DOI 10.1007/s00170-004-2404-0

O R I G I N A L A R T I C L E

Int J Adv Manuf Technol (2006) 28: 626–637

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 onthe practical industry, it is understood that the proper use ofstorage assignment policies can use minimum storage spaceto reach the purpose of minimum total traveling distance, andthis has a direct impact on enhancing the order picking per-formance. At the same time, proper routing planning can min-imize overall order picking cost, and finally reach the goal ofpicking performance enhancement in unit time. Therefore, thispaper considers the effects on the order picking system per-formance for factors such as quantity and layout type of crossaisles in a warehouse system, storage assignment policy, pick-ing route, average picking density inside an aisle, and ordercombination type, etc. A software, eM-plant, will be used asa simulation and analysis tool, a warehouse design database willbe developed, which is based on the minimum overall travel-ing distance as the optimum performance index, the cross aislequantity, warehouse layout, storage assignment, picking routeplanning, picking density and order combination type will beoptimally integrated and planned in the warehouse system. Fi-nally, we provide this database to the industry as a reference inthe warehouse planning or warehouse design improvement in thefuture.

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, orderpicking operation is an important and yet tedious task. From thelabor requirement point of view, currently, most of the distribu-

L.-F. Hsieh (�) · L. TsaiDepartment of Industrial Management,Chung Hua University,No. 707 Sec. 2 WuFu Road, Hsin-chu, Taiwan 300, R.O.C.E-mail: lfhsieh@chu.edu.tw

tion center still belongs to labor-intensive industry, and the laborcost directly related to the order picking operation occupies evenabove 50% of the overall cost. Many complicated merchandisetypes are its characteristic, and some internal operation modifi-cation can reduce the company’s cost easily. It is an urgent topicthat needs to be taken care of. Therefore, order picking opera-tion performance has an overwhelming effect on the warehouse’soperating cost. Thus, warehouse design plus storage assignmentand picking routing planning will undoubtedly enhance the op-erating efficiency and the space utilization, and reduce the orderpicking cost.

This paper is based on the model provided by Vaughan andPetersen [1], adding to it three factors: storage assignment poli-cies, order picking strategies and order combination type. Be-cause all three factors will affect the order picking efficiency,we take them into account in the model, and add also differ-ent ways of storage location planning, different picking dens-ity inside an aisle, different picking strategies and single orderpicking or picking by combining similar order plus recombin-ing later. We hope that by doing simulations on different com-binations, we can produce an optimum design for the ware-house system in order to enhance the order picking operationefficiency.

A good warehouse system should ensure easy and efficientaccess of merchandise, properly use the storage location to findthe shortest path, and finally to deliver the merchandise in a rea-sonable time. This paper is focusing on the factors such as crossaisle quantity, storage assignment, picker route, picking densityinside an aisle, and different ways of combination of order in thepicking operation storage area of the distribution center. We hopeto perform a systematic analysis and research on the factors inorder to obtain shortest travel distance.

Finally, verified by simulation result, a database for ware-house system design will be developed, and we provide thisdatabase to the warehouse industry as a reference in the ware-house system planning. Good picking operation is expected toenhance the production efficiency, and accompanied with per-fect warehouse system planning and picking policy decision willsurely help the company to reduce cost effectively.

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2 Literature review

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

2.1 Warehouse layout design

One of the very important factors affecting the order picking sys-tem is the storage area planning. Ashayeri [2] suggests a solutionfor the warehouse layout problem, targeting a goal of minimumbuilding cost or material handling cost. Generally speaking, thewarehouse layout is based on a rectangular shape. Caron et al. [3]propose that the warehouse layout can be divided into threetypes. The first is parallel storage aisle with I/O station that is lo-cated in the middle of the head or end of the aisle; the second andthird are vertical aisle, but the I/O station is located in the middleand lower left, respectively.

According to the research from Roodbergen and Koster [4],they consider to put cross aisle between the originally paral-lel aisles, and compare the result with that without cross aisle.They found a distinguished difference of average picking dis-tance between the two cases. Ratliff and Rosenthal [5] studythe picking problem in rectangular warehouse, where there areonly pathways at the two ends of an aisle. They use graph the-ory to find the shortest picking time, and find that the pick-ing time is independent of the merchandise items quantity butlinearly dependent on the quantity of the pathways. Vaughanand Petersen [1] study the effect of order combination typein the cross aisle layout on the picking distance. They foundthat when the cross aisle is in the optimum condition, a mostbeneficial effect will be generated. Roodbergen and Koster [6]find an optimum combination of multiple cross aisles and pick-ing path.

Caron et al. [7] find that the warehouse layout has a distin-guished effect on picking travel distance. They prove that thelayout design has an effect of more than 60% on the total traveldistance, and also find the relationship between warehouse lay-out and picking travel distance. Vaughan and Petersen [1] de-velop a heuristic algorithm to obtain an optimum quantity oncross aisles in order to generate an optimal performance, whereasRoodbergen and Koster [4] compare the average travel time be-tween normal layout and a cross aisle layout and prove that thewarehouse with cross aisle will have a shorter average traveltime. Therefore, one of their research highlights is to build anoptimum aisle design of a warehouse system.

2.2 Storage assignment policy

Generally, the storage assignment policies are as follows: ran-dom storage, classified storage, fixed storage, volume-based stor-age, etc. Rosenblatt and Eynan [8] suggest that the assignmentbasis 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 everyitem has the same picking time. The picking time is propor-tional to picking distance, so they use fixed storage method tocalculate the expected picking time. Rosenblatt and Eynan [8] di-vide the warehouse into some smaller zones and use classifiedstorage assignment policy to reduce the total picking time, andfinally derive an optimum automatic warehouse system. Guenovand Raeside [10] study the optimum aisle width under bandheuristic layout and automatic storage/retrieval system (AS/RS).They suggest that using the ABC storage principle will effec-tively increase the capacity of the AS/RS machine. Jeroen andGademann [11] explain that classified storage policy is based onthe customer requirement proportion, and give ways to classifystorage location and product effectively. Petersen and Schmen-ner [12] investigate the heuristic picking path, and the storageassignment policy that is based on picking quantity. They pointout that among all the storage methods based on picking quantity,storing between aisle saves about 10 to 20% picking than that ofother storage methods. Jarvis and McDowell [9] develop a ran-dom model that when under transversal policy, their assignmentcan obtain minimum average storage/retrieval time.

2.3 Picker routing policy

The purpose of picker routing planning is to reduce the unneces-sary picking distance that in turn results in the shortest and themost efficient picking. Ratliff and Rosenthal [5] propose a newsolution to the picker routing problem: first to find out individu-ally the picking distance of each path, then find out the distanceconnecting to next path, and repeat in this manner until finishpicking all merchandise items.

Goetschalckx and Ratliff [13] develop an efficient optimal al-gorithm and show to yield policies with up to 30% savings intravel time over commonly used policies. It is also shown that,for most practical aisle widths, it is significantly more efficientto pick both sides of the aisle in the same pass rather than pickone side and then pick the other side, unless the pick densi-ties are greater than 50%. Most warehouses that employ manualorder picking are composed of one or more sections of parallelaisles similar to those illustrated in Fig. 1 (circles indicate loca-tions of items in the order). There are four possible policies forpicking within an aisle: traversal, split traversal, return and splitreturn. A traversal policy enters at one end of an aisle and ex-its at the other end. A return policy enters and exits at the sameend of the aisle. A split policy is a traversal policy from bothends or a return policy from both ends. In Fig. 1, aisle 1B rep-resents a traversal policy, aisle 4A a split traversal policy, aisle2A a return policy, and aisle 3A a split return policy. Jeroen andGademann [14] consider the picking sequence between zonesunder 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 thetravel distance and aisle quantity. The results show that the pick-

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Fig. 1. Four types of picking policy [6]

ing distance of a warehouse with cross aisle is proportional toaisle quantity, the picking travel distance increases rapidly as thecross aisle quantity increases, and the picking travel distance of“Z” shape aisle is independent of aisle quantity.

Hall [15] investigates three different picker routing policiesin a rectangular warehouse including transversal, mid-point re-turn and largest gap return. The simulation method is used tocompare the travel distance of different policies, and the resultshows that the largest gap return has better performance thanothers. Vaughan and Petersen [1] investigate the warehouse lay-out that has cross aisle, to find out a shortest order picking dis-tance. They calculate picking distance by different experimentalcombination designs based on four factors and also by dynamicplanning. The result shows that when the aisle length increasesrelatively to the aisle width, an optimal cross aisle quantity canbe obtained. Roodbergen and Koster [6] decide the average traveltime of different warehouse sizes and different picking lists byusing dynamic planning calculation method and find out that ifthe layout is a middle aisle type (three cross aisles), the averagetravel time is obviously lower. Seven methods of order pick-ing path are mentioned in that paper. Among them, combinedmethod has the best performance and the largest gap heuristicis better when applied to the case with two cross aisles and lowpicking density.

2.4 Combination of order

Single order picking means that the picking is performed basedon a single order. Instead, the batching and zoning picking isa picking method that combines different order and performs thepicking in different picking areas, respectively. Lin and Lu [16]propose five kinds of order classification, accompanied with twopolicies and verified by simulation results, they find that eachorder type has its own appropriate policy. A consistent result

can be obtained in both minimum picking time and enhancementof the labor utilization rate. Gademann et al. [17] use a vari-able picking operation in parallel aisle warehouse, studying orderbatching method in wave picking, give several batches to a setof pickers, and solve the order batching problem by branch-and-bound method. They find that the major improvement is obtain-ing a very simple and efficient process to improve the lowerbound of batch size. Chiang [18] proposes that when the orderassignment cost is high, one can divide the order into multiple-delivery or two-delivery mode. Then it is possible to study theorder division method under periodic review system to find outthe 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 fac-tors in the distribution center warehouse system design such asquantity of cross aisle, picking path, picking density and ordercombination. It also describes how to use the minimum pick-ing distance as a basis to obtain a warehouse system designof optimum picking performance combination under differentwarehouse environments.

Conventional warehouse layout has no cross aisle design.Therefore, even if the first aisle need only to take a short courseto a certain storage location to pick up some merchandise, youstill must go from the first storage location to the last location orgo back to the first location and then to the second aisle. There-fore, a lot of unnecessary overlapped distance is taken. To solvethe above-mentioned problem, Vaughan and Petersen [1] pro-pose an idea of cross aisle as shown in Fig. 2. After adding the

Fig. 2. Warehouse layout with one cross aisle

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Fig. 3. Warehouse layout with too many cross aisles

cross aisle, the total storage locations are not changed, but themain aisle length has been increased, and therefore the neces-sary total space has been increased and the space utilization ratehas been decreased. But adding the cross aisle in turn adds thepicking path flexibility and picking efficiency can be enhanced.This helps to reduce the overall picking distance. But when ex-cess quantity of cross aisles are added, as shown in Fig. 3, thestorage space is increased too much, which in turn results in anincreasing order picking distance.

3.1 Warehouse system simulation structure

3.1.1 Warehouse layout considerationand classification assumption

This article is based on cross aisle quantity (1 ∼ 9) proposed byVaughan and Petersen [1], and extends further the cross aislequantity to 11 in the assumption, 0 to 10, respectively. Thisarticle only considers the input and output points (I/O points)located at both lower left and lower right. In each picking, thepicker starts from the input point, and finishes it by walking tothe output point to finish the picking of an order. If the pick-ing is based on order combination, it is then to finish all ordersin that picking mission, considering the actual travel distance inthe picking. In other words, it is calculated based on rectilineardistance.

