Improvement order picking in mobile storage systems with a middle cross aisle

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1 International Journal of Production Research, Vol. 47, No. 4, 15 February 2009, Improvement order picking in mobile storage systems with a middle cross aisle KUAN-YU HUy, TIEN-HSIANG CHANGz, HSIN-PIN FU*x and HSIAOPING YEHx ydepartment of Marketing and Distribution Management, Tajen University, Pingtung Taiwan, Republic of China zdepartment of Information Management, National Kaohsiung University of Applied Science, Kaohsiung, Taiwan, Republic of China xdepartment of Marketing and Distribution Management, National Kaohsiung First University of Science and Technology, Kaohsiung (811), Taiwan, Republic of China (Revision received July 2007) Mobile automated storage/retrieval system (M-AS/RS) is more efficient than mobile storage system (MSS). However, the problems of huge rack row movement and long travel distance have not been effectively solved, especially for heavy items. This study proposes the middle cross aisle model (MCAM) based on the perspective of warehouse layout of M-AS/RS. By designing the layout of cross aisle from front to middle, the warehouse was divided into two small blocks. Picker travel distance could thus be reduced significantly, reducing the huge rack row and making rack row movement more economic and safe. This study formulates the MCAM operation and decomposes the order picking process into three stages, integrating with routing algorithms to achieve better picking routes. Simulation results showed that the MCAM model outperformed the M-AS/RS model. It is suitable for application to lower order density, heavy items with deep racks rows. The optimal ratio for simulation experiment rack shape is 0.6 to 1. Finally, the authors compared typical M-AS/RS and MCAM and also raised some practical concerns regarding its application to industry and addressed future research directions. Keywords: Mobile storage system; Automated mobile storage/retrieval system; Warehouse layout; Integrated multi-level conveying device 1. Introduction Existing warehousing systems can be divided into two types: (i) static-rack storage systems; and (ii) mobile-rack storage systems (MSS). MSS uses 85% of the system area, compared with just 40% for the static rack system (MMH 2000). Therefore, it can achieve high storage volume where space is expensive. It can also provide a buffer for on-site storage systems, while reducing the costs of off-site storage and transportation, minimising the need for material handling, and improving material flow. *Corresponding author. hpfu@ccms.nkfust.edu.tw International Journal of Production Research ISSN print/issn X online ß 2009 Taylor & Francis DOI: /

2 1090 K.-Y. Hu et al. Figure 1. MCAM with IMCD illustration. Although MSS possess some advantages, the present system has some weaknesses. These include: manual operation, large rack row movement, limitation (height) of store items and long access time. To improve problems of manual operation and limitation of store items, Chang et al. (2006b, 2007) proposed MSS with automated S/R function (so-called M-AS/RS). However, due to the design of picker travel on the front cross aisle, the problems of huge rack row movement and long travel distance have not been effectively solved, especially for heavy items. Therefore, this paper is to review a view of the warehouse layout of an M-AS/RS model. By designing the cross aisle layout to establish a M-AS/RS with a middle cross aisle picking model (MCAM) (figure 1), the rack rows can be reduced in size, and their movement can be made safe and more economic. Additionally, the travel distance can be significantly reduced. This study first highlights the advantages of MSS and presents the history of M-AS/RS. Few studies have examined MSS. This study surveys related works on MSS and arranges articles dealing with static rack system in the literature review section. This study then describes the MCAM and its routing algorithm in the section dealing with the middle cross aisle model. To validate the proposed model, simulation experiments are performed in section 4 that aim to compare the performance between MCAM and M-AS/RS. Finally, section 5 presents conclusions, makes practical suggestions and proposes further study directions. 2. Literature review To enhance order picking efficiency, many studies have focused on static rack systems during recent decades (De Koster et al. 2007). This paper arranges the related works into several areas.

3 Improvement order picking in mobile storage systems 1091 By arranging the picking sequence (path) to minimise travel distance, the operating efficiency of AS/RS was enhanced (Hwang and Song 1993, Daniels et al. 1998). In relation to material handling, many studies have examined the planning of material handling path (Yang et al. 2000, Castillo and Peters et al. 2002). Regarding warehouse layout, Roodbergen and de Koster (2001) considered routing and layout issues in warehouses with multiple cross aisles. The cross aisles provide greater flexibility in order picker routing, thus reducing order picking travel distances. Moