1, is then 2-opt changed to point 3, 2, 1 and 4, shown in Fig. 6b,
which is an improved solution.
3.1.4 Picking density inside an aisle
The setup of picking density inside an aisle is mainly based on the
experimental results from Goetschalckx and Ratliff [13], take three
picking density within 50%, such as 10%, 20% and 30%, as an
experimental level.

Fig. 6. a
solution of Zpick picking path
initial solution of Z-pick picking path b improved
3.1.5 Combination of order

In order combination, the main purpose is to reduce the picking
distance. Two main types are considered and explained, namely,
single order picking, and similar order combination picking.

1. Single order picking is picking based on a single order.
2. Similar order combination picking is mainly attributed to the
combination of two orders, where the main condition for
order combination is the similarity between orders.

This article focuses on the distribution center warehouse design
problems. It attempts to construct a model that combines

631
Fig. 7. Combination relationship of 5 experimental factors with different levels
back to point O and starts picking for the next order. The details
constructed by eM-plant simulation software is as shown below.

factors such as cross aisle quantity,
storage assignment, picking path, picking density, order
combination, etc. The combination relationship is composed of
eleven different cross aisle quantities, two storage assignment
policies, two types of picking path, three types of picking density
and two types of order combination, as shown in Fig. 7. The
relationship mainly discusses the effect of the five different factors
on the warehouse picking system at different levels. eM-plant
software will be used as a simulation and verification analysis tool
too.
4 Model construction and simulation analysis 4.1
Simulation environment setup
The picking environment in this simulation experiment is a rect-
angular warehouse. Assuming each storage location is 5 meters and
1 meter in width and depth, respectively, and the IO point is in the
lower left and lower right corner of the warehouse, respectively, the
picker starts from point I to pick merchandise
from the picking point, and after finishing picking operation, goes
1. Aisle width is 3 meters.
2. Every storage location has merchandise on it.
3. There are 240 storage locations in the warehouse, with 240
different kinds of merchandise.
4. The average moving speed of the material handling equip
ment is 30 m

min.
5. The material handling equipment and warehouse system has
no mechanical trouble or out of merchandise situation.
One hundred orders are generated randomly by a computer. The
access rate and the similarity of merchandise are analyzed. In each
test combination, the merchandise item data is transformed to
corresponding same storage locations in order to calculate picking
distance. Numerous combination models are performed ten times
based on factors such as eleven types of cross aisles, two types of
storage assignment policy (SS1, SS2), two types of

632
order picking policy, two types of order combination and three types
of picking density. The current simulation system collects the
related evaluation index data, for example, the average overall
picking distance.
4.2 Simulation experimental result
This article is based on three different picking densities. About 100
orders are used to perform batch experiments on a different number
of cross aisles, storage assignment, picking path, picking density and
combination of orders. About 264 (11× 2× 2× 3× 2) sets of
experiments are performed, and each set of experiment is repeated
ten times. SAS statistical software is used to process the
experimental data for data analysis in this article. The experimental
data is arranged and planned according to differ

Order combination
_storage assignment
_order picking policy
Single order_SS1_
Return
Single order_SS2_
Return
Single order_SS1_
Modified Z-pick
Single order_SS2_
Modified Z-pick
Combined order_SS1_
Return
Combined order_SS2_
Return
Combined order_SS1_
Modified Z-pick
Combined order_SS2_
Modified Z-pick
Table 1. Average order picking distance of density 10% (unit: meter)
ent picking paths, as shown in Tables 1, 2, and 3 for different picking
density of 10%, 20% and 30%, respectively.
From Tables 1, 2, and 3 we know that the average order picking
distance of single order and combined order, under different
storage assignment policies (SS1 denotes the first storage assign-
ment policy that is based on the merchandise item access fre-
quency; SS2 denotes the second storage assignment policy that is
based on the merchandise item access frequency plus merchandise
item similarity) at different density 10%, 20%, and 30% at return
and modified Z-pick picking principles, at different cross aisle
quantity, respectively. The trend of average overall picking distance
versus overall experimental performance, and plot is drawn in order
to understand the effect of these factors on the overall performance
of an order picking system. The comparison of average overall
picking distance for densities of 10% is shown in
Cross aisle quantity
4 5
19054
18432
16469
16105
18874
18082
16069
19066
18760
16676
16401
18925
18413
16262
16025
6
19250
18925
16874
16581
19102
18577
16452
16205
7
19701
19350
17324
16985
19550
19000
16889
16609
8
20315
19955
17899
17569
20167
19599
17453
17174
9
20980
20704
18525
18258
20838
20317
18065
17846
10
21602
21338
19210
18883
21457
20940
18722
18455
0
23968
24105
22420
21529
23544
23386
21128
21055
1
19762
19630
17107
16863
19436
19217
16764
16485
2
18812
18247
16136
15754
18532
17980
15793
15409
3
18777
18221
16211
15983
18588
17833
15835
15662

15784
Table 2. Average order picking distance of density 20% (unit: meter)
Order combination
_storage assignment
_order picking policy
Single order_SS1_
Return
Single order_SS2_
Return
Single order_SS1_
Modified Z-pick
Single order_SS2_
Modified Z-pick
Combined order_SS1_
Return
Combined order_SS2_
Return
Combined order_SS1_
Modified Z-pick
Combined order_SS2_
Modified Z-pick

0 1 2 3
Cross aisle quantity
4 5 6
7 8 9 10
29959
30402
28684
31040
18988
19292
21684
21525
27915
27987
24949
25005
18576
18725
17535
17695
27342
27117
23873
23829
18654
18931
16673
16836
27276
26885
23918
24036
18747
19126
16796
17065
27957
27476
24403
24473
19323
19640
17195
17549
28047
27483
24981
24999
19792
19697
17704
18094
28417
27866
25254
25331
20110
20023
17984
18375
29178
28631
25882
25939
20729
20650
18452
18877
30097
29538
26672
26768
21382
21274
19023
19388
31115
30612
27584
27732
22138
21949
19632
20006
32227
31701
28602
28697
22908
22730
20322
20651

633
Table 3. Average order picking distance of density 30% (unit: meter)
Order combination
_storage assignment
_order picking policy
Single order_SS1_
Return
Single order_SS2_
Return
Single order_SS1_
Modified Z-pick
Single order_SS2_
Modified Z-pick
Combined order_SS1_
Return
Combined order_SS2_
Return
Combined order_SS1_
Modified Z-pick
Combined order_SS2_
Modified Z-pick

0 1 2 3
Cross aisle quantity
4 5
34112
34335
29598
30664
14161
14140
13500
34338
34879
30745
31591
14606
14602
13981
14359
6
34835
35476
31171
32144
14995
15030
14349
14727
7 8 9 10
32123
32662
36618
38230
11815
11941
15603
16539
32809
33216
30562
31224
12415
12541
13419
14132
33110
33070
28879
29465
13009
13092
12779
13280
33194
33406
29192
29977
13597
13570
13019
13555
36008
36636
32108
33064
15570
15611
14798
15240
37250
37967
33074
34182
16151
16211
15312
15763
38595
39197
34098
35249
16751
16757
15773
16202
39862
40390
35277
36445
17345
17293
16226
16793

13954
Fig. 8; the comparison of average overall picking distance for den-
sities of 20% is shown in Fig. 9; and the comparison of average
overall picking distance for densities of 30% is shown in Fig. 10.
4.3 ANOVA statistical testing analysis
The collected average overall picking distance data from the
simulation is arranged and variance analysis is performed. The
Fig. 8. The comparison of
average overall picking dis-
tance for density of 10%
that the order combination, picking density, storage assignment
planning and cross aisle quantity all have obvious different effects
on the average overall picking distance. This article performs
Duncan tests under such a large differing situation to analyze mainly
the average overall picking distance at different cross aisle quantity,
different order combination, different picking density within an aisle,
different order pick-
result is shown in Table 4.
From Table 4, we know

634

ing policy and different storage assignment strategy. The re- From the result of Table 5, we know that the average overlated results and
analysis is shown in Tables 5, 6, 7, 8, all picking distance is no different in two or three cross aisles and 9.
conditions. In set 2, the cross aisle quantities are 1, 4, or 5, re-

Table 4. ANOVA results for relative
travel distance

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e
b
~
c
~
d
~
e
a
~
b
~
c
~
d
~
e
Total

D.F.
1
1
1
2
2
2
2
1
1
1
1
2
2
2
2
10
10
10
10
20
20
20
20
10
10
10
10
20
20
20
20
1451

SS
13007030.88
46314.12
50008.36
2408785.85
6951007.09
270067.59
171726.59
226417.49
181.32
46128.64
75141.25
63255.36
268487.86
141427.74
137971.56
1173055.48
55436.93
2938.91
5182.91
140305.46
35669.73
2624.49
2657.37
181186.60
10635.35
13977.16
11949.41
83123.17
20054.58
11448.67
6409.50
78987256.51

MS
13007030.88
46314.12
50008.36
1204392.93
3475503.54
135033.80
85863.29
226417.49
181.32
46128.64
75141.25
31627.68
134243.93
70713.87
68985.78
117305.55
5543.69
293.89
518.29
7015.27
1783.49
131.22
132.87
18118.66
1063.53
1397.72
1194.94
4156.16
1002.73
572.43
320.47


F test
2616.30
9.32
10.06
242.26
699.08
27.16
17.27
45.54
0.04
9.28
15.11
6.36
27.00
14.22
13.88
23.60
1.12
0.06
0.10
1.41
0.36
0.03
0.03
3.64
0.21
0.28
0.24
0.84
0.20
0.12
0.06

635
p
-value
<
.0001
~

0.0023
~

0.0016
~

<
.0001
~

<
.0001
~

<
.0001
~

<
.0001
~

<
.0001
~

0.8486
0.0024
~

0.0001
~

0.0018
~

<
.0001
~

<
.0001
~

<
.0001
~

<
.0001
~

0.3470
1.0000
0.9998
0.1070
0.9959
1.0000
1.0000
<
.0001
~

0.9951
0.9854
0.9921
0.6705
0.9999
1.0000
1.0000
~
P
<
0.05
































~
a: order combination b: storage assignment strategy c: picking density d: order picking policy e: cross
aisle quantity
Table 5. Comparison of
average picking distance for
different cross aisle quantity
Cross aisle quantity
3
2
1
4
6
7
8
9
10
Duncan group
H
H
G
G 5 G F
F
E
D
C 0 B
A
Picking density
within an aisle
30%
20%
10%
Average picking distance Ranking