3.1.2 Storage assignment planning

In the warehouse system storage assignment policies, two differ-ent policies exist, namely, one that is based on the merchandiseitem access frequency, another is based on merchandise item ac-cess frequency plus merchandise item similarity. Previous study

has proved that the storage assignment policy based on consid-ering merchandise item similarity as well as access frequency,has helped to improve the picking efficiency in the warehousesystem. This article focuses mainly on the effectiveness of theimprovement.

3.1.3 Picker routing planning

For the picker routing planning, consider the two picking policiesproposed by Goetschalckx and Ratliff [13], namely, the modi-fied Z-pick policy, and the return policy. To deal with the actualsituation of modified Z-pick and return policies, the distance cal-culation of return policy is based on rectilinear distance. Thecalculation is as shown below:

1. The horizontal distance M(i, m), is the distance from the ithaisle transfer to the mth aisle, where a is the width of eachstorage location, b is the depth of each storage location, andw 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 theproduct 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 basedon the basic principles of Z-pick picking policy proposed byGoetschalckx and Ratliff [13], where the aisle width should begreater than 2.1 m. In the picking operation, the picker has tocross the aisles frequently. The track of the paths passed by thepicker is similar to a Z shape, so it is named the Z-pick pick-ing principle, as shown in Fig. 4. The picking distance calculated

Fig. 4. Standard Z-pick pattern

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in Z-pick policy is based on Euclidean distance. For example, inFig. 4, the picking locations of a single order are storage loca-tion i, storage location j , storage location k and storage locationl, respectively. Then, the total picking distance is the sum of thefollowing five distances (in the figure, x is the sum of the storagelocation number at one side of an aisle):

1. The distance from point o to point o′ is:

Dist(o, o′) =

√

a2 + 1

4w2 .

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 pickingpath, its main purpose is to delete the conventional limit of Z-pick, which has to go back and forth the two sides of an aisle. Thetypical Z-pick picking path planning is as shown in Fig. 5. Be-cause Z-pick picking principle has the limitation of having to goback and forth around the two sides of the aisle, when the pick-ing density inside the aisle is too high, it will add unnecessarydistance to cross the aisle. Therefore, in this article we proposea policy of modified Z-pick picking path, mainly to modify thepicking order inside a single aisle, hopefully to help the pickingperformance. The modified Z-pick method is based on Z-pickbasic principle and the most neighboring method to decide thepicking order inside an aisle. It uses further 2-opt to change thepicking order, without the limitation of having to go back andforth around the two sides of the aisle, to find a picking order in-side an aisle, which has minimum picking distance. For example,at the entrance of each aisle, judge the picking order inside anaisle as point 2, 3, 4 and 1, as shown in Fig. 6a, which is an initialsolution. Then, use the inner path exchange method to enhancethe picking path. The initial picking path of point 2, 3, 4, and 1, isthen 2-opt changed to point 3, 2, 1 and 4, shown in Fig. 6b, whichis an improved solution.

3.1.4 Picking density inside an aisle

The setup of picking density inside an aisle is mainly based onthe experimental results from Goetschalckx and Ratliff [13], takethree picking density within 50%, such as 10%, 20% and 30%, asan experimental level.

Fig. 5. Typical Z-pick picking path

Fig. 6. a initial solution of Z-pick picking path b improved solution of Z-pick picking path

3.1.5 Combination of order

In order combination, the main purpose is to reduce the pickingdistance. 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 fororder combination is the similarity between orders.

