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附錄 英文原文 Ling-feng Hsieh · Lihui Tsai The optimum design of a warehouse system on order picking efficiencyReceived: 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@chu.edu.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 modification 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 operating 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 reasonable 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. 627 2 Literature review Take into account factors that affect order picking system performance, 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 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 distinguished 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 improvement 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 algorithm 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 represents 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- Fig. 2. Warehouse layout with one cross aisle 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 629 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 ith aisle transfer to the mth 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 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 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