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 of Industrial Management,
Chung Hua University,
No. 707 Sec. 2 WuFu Road, Hsin-chu, Taiwan 300, R.O.C. E-mail:
lfhsieh@https://www.doczj.com/doc/189101167.html,.tw
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
T ake 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 “ware house 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 I/O station that is located in the middle of the head or end of the aisle; the second and third are vertical aisle, but the I/O 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, 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 storage/retrieval system (AS/RS). They suggest that using the ABC storage principle will effectively increase the capacity of the AS/RS 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 storage/retrieval 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-
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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. T o 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 (I/O 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 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
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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+ 14w2 .
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)2a2.
4. The distance from point j to point k is: Dist
( j, k) = 2 (x - 1) a + a .
5. The distance from point k to point l is:
~ ____________
Dist (k, l) = w2+ (x - 1)2a2.
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 initial solution of Z-pick picking path b improved solution of Zpick picking path
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
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Fig. 7. Combination relationship of 5 experimental factors with different levels
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 I/O 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 back to point O and starts picking for the next order. The details constructed by eM-plant simulation software is as shown below.
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
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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 Table 1. Average order picking distance of density 10% (unit: meter)
ent picking paths, as shown in T ables 1, 2, and 3 for different picking density of 10%, 20% and 30%, respectively.
From T ables 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
Order combination
_storage assignment
_order picking policy 0 1 2 3
Cross aisle quantity
7 8 9 10 4 5 6
Single order_SS1_
Return 23968 19762 18812 18777 19054 19066 19250 19701 20315 20980 21602 Single order_SS2_
Return 24105 19630 18247 18221 18432 18760 18925 19350 19955 20704 21338 Single order_SS1_
Modified Z-pick 22420 17107 16136 16211 16469 16676 16874 17324 17899 18525 19210 Single order_SS2_
Modified Z-pick 21529 16863 15754 15983 16105 16401 16581 16985 17569 18258 18883 Combined order_SS1_
Return 23544 19436 18532 18588 18874 18925 19102 19550 20167 20838 21457 Combined order_SS2_
Return 23386 19217 17980 17833 18082 18413 18577 19000 19599 20317 20940 Combined order_SS1_
Modified Z-pick 21128 16764 15793 15835 16069 16262 16452 16889 17453 18065 18722 Combined order_SS2_
Modified Z-pick 21055 16485 15409 15662 15784 16025 16205 16609 17174 17846 18455
Table 2. Average order picking distance of density 20% (unit: meter)
Order combination
_storage assignment
_order picking policy 0 1 2 3
Cross aisle quantity
7 8 9 10 4 5 6
Single order_SS1_
Return 29959 27915 27342 27276 27957 28047 28417 29178 30097 31115 32227 Single order_SS2_
Return 30402 27987 27117 26885 27476 27483 27866 28631 29538 30612 31701 Single order_SS1_
Modified Z-pick 28684 24949 23873 23918 24403 24981 25254 25882 26672 27584 28602 Single order_SS2_
Modified Z-pick 31040 25005 23829 24036 24473 24999 25331 25939 26768 27732 28697 Combined order_SS1_
Return 18988 18576 18654 18747 19323 19792 20110 20729 21382 22138 22908 Combined order_SS2_
Return 19292 18725 18931 19126 19640 19697 20023 20650 21274 21949 22730 Combined order_SS1_
Modified Z-pick 21684 17535 16673 16796 17195 17704 17984 18452 19023 19632 20322 Combined order_SS2_
Modified Z-pick 21525 17695 16836 17065 17549 18094 18375 18877 19388 20006 20651 632
T able 3. Average order picking distance of density 30% (unit: meter) Order combination
_storage assignment
_order picking policy 0 1 2 3
Cross aisle quantity
7 8 9 10 4 5 6
Single order_SS1_
Return 32123 32809 33110 33194 34112 34338 34835 36008 37250 38595 39862 Single order_SS2_
Return 32662 33216 33070 33406 34335 34879 35476 36636 37967 39197 40390 Single order_SS1_
Modified Z-pick 36618 30562 28879 29192 29598 30745 31171 32108 33074 34098 35277 Single order_SS2_
Modified Z-pick 38230 31224 29465 29977 30664 31591 32144 33064 34182 35249 36445 Combined order_SS1_
Return 11815 12415 13009 13597 14161 14606 14995 15570 16151 16751 17345 Combined order_SS2_
Return 11941 12541 13092 13570 14140 14602 15030 15611 16211 16757 17293 Combined order_SS1_
Modified Z-pick 15603 13419 12779 13019 13500 13981 14349 14798 15312 15773 16226 Combined order_SS2_
Modified Z-pick 16539 14132 13280 13555 13954 14359 14727 15240 15763 16202 16793
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%
result is shown in Table 4.
From Table 4, we know 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-
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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-
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T able 4. ANOVA results for relative travel distance
Source D.F. SS MS F test p -value a 1 13007030.88 13007030.88 2616.30 < .0001~ b 1 46314.12 46314.12 9.32 0.0023~ a ~b 1 50008.36 50008.36 10.06 0.0016~ c 2 2408785.85 1204392.93 242.26 < .0001~ a ~c 2 6951007.09 3475503.54 699.08 < .0001~ b ~c 2 270067.59 135033.80 27.16 < .0001~ a ~b ~c 2 171726.59 85863.29 17.27 < .0001~ d 1 226417.49 226417.49 45.54 < .0001~ a ~d 1 181.32 181.32 0.04 0.8486 b ~d 1 46128.64 46128.64 9.28 0.0024~ a ~b ~d 1 75141.25 75141.25 15.11 0.0001~ c ~d 2 63255.36 31627.68 6.36 0.0018~ a ~c ~d 2 268487.86 134243.93 27.00 < .0001~ b ~c ~d 2 141427.74 70713.87 14.22 < .0001~ a ~b ~c ~d 2 137971.56 68985.78 13.88 < .0001~ e 10 1173055.48 117305.55 23.60 < .0001~ a ~e 10 55436.93 5543.69 1.12 0.3470 b ~e 10 2938.91 293.89 0.06 1.0000 a ~b ~e 10 5182.91 518.29 0.10 0.9998 c ~e 20 140305.46 7015.27 1.41 0.1070 a ~c ~e 20 35669.73 1783.49 0.36 0.9959 b ~c ~e 20 2624.49 131.22 0.03 1.0000 a ~b ~c ~e 20 2657.37 132.87 0.03 1.0000 d ~e 10 181186.60 18118.66 3.64 < .0001~ a ~d ~e 10 10635.35 1063.53 0.21 0.9951 b ~d ~e 10 13977.16 1397.72 0.28 0.9854 a ~b ~d ~e 10 11949.41 1194.94 0.24 0.9921 c ~d ~e 20 83123.17 4156.16 0.84 0.6705 a ~c ~d ~e 20 20054.58 1002.73 0.20 0.9999 b ~c ~d ~e 20 11448.67 572.43 0.12 1.0000 a ~b ~c ~d ~e 20 6409.50 320.47
0.06
1.0000
Total
1451
78987256.51
~P < 0.05
~a: order combination b: storage assignment strategy c: picking density d: order picking policy e: cross aisle quantity
T able 6. Comparison of average picking distance for different order combination
T able 7. Comparison of average picking distance for different picking density within an aisle 30% 678.524 1 20% 885.669 2 10%
1080.256 3
T able 8. Comparison of average picking distance for different order picking policy Order picking policy Average picking distance
Ranking
Modified Z-pick 860.267 1 Return
902.699
2
result in the order picking efficiency. Therefore, the addition of two or three appropriate cross aisles is the best design for en
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 T able 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
T able 5. Comparison of average picking distance for different cross aisle quantity
Cross aisle quantity
Duncan group
3 H 2 H 1 G
4 G
5 G F
6 F
7 E
8 D
9 C 0 B 10
A
Order combination Average picking distance
Ranking
Combined order 582.184 1 Single order
911.413
2
with one or too many cross aisles, they all have the same bad
T able 9. Comparison of average picking distance for different storage assignment strategy
Storage assignment strategy Average picking distance Ranking
ABC access frequency plus 863.309 1 merchandise item similarity
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 T able 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 T able 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 T able 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 This research was supported partially by a research grant from National Science Council of Taiwan, R.O.C. under the project number: NSC 92-2213-E-216-026.
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637
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 Petersen[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 " Z" 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:
Dist （o ，o ＇）= 2
21a +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:
Dist(i,j)= 22w +x a ?2
（-1）
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:
Dist(k,l)= 22w +x a ?2
（-1）.
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。