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

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Fig. 7. Combination relationship of5 experimental factors with differentlevels

factors such as cross aisle quantity, storage assignment, pickingpath, picking density, order combination, etc. The combinationrelationship is composed of eleven different cross aisle quanti-ties, two storage assignment policies, two types of picking path,three types of picking density and two types of order combi-nation, as shown in Fig. 7. The relationship mainly discussesthe effect of the five different factors on the warehouse pick-ing system at different levels. eM-plant software will be used asa 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 metersand 1 meter in width and depth, respectively, and the I/O pointis in the lower left and lower right corner of the warehouse, re-spectively, 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. Thedetails constructed by eM-plant simulation software is as shownbelow.

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. Theaccess rate and the similarity of merchandise are analyzed. Ineach test combination, the merchandise item data is transformedto corresponding same storage locations in order to calculatepicking distance. Numerous combination models are performedten 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 threetypes of picking density. The current simulation system collectsthe related evaluation index data, for example, the average over-all picking distance.

4.2 Simulation experimental result

This article is based on three different picking densities. About100 orders are used to perform batch experiments on a differentnumber of cross aisles, storage assignment, picking path, pick-ing density and combination of orders. About 264 (11×2×2×3×2) sets of experiments are performed, and each set of experi-ment is repeated ten times. SAS statistical software is used toprocess the experimental data for data analysis in this article. Theexperimental data is arranged and planned according to differ-

Table 1. Average order picking distance of density 10% (unit: meter)

Order combination_storage assignment Cross aisle quantity_order picking policy 0 1 2 3 4 5 6 7 8 9 10

Single order_SS1_Return 23968 19762 18812 18777 19054 19066 19250 19701 20315 20980 21602Single order_SS2_Return 24105 19630 18247 18221 18432 18760 18925 19350 19955 20704 21338Single order_SS1_Modified Z-pick 22420 17107 16136 16211 16469 16676 16874 17324 17899 18525 19210Single order_SS2_Modified Z-pick 21529 16863 15754 15983 16105 16401 16581 16985 17569 18258 18883Combined order_SS1_Return 23544 19436 18532 18588 18874 18925 19102 19550 20167 20838 21457Combined order_SS2_Return 23386 19217 17980 17833 18082 18413 18577 19000 19599 20317 20940Combined order_SS1_Modified Z-pick 21128 16764 15793 15835 16069 16262 16452 16889 17453 18065 18722Combined 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 Cross aisle quantity_order picking policy 0 1 2 3 4 5 6 7 8 9 10

Single order_SS1_Return 29959 27915 27342 27276 27957 28047 28417 29178 30097 31115 32227Single order_SS2_Return 30402 27987 27117 26885 27476 27483 27866 28631 29538 30612 31701Single order_SS1_Modified Z-pick 28684 24949 23873 23918 24403 24981 25254 25882 26672 27584 28602Single order_SS2_Modified Z-pick 31040 25005 23829 24036 24473 24999 25331 25939 26768 27732 28697Combined order_SS1_Return 18988 18576 18654 18747 19323 19792 20110 20729 21382 22138 22908Combined order_SS2_Return 19292 18725 18931 19126 19640 19697 20023 20650 21274 21949 22730Combined order_SS1_Modified Z-pick 21684 17535 16673 16796 17195 17704 17984 18452 19023 19632 20322Combined order_SS2_Modified Z-pick 21525 17695 16836 17065 17549 18094 18375 18877 19388 20006 20651

ent picking paths, as shown in Tables 1, 2, and 3 for differentpicking density of 10%, 20% and 30%, respectively.