678.524
885.669
1080.256
1
2
3
Table 8. Comparison of average picking distance for different order picking policy
Order picking policy
Modified Z-pick
Return

Average picking distance
860.267
902.699
Ranking
1
2
Table 6. Comparison of average picking distance for
different order combination
Table 7. Comparison of average picking distance for different picking density
Order combination
Combined order
Single order
Average picking distance
582.184
911.413
Ranking
1
2
result in the order picking efficiency. Therefore, the addition of two
or three appropriate cross aisles is the best design for en

with one or too many cross aisles, they all have the same bad
spectively. These three cross aisle quantities all belong to Group
hancing the order picking efficiency as well as space utilization G.

In set 3, the cross aisle quantities are 5 and 6, where these rate. From the result in Table 6, we know that the average overtwo cross aisle
quantities all belong to Group F because in cases all picking distance in a different order combination has obvious

636
Table 9. Comparison of average picking distance for different storage assignment
strategy
Storage assignment strategy Average picking distance Ranking
ABC access frequency plus
merchandise item similarity
863.309

1
ABC access frequency 899.657 2

difference. Comparing single order and combination order, we find
that the latter has better average overall picking distance. From the
result of Table 7, we know that the picking density inside the aisle
has distinguished effect on the average overall picking distance: the
higher the picking density inside the aisle, the shorter the picking
distance. From the result of Table 8, the order picking policy has
obvious effect on the average overall picking distance. Comparing
the modified Z-pick picking policy proposed by this article and the
return policy from the reference, the former is more helpful in
enhancing the order picking performance. From the result in Table
9, the different storage assignment strategy has distinguished effect
on the average overall picking distance. The first strategy is based
on ABC access frequency and the other strategy is based on ABC
access frequency plus merchandise item similarity. From the result,
we find that the strategy based on ABC access frequency plus
merchandise item similarity has a helpful effect in enhancing the
order picking performance.
5 Conclusion
In the previous studies on the problems of enhancing the order
picking operation efficiency of a warehouse, from scholars overseas
or domestically, they mostly focus on and are limited to order
picking policy, picking path and storage assignment planning. Few
focus on a combined discussion on the design of cross aisle
quantity of the original warehouse layout, the order picking policy,
storage assignment planning, average picking density inside an aisle,
etc. Therefore, this article develops a combination model for
combining factors such as cross aisle quantity (0, 1, 2, . . . , 9),
storage assignment planning (ABC access frequency, ABC access
frequency plus merchandise item similarity), order picking
policy(return and modified Z-pick), different picking density inside
an aisle(10%,20%,30%), and order combination. Through system
simulation experiments, we verify that we can find optimum
combination for warehouse design in different environment and
better performance is found. It is hoped that this article can be a
practical and useful reference to the industry in the design and
planning of an order picking system in a warehouse system.
From the simulation experiments and statistical analysis, the
current warehouse design environments can be summarized as
follows:
1. The modified Z-pick picking policy developed by this article is
better than return policy in obtaining a better average picking
distance. Therefore, the modified Z-pick picking policy
proposed by this article has more practical use than that of
others.
2. The research presented here finds optimum warehouse design
combination in three different picking densities inside an aisle,
and in different factors such as different cross aisle quantity,
different order picking policy, different order combinations and
different storage assignment planning.
3. The picking distance is better in combined order than that of
single order, and the effect is more distinguished when the
picking density inside an aisle became larger.
4. Storage assignment planning, based on ABC access frequency
plus merchandise item similarity, is sure to be helpful on the
picking performance.
5. There exist interactions among those five factors such as picking
density, cross aisle quantity, picking policy, order combination
and storage assignment planning.
6. From the simulation result verification, we know that appropriate
cross aisle quantity accompanied with storage assignment
planning has a distinguished effect in reducing the overall picking
distance.
7. Plan the storage assignment according to ABC access frequency
plus merchandise item similarity when the order has more
merchandise picking items, and use the similar order
combination method and the modified Z-pick picking policy,
which have better picking performance.
8. This article considers the combination of factors such as cross
aisle quantity, storage assignment planning, order picking policy,
order combination, etc. The work presented here provides a
database based on average overall picking distance as an
evaluation index to the industry as a reference for the
warehouse design or improvement of the warehouse planning.