From Tables 1, 2, and 3 we know that the average order pick-ing distance of single order and combined order, under differentstorage 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 isbased on the merchandise item access frequency plus merchan-dise item similarity) at different density 10%, 20%, and 30% atreturn and modified Z-pick picking principles, at different crossaisle quantity, respectively. The trend of average overall pick-ing distance versus overall experimental performance, and plot isdrawn in order to understand the effect of these factors on the over-all performance of an order picking system. The comparison ofaverage overall picking distance for densities of 10% is shown in

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Table 3. Average order picking distance of density 30% (unit: meter)

Order combination_storage assignment Cross aisle quantity_order picking policy 0 1 2 3 4 5 6 7 8 9 10

Single order_SS1_Return 32123 32809 33110 33194 34112 34338 34835 36008 37250 38595 39862Single order_SS2_Return 32662 33216 33070 33406 34335 34879 35476 36636 37967 39197 40390Single order_SS1_Modified Z-pick 36618 30562 28879 29192 29598 30745 31171 32108 33074 34098 35277Single order_SS2_Modified Z-pick 38230 31224 29465 29977 30664 31591 32144 33064 34182 35249 36445Combined order_SS1_Return 11815 12415 13009 13597 14161 14606 14995 15570 16151 16751 17345Combined order_SS2_Return 11941 12541 13092 13570 14140 14602 15030 15611 16211 16757 17293Combined order_SS1_Modified Z-pick 15603 13419 12779 13019 13500 13981 14349 14798 15312 15773 16226Combined 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 averageoverall 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 thesimulation is arranged and variance analysis is performed. The

Fig. 8. The comparison ofaverage overall picking dis-tance for density of 10%

result is shown in Table 4. From Table 4, we know that theorder combination, picking density, storage assignment plan-ning and cross aisle quantity all have obvious different ef-fects on the average overall picking distance. This article per-forms Duncan tests under such a large differing situation toanalyze mainly the average overall picking distance at dif-ferent cross aisle quantity, different order combination, dif-ferent picking density within an aisle, different order pick-

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Fig. 9. The comparison of aver-age overall picking distance fordensity of 20%

Fig. 10. The comparison of averageoverall picking distance for densityof 30%

ing policy and different storage assignment strategy. The re-lated results and analysis is shown in Tables 5, 6, 7, 8,and 9.

From the result of Table 5, we know that the average over-all picking distance is no different in two or three cross aislesconditions. In set 2, the cross aisle quantities are 1, 4, or 5, re-

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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 0.8486b∗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 0.3470b∗e 10 2938.91 293.89 0.06 1.0000a∗b∗e 10 5182.91 518.29 0.10 0.9998c∗e 20 140305.46 7015.27 1.41 0.1070a∗c∗e 20 35669.73 1783.49 0.36 0.9959b∗c∗e 20 2624.49 131.22 0.03 1.0000a∗b∗c∗e 20 2657.37 132.87 0.03 1.0000d∗e 10 181186.60 18118.66 3.64 < .0001∗a∗d∗e 10 10635.35 1063.53 0.21 0.9951b∗d∗e 10 13977.16 1397.72 0.28 0.9854a∗b∗d∗e 10 11949.41 1194.94 0.24 0.9921c∗d∗e 20 83123.17 4156.16 0.84 0.6705a∗c∗d∗e 20 20054.58 1002.73 0.20 0.9999b∗c∗d∗e 20 11448.67 572.43 0.12 1.0000a∗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 policye: cross aisle quantity

Table 4. ANOVA results for relativetravel distance

Cross aisle quantity Duncan group

3 H2 H1 G4 G5 G F6 F7 E8 D9 C0 B

10 A

Table 5. Comparison ofaverage picking distancefor different cross aislequantity

Table 6. Comparison of average picking distance for different order combi-nation

Order combination Average picking distance Ranking

Combined order 582.184 1Single order 911.413 2

spectively. These three cross aisle quantities all belong to GroupG. In set 3, the cross aisle quantities are 5 and 6, where thesetwo cross aisle quantities all belong to Group F because in cases

Table 7. Comparison of average picking distance for different picking dens-ity

Picking density Average picking distance Rankingwithin an aisle

30% 678.524 120% 885.669 210% 1080.256 3

Table 8. Comparison of average picking distance for different order pickingpolicy