Acknowledgement
from National Science Council of Taiwan, R.O.C. under the project number: NSC
This research was supported partially by a research grant
92-2213-E-216-026.
References
1. Vaughan TS, Petersen CG (1999) The effect of cross aisles on order
picking efficiency. Int J Prod Res 37:881–897
2. Ashayeri J, Gelders LF (1985) Warehouse design optimization. Eur J
Oper Res 21:285–294
3. Caron F, Marchet G, Perego A (2000) Layout design in manual picking
system: a simulation approach. Integr Manuf Syst 11:94–104
4. Roodbergen KJ, Koster RD (2001) Routing order picking in a ware

house with a middle aisle. Eur J Oper Res 133:32–43
5. Ratliff HD, Rosenthal S (1983) Order-picking in a rectangular ware

house: a solvable case of the traveling salesman problem. Oper Res
31:507–521
6. Roodbergen KJ, Koster RD (2001) Routing method for warehouse with
multiple aisles. Int J Prod Res 39:1865–1883
7. Caron F, Marchet G, Perego A (2000) Optimal layout in low-level
picker-to-part systems. Int J Prod Res 38:101–117
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637
9. Jarvis JM, McDowell ED (1991) Optimal product layout in an order picking
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10. Guenov M, Raeside R (1992) Zone shapes in class based storage and
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13. Goetschalckx M, Ratliff HD (1988) Order picking in an aisle. IIE Trans 20:53–62
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15. Hall RW (1993) Distance approximations for routing manual pickers in
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16. Lin CH, Lu IY (1999) The procedure of determining the order picking
strategies in distribution center. Int J Prod Econ 60:301–307
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batching algorithm for wave picking in a parallel-aisle warehouse. IIE
Trans 33:385–398
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tems. Int J Prod Econ 70:67–76

中文译文


在仓库系统中存取货的优化设计


收到: 2004年6月11号 发表: 2004年9月6号在线出版: 2005年5月4号
Springer-Verlag伦敦有限公司于2005出版
摘要 根据在实际的工业上的文献和深层次调查, 据了解，正确使用的存储空间转存
的规划，可以用最低的存储空间，以达到目的的最短总工作距离。 同时，计划出适当工
作路线可以将存放费用减少到最低, 而且最后在单位时间内实现到提高效率的目标。 因
此, 本文考虑在次序存放系统方面的效果每一因素，比如是仓库系统的数量和地面区划,
储藏任务, 交叉巷道的执行路径, 一个巷道内平均存放密度, 和次序组合类型等等。软件,
设备,将会被当作 一个模拟和分析工具使用，一个关于仓库设计的数据库将会被发展，这
以最小的全部的距离当做最适宜的 表现索引、交叉的行动量、仓库地面区划, 储藏任务，
存放路径计划, 存放密度和次序组合类型将会被最佳地整合而且在仓库系统中被规划。
最终, 当在仓库计划或者将来仓库的创新设计进步的時候，我们提供这一个数据库给工业。
关键字：平均一个巷道存取效率,交叉的巷道，次序存放表现，存放路线 ,储藏任务方案
介绍
在分配中心, 来回存放是一重要的和仍然沉闷的工作。 从劳动需求观点，现在，大
部份的分配中心仍然属于劳力密集的工业, 和直接地讲到次序的劳动费用存放操作占领
甚至高于全部的费用的 50% 的。 许多复杂的货物类型是它的特性、和一些内在的操作能
容易地减少公司的费用。 它是需要被照看的一个紧急的主题。 因此, 次序存放工作就像
在仓库的操作费用上有压倒性的效果。 因此, 仓库设计加储藏任务和来回存放计划将会
毫无疑问地提高操作效率和空间利用, 而且减少次序存放花费。
本文以由佛恩和皮得斯提供的模型[1]为基础,加到它三个因素: 储藏任 务计划、次序
存放策略和次序组合类型。因为所有的三个因素将会影响次序存放效率，我们拿他们进入< br>模型的帐户, 而且增加也不同储藏的方式位置计划,不同的存放密度，在一个巷道、不同
的存放 策略和单独次序存放，或由加上相似的次序稍后的重组。 我们藉由在不同的设备
上做模拟, 我们能为产品生产最适宜的设计，存放系统为了要提高次序存放操作效率。
一个好仓库系统应该确定货物的容易又有效率通路,适当地使用储藏位置找最短的路
径, 和最后递送货物的合理的时间。 本文的重心集中在如下因素，像交叉的巷道量，储
藏任务, 工作路径, 在分配中心的存放操作储藏区域中在一个巷道、和次序的组合的不同
方式内存放密度。 我们希望在因素身上运行一项有系统的分析而且研究为了要获得短的
工作距离。

最后，根据模拟结果查证, 一个数据库为仓库系统设计将会被发展，而且我们当做物
品的叁考提供这一个数据库给仓库系统计划。 好存取操作被期望提高生产效率而且带着
每一计划而且存取决定的仓库系统将会当然帮助公司有效地减少 费用。
2 文献评论
考虑到影响因素，以便存放系统的性能，本文将着眼于问题的解决仓库 系统的设计，
在4个方向的研究，如“仓库布局” ， “存储转让政策” ， “选择路线政策”和“组
合命令“ 。
2.1 仓库地面区划设计
非常重要因素之一影响按顺序存放系统是储藏区域计划。 Ashayeri[2]提出了一个解
决仓库地面区划问题的办法，目的是达到一个最小建筑费用的目标或者资源耗费花费。 一
般来说，仓库地面区划以矩形的形状为基础。 Caron 等人 [3] 计划仓库地面区划能被区
分为三类型。 第一是有输入／输出车站的平行储藏巷道到中央或巷道;那第二和第三是垂
直的巷道, 但是分别地,输入／输出车站位于中央和比较低的左边。
依照来自 Roodbergen 和 Koster 的研究 [4], 他们考虑放交叉的巷道在那之间本
来平行巷道、和比较结果与那没有交叉的巷道。 他们发现一种平均这二个存取设备之间
的平均距离。 Ratliff 和罗森塔尔 [5] 在只有路在巷道的这二个结束的矩形的仓库中研
究存放问题。 他们使用图论找最短的存放时间, 而且找哪一段存取时间不依赖货物计算
量除了路线依赖之外在路的量上。 佛恩和 Petersen[1] 在存放距离上的交叉巷道地面区
划中学习次序组合类型的效果。 他们发现当交叉的巷道在最适宜的情况的时候，最有益
的效果将会被产生。 Roodbergen 和 Koster[6] 找一个多个交叉的巷道最适宜组合而且
存取路径。Caron 等人 [7] 找仓库地面区划有显著的效果关于存取工作距离。 他们证明
地面区划设计有超过 60% 对完全的旅行距离的效果, 以及找仓库绞之间的关系?在外和
存放旅行距离。 佛恩和 Peters en[1]发展了一个启发式的运算法则在交叉的巷道上获得
最适宜的量为了要产生最佳的表现, 然而 Roodbergen 和 Koster[4] 比较平均的工作时
间是常态地面区划和一个交叉的巷 道地面区划的时间段，而且证明仓库与交叉的巷道将会
有比较短平均的工作时间。 因此，他们的研究加亮区之一将建立仓库系统的最适宜巷道
设计。
2.2 储藏任务政策
通常，储藏任务政策依下列各项: 随意储藏、密封的储藏、固定的储藏,以体积为基
础的储藏库, 等等，Rosenblatt 和 Eynan[8] 意味着密封储藏方法的任务基础主要地在
比率上的旋转上。 他们的结论意味着当做密封的项目增加,工作时间被期望被减少, 和一
比较好的改进被发现当密封的项目在下面第十页。贾维斯和 McDowell[9] 把重心集中在

矩形的仓库,最后包括交叉的巷道位置，而且承担每个项目有同存放时间。 存放时间指成
比例所存放距离的时间, 因此他们使用固定的储藏方法计算预期的存放时间。
Rosenblatt 和 Eynan[8] 参阅仓库进入一些较小的地域而且使用机密的存放任务政策减
少总计的存放时间, 而且最后源自一个最适宜的自动仓库系统。 Guenov 和
Raeside[10] 在研究所启发地面区划和自动机械储藏取回系统之下学习最适宜的巷道宽
度.(自动化存储仓库) 他们建议使用美国广播公司储藏原则决意有效的增加能力那自动
化存储仓库以机器制造。 Jeroen 和 Gademann[11] 解释机密的储藏政策以客户需求比例
为基础, 而且屈服于有效地分类储藏位置和产品。 Petersen 和Schmenner[12] 调查启发
式的存放路径, 和储藏任务以政策为基础的存取量。 他们指出在被基于的所有的储藏方
法之中存取量, 储存在巷道之间其他储藏方法超过那节省了大约 10-20%存取量。 贾维斯
和 McDowell[9] 发展任意模型当在横向的政策之下，他们的任务能获得最小的平均储藏
取回时间的时候。
2.3 存取机器工作路线按排政策
计划的存取机器工作路线排定的目的将减少多余的距离存 放距离依次造成最短的和
最有效率的存放。 Ratliff 和罗森塔尔 [5] 计划对发送问题的存取机器新解决办法: 第
一的发现个别的路径的存放距离,然后发现距离对下个路径连接, 而且以这一样子重复直
到完成存取所有的物品项目。
Goetschalckx 和 Ratliff[13] 发展了一个有效率的最佳运算法则和模拟产生政策
决定于 30% 储蓄在旅行时间中过度普遍用了政策。 它也被显示, 大部分来说实际的巷道
宽度, 它重要地是更有效率的宁可在相同的途径中存放巷道的两者边超过精选一边然后
存放另一边, 除非精选密度比 50% 大。雇用人工的次序存放的大多数的仓库由与在图 1
被举例的那些类似的平行巷道的一或者较多区段组成 (圆周指出在次序中的项目的位置).
有在一个巷道里面存放的四个可能的政策: 横越,分散的横越、回返和劈开回返。 一个横
越政策在巷道和出口的一端进入和入口它的在另一端。 一个回返政策在巷道的相同结束
进入而且退出。 一个分散的政策是来自两者的结束的来自两者的结束或一个回返政策的
一个横越政策。 在图 1, 巷道 1 B 一个横越政策, 巷道 4 A 一个分散的横越政策, 巷
道 2 A 一个回返政策、和巷道 3 A 一个分散的回返政策。 Jeroen 和 Gademann[14] 考
虑在地域之间的存放序列在自动仓库系统, 依次造成最短的工作固定储藏政策之下在通
路期间计时。 Caron 等人 [3] 比较不同巷道类型对旅行距离和巷道的效果量。