Order picking policy Average picking distance Ranking

Modified Z-pick 860.267 1Return 902.699 2

with one or too many cross aisles, they all have the same badresult in the order picking efficiency. Therefore, the addition oftwo or three appropriate cross aisles is the best design for en-hancing the order picking efficiency as well as space utilizationrate. From the result in Table 6, we know that the average over-all picking distance in a different order combination has obvious

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Table 9. Comparison of average picking distance for different storage as-signment strategy

Storage assignment strategy Average picking distance Ranking

ABC access frequency plus 863.309 1merchandise item similarityABC access frequency 899.657 2

difference. Comparing single order and combination order, wefind that the latter has better average overall picking distance.From the result of Table 7, we know that the picking densityinside the aisle has distinguished effect on the average overallpicking distance: the higher the picking density inside the aisle,the shorter the picking distance. From the result of Table 8, theorder picking policy has obvious effect on the average overallpicking distance. Comparing the modified Z-pick picking policyproposed by this article and the return policy from the refer-ence, the former is more helpful in enhancing the order pickingperformance. From the result in Table 9, the different storage as-signment strategy has distinguished effect on the average overallpicking distance. The first strategy is based on ABC access fre-quency and the other strategy is based on ABC access frequencyplus merchandise item similarity. From the result, we find thatthe strategy based on ABC access frequency plus merchandiseitem similarity has a helpful effect in enhancing the order pickingperformance.

5 Conclusion

In the previous studies on the problems of enhancing the orderpicking operation efficiency of a warehouse, from scholars over-seas or domestically, they mostly focus on and are limited toorder picking policy, picking path and storage assignment plan-ning. Few focus on a combined discussion on the design of crossaisle quantity of the original warehouse layout, the order pick-ing policy, storage assignment planning, average picking densityinside an aisle, etc. Therefore, this article develops a combina-tion model for combining factors such as cross aisle quantity(0, 1, 2, . . . , 9), storage assignment planning (ABC accessfrequency, ABC access frequency plus merchandise item similar-ity), order picking policy(return and modified Z-pick), differentpicking density inside an aisle(10%,20%,30%), and order com-bination. Through system simulation experiments, we verify thatwe can find optimum combination for warehouse design in dif-ferent environment and better performance is found. It is hopedthat this article can be a practical and useful reference to the in-dustry in the design and planning of an order picking system ina warehouse system.

From the simulation experiments and statistical analysis, thecurrent warehouse design environments can be summarized asfollows:

1. The modified Z-pick picking policy developed by this articleis better than return policy in obtaining a better average pick-ing distance. Therefore, the modified Z-pick picking policy

proposed by this article has more practical use than that ofothers.

2. The research presented here finds optimum warehouse de-sign combination in three different picking densities insidean aisle, and in different factors such as different cross aislequantity, different order picking policy, different order com-binations and different storage assignment planning.

3. The picking distance is better in combined order than that ofsingle order, and the effect is more distinguished when thepicking density inside an aisle became larger.

4. Storage assignment planning, based on ABC access fre-quency plus merchandise item similarity, is sure to be helpfulon the picking performance.

5. There exist interactions among those five factors such aspicking density, cross aisle quantity, picking policy, ordercombination and storage assignment planning.

6. From the simulation result verification, we know that ap-propriate cross aisle quantity accompanied with storage as-signment planning has a distinguished effect in reducing theoverall picking distance.

7. Plan the storage assignment according to ABC access fre-quency plus merchandise item similarity when the order hasmore merchandise picking items, and use the similar ordercombination method and the modified Z-pick picking policy,which have better picking performance.

8. This article considers the combination of factors such ascross aisle quantity, storage assignment planning, order pick-ing policy, order combination, etc. The work presented hereprovides a database based on average overall picking dis-tance as an evaluation index to the industry as a referencefor the warehouse design or improvement of the warehouseplanning.

Acknowledgement This research was supported partially by a researchgrant from National Science Council of Taiwan, R.O.C. under the projectnumber: NSC 92-2213-E-216-026.

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