结果表示仓库的存放距离与交叉的巷道与巷道量成比例, 存放旅行距离快速地增加
当做交叉的巷道量增加, 和存放旅行 形状巷道的距离不依赖巷道量。门厅 [15] 在
包括的一间矩形的仓库截线中调查三个不同的存取工具工作路线排定政策, 在其中点回< br>返和大的缝隙回返。模拟方法用来比较不同政策的工作距离，而且最大的缝隙归还的结果
成绩跟其 他比起来有较好的表现。 佛恩Petersen[1] 调查有交叉的巷道的仓库地面区划,
发现短的次序存放距离。 他们计算存放以四个因素为基础的不同实验的组合设计的距离
以及藉着计划的电动。 结果表示当巷道长度相对地增加到巷道宽度的时候, 最佳的交叉
巷道量能被获得。 Roodbergen 和 Koster 如果地面区划是一个中央的巷道类型 (三个交
叉的巷道) ， [6] 藉由使用出自那计划计算方法和发现的电动决定不同仓库大小的平均
旅行时间和不同存放目录, 平均的旅行时间显然地比较低。 次序存放路径的七个方法在
那纸中被提到。 当以二个交叉的巷道和低 的存放密度适用于情形，在他们之中，组合的
方法有最好的表现，而且最大的缝隙启发比较好。
2.4 次序的组合
单拣货，即存放，是表现的基础上，单一的秩序。相反，配料和分区存放 是一个反复
的方法，结合不同的秩序和执行存放在不同存储领域，分别为。林和 Lu[16] 设计次序分
类的五个类型, 以二个政策陪伴而且被模拟结果查证, 他们找，那个每个次序类型有它自
己的适当政策。 一个一致的结果
能在劳动利用的最小的存放时间和提高中被获得评估。 在平行的巷道仓库的
Gademann 等人 [17] 使用可变的存放操作, 学习在波存放中一届方法的次序, 把一些给
一组存取工具, 而且解决这种难题需要分步骤阿理论。 他们找主要的进步正在获得一个
非常简单和有效率的程序改善一届大小的较低的范围。 Chiang[18] 设计当次序任务费用
是高的时候，一能把次序分为多次递送或二递送的模态。 然后在周期的检讨制度之下学

习次序区分方法在次序递送时间时期内发现最适宜的递送数 字, 而且最后有效地减少全
部的费用是可能的。
3 样板的工程
这一个文章将会 详细地描述分配的存放表现因素中心仓库系统设计，像是交叉巷道的
量,存放路径,存放密度和次序组合 。 它也描述该如何以最小的存放距离作为一种基础在
不同的仓库环境之下获得最适宜存放表现组合的仓 库系统设 计。
传统的仓库地面区划没有交叉的巷道设计。 因此，即使第一段巷道仅需要一小段距
离来存放货物, 你仍然一定从第一个储藏位置到最后一个位置或者回去第一个位置然后
到第二个巷道。 因此，许多不必要的被重叠的距离被采取。 解决上述的问题、佛恩和
Petersen[1] 设计如图 2 所显示的一个交叉巷道的设计.
在增加巷道之后，完全的储藏位置没被改变，但是主要的巷道长度已经被增加, 因此
必要的完全的空间已经被增加，而且空间利用率已经被减少。 但是依次增加交叉的巷道
增加存放路径柔性而且存放效率能被提高。 这帮助减少全部的存放距离。 但是当巷道中
额外的行走路程过多时 , 当做显示加入图 3 , 储藏空间被增加太多，这依次造成逐渐增
加的次序存放距离。

3.1 仓库系统模拟结构
3.1.1 仓库地面区划考量和分类假定

这一个文章以佛恩和 Petersen[1]提出的一个交叉的巷道量 (1~9) 设计方案为基础,
而且在假定中更进一步扩充交叉的巷道量至 11, 0-10, 分别地。 这一个文章只考虑输入
和输出点 (输入／输出点) 被位于在两者的比较低的左边和比较低的右边。 在每存放中,
来自输入点的存放开始, 而且藉由走路去输出点完成次序的存放完成它。 如果存放以 次
序组合为基础，它然后将在那一存放任务中完成所有的次序,考虑在存放中的真实旅行距
离。 换句话说, 它被计算基于直线的距离。
3.1.2 储藏任务计划
在仓库系统储藏任务政策，二个不同的政策即存在以货物项目通路频率为基础的一个,
另外的加上货物项目类似以货物项目通路频率为基础。 早先的研究
已经证明，以货物看来基 于的储藏任务政策计算类似和通路频率,已经帮助改善仓库
系统的存放效率。 这一个文章主要地把重心集中在进步的效力。

3.1.3 存放工作路线排定计划
对于存放工作路线排定计划，考虑被 Goetschalckx 和 Ratliff[13] 规划的这二种
存取方法, 即那修正 Z-精选的方法和回返方法。 处理真实情形修正 Z-存放而且归还方
法, 回返方法的距离计算以直线的距离为基础。 计算如下图所示:
1. 水平的距离 M(i,m),是从 ith 巷道移动到 mth 巷道的距离, 哪里一是每个储藏
位置的宽度, b 是每个储藏位置的深度，而且 w 是巷道宽度:
M(i,m)=2 ×|m-i |× b+|m-i- 1|× W;
For i, m=1,2, ····· N 。
2.当位置宽度的产品和真实的位置通过的時候，旅行距离一个巷道里的 Mw 被计算,
那是:

Mw= a× 真实的储藏位置通过路程
修正 Z-精选的存放政策的形成以被 Goetschalckx 和 Ratliff 巷道宽度应该比
2.1 m 大的 [13] 计划的 Z-精选存取方法的基本原则为基础。 在存放操作方面，存放必
须时常越过巷道。 被经过存放的路径的轨道与 a Z 形状类似，因此，它叫做 Z-精选的
存放原则,如图 4 所示。

存放距离Z方案是以欧几里得几何的距离为基础。 举例来说，在图 4 ，次序的存放
位置是储藏位置 i, 储藏位置 j, 储藏位置 k 和储藏位置 l, 分别地。 然后，总计的存
放距离是下列五距离的总数:(在身材， x 在巷道的一边是储藏位置数字的总数)
1. 来自点 o 的距离指出 o~ 是:
1
22
Dist（o，o＇）=

a+w

4
2. 来自点 o 的线的距离~ 指出 i 是:
Dist（o＇，i）= ax。

3. 来自点 i 的距离指出 j 是:

2
Dist(i,j)=
w
2
+（x-1）a
2


4. 来自点 j 的距离指出 : Dist( j,k)=2(x- 1)a +a。

5. 来自点 k 的距离指出 l 是:

2
Dist(k,l)=
w
2
+（x-1）a
2
.

本文设计了一个修改 Z-精选的存放路径的办法，它的主要目的将划除Z方案的传统界
限,必须来回地去巷道的这二边。 计划的典型 Z-精选的存放路径如图 5 所示。 因为 Z-
精选的存放原则有有来回地去巷道的大 约这二边的限制，当巷道里的存放密度太高的时候，
它将会增加不必要的距离越过巷道。 因此，在这一个文章中，我们修正 Z-精选的存放路
径设计政策, 主要地修正存放次序进一个巷道, 希望帮助存放表现。 那修正 Z-精选的方
法以 Z-精选的基本原则和最附近的方法为基础在一个巷道内决定存放次序。它更进一步
使用 2-选择改变存放次序, 没有有来回地去巷道的大约这二边的限制, 在一个巷道内找
存放次序, 有最小的存放距离。 当做点 2,3, 4 和 1 在一个巷道内举例来说，在每个巷
道的入口，判断存放次序, 如图 6 所示一, 哪一个是开始的解决。 然后，使用内部的路
径交换方法提高存放路径。 点 2,3,4 的开始存放路径, 和 1, 然后是 2-选择改变指出
3,2, 1 和 4, 在图 6 b,是改良的解决显示。
3.1.4 在一个巷道内的存放密度
主要地存放一个巷道里的密度的装备以来自 Goetschalckx（人名）的实验的结果为
基础和 Ratliff[13],在 50% 里面采取三存放密度, 如此的当做 10% 、 20% 和 30%, 当
做一个实验的水平。

3.1.5 次序的组合
次序存放、和相似的次序组合存放。
1. 单一次序存放正在存放基于一个次序。

井然有序组合, 主要的目的将减少存放距离。 二主要的类型即被考虑而且解释单一
2. 类似的组合，以便存放的主要原因是该相结合的两项命令，其中的主要条件为了
组合之间的相似性订单。

这一个文章把重心集中在分配中心仓库的签署问题。 它尝试构造一个联合的模型因
素，像是交叉的巷道量，储藏任务, 存放路径,存放密度, 命令组合，等等组合关系由十
一不同的交叉巷道量组成, 二储藏任务政策、存放路径的二类型, 存放密度和次序组合的
二类型的三类型, 如图 7 所示. 关系主要地在不同的水平讨论五个不同的因素对仓库存
放系统的效果。 eM- 植物的软件也将会被当作一个模拟和确认分析工具使用。
4 做模型工程和模拟分析
4.1种模拟环境装备
这模拟实验的存放环境是一间矩形的仓库。假定每储藏位置是 5 公尺和宽度 1 公尺
和深度, 分别地，而且分别地,输入／输出点在较低的左边中而且降低仓库的右 边角落，
存放从第一点开始作为存放点, 和在完成之后存放操作, 回去指出 O 而且开始为下一个
次序存放。 被 eM-植物模拟软件构造的细节如图所示。
1. 巷道宽度是 3 公尺。
2. 每储藏位置在它上有货物。
3. 有 240 储藏位置在仓库中, 与 240不同类型的货物。
4. 物质操作的设备的平均感人速度是 30 m最小。
5. 物质的操作设备和仓库系统有没有机械的麻烦或从货物情形。

一百多个次序任意地被一部计算机所产生。 通路率和货物的类似被分析。 在每个测
试组合，货物项目数据被转换到符合相同的储藏位置为了要计算存放距离。 很多的组合
模型被运行被基于因素，像是十一交叉巷道的类型、储藏任务政策 (SS1,SS2) 的二类型
的二种类型
次序存放规划,包括存放密度的次序组合和三类型中的二个类型。 现在的模拟制度举
例来说是收集相关的评估索引数据平均的全部存放距离。
4.2 模拟实验的结果
这一个文章以三不同的存放密度为基础。 大约 100个次序用来在一个交叉巷道的不
同数字上运行一届实验, 储藏任务, 存放路径, 存放密度和次序的组合。 大约 264(11
× 2 × 2 × 3 × 2) 组实验被运行， 而且实验的每组被重复十次。斯堪的纳维亚航空
公司的统计的软件用来为这一个文章的数据分析处理实验 的数据。 实验的数据被安排而
且被根据设计到不同的存放路径,如表 1,2 所示, 和 3 为 10% 、 20% 和 30% 的不同存
放密度, 分别地。
从表 1,2和 3 我们知道平均的存放次序，单一次序和组合的次序的工作距离, 在不同的
储藏任务政策之下 (SS1 指示第一个储藏任务以运输货物频率为基础的方案; SS2 指示第
二个储藏任务加上货物项目类似以货物项目通路频率为基础的方案)， 在回返的不同密度
10% 、 20% 和 30% 而且修正 Z-精选的存放原则, 在不同的交叉巷道量,分别地。 整体
来说存放距离和整体来说实验的表现比较、和情节的平均的趋势被画为了要了解这些因素
对 次序存放系统的全部表现的效果。 10% 的密度的平均全部的存放距离的比较被显示。

表一
次序组合_储藏任
务
_
次序存放政策

单独指令_SS1_
返回
单独指令_SS2_
返回
单独指令_SS1_
修正 Z-pick
单独指令_SS2_
修正Z-pick
组合指令_SS1_
返回
组合指令_SS2_
返回
组合指令_SS1_
修正Z- pick
组合指令_SS2_
修正Z-pick
0
23968
24105
22420
21529
23544
23386
21128
21055
1
19762
19630
17107
16863
19436
19217
16764
16485
2
18812
18247
16136
15754
18532
17980
15793
15409
3
18777
18221
16211
15983
18588
17833
15835
15662
4
交叉的走廊量

5 6
19250
18925
16874
16581
19102
18577
16452
16205
7
19701
19350
17324
16985
19550
19000
16889
16609
8
20315
19955
17899
17569
20167
19599
17453
17174
9
20980
20704
18525
18258
20838
20317
18065
17846
10
21602
21338
19210
18883
21457
20940
18722
18455
19054
18432
16469
16105
18874
18082
16069
15784
19066
18760
16676
16401
18925
18413
16262
16025

表二.
密度 20% 的平均次序存放距离 (单位: 公尺)

次序组合_储藏任务
_
次序存放政策

单独指令_SS1_
返回
单独指令_SS2_
返回
单独指令SS1_
修正 Z-pick
单独指令SS2_
修正Z-pick
组合指令_SS1_
返回
组合指令_SS2_
返回
组合指令_SS1_
修正Z- pick
组合指令SS2_
修正Z-pick
0 1 2 3
4
交叉的走廊量

5 6
7 8 9 10
29959
30402
28684
31040
18988
19292
21684
21525
27915
27987
24949
25005
18576
18725
17535
17695
27342
27117
23873
23829
18654
18931
16673
16836
27276
26885
23918
24036
18747
19126
16796
17065
27957
27476
24403
24473
19323
19640
17195
17549
28047
27483
24981
24999
19792
19697
17704
18094
28417
27866
25254
25331
20110
20023
17984
18375
29178
28631
25882
25939
20729
20650
18452
18877
30097
29538
26672
26768
21382
21274
19023
19388
31115
30612
27584
27732
22138
21949
19632
20006
32227
31701
28602
28697
22908
22730
20322
20651

633
表三.
密度 30% 的平均次序存放距离 (单位: 公尺)

次序组合_储藏任务
_
次序存放政策

0 1 2 3
交叉的走廊量

4 5 6
7 8 9 10
单独指令SS1_
单独指令_SS2_
单独指令_SS1_
单独指令_SS2_
组合指令_SS1_
组合指令SS2_
组合指令_SS1_
组合指令_SS2_
修正Z-pick
32123
32662
36618
38230
11815
11941
15603
16539
32809
33216
30562
31224
12415
12541
13419
14132
33110
33070
28879
29465
13009
13092
12779
13280
33194
33406
29192
29977
13597
13570
13019
13555
34112
34335
29598
30664
14161
14140
13500
13954
34338
34879
30745
31591
14606
14602
13981
14359
34835
35476
31171
32144
14995
15030
14349
14727
36008
36636
32108
33064
15570
15611
14798
15240
37250
37967
33074
34182
16151
16211
15312
15763
38595
39197
34098
35249
16751
16757
15773
16202
39862
40390
35277
36445
17345
17293
16226
16793

4.3 ANOVA 统计的测试分析
收集成的平均整体来说来自模拟的存放距离数据被安排和不一致分析被运
行。 从表 4, 我们知道次序组合, 存放密度, 储藏任务计划和十字架巷道量全
部整体来说一般说来有明显的不同效果存放距离。 这一个文章运行邓肯 测试在
如此的之下一大的不一致情形在不同的交叉巷道量、不同的次序组合主要地分析
平均的全 部存放距离, 不同的存放密度在一个巷道里面, 不同的次序存放政策
和不同的储藏任务策略。从结果表5 ，我们知道的平均总体的存放距离是没有什么不同，在两个或三个交叉的过道条件。在订定二，两岸走道的数量是1 ， 4
或5 。
这三个跨走道的数量都属于组g.在一套的三，两岸走道的数量是第5和第6 ，
如果这些两条 过走道的数量都属于F组，因为在方案中与一个或太多的交叉过道，
他们都有同样的坏结果在该命令中存 放的效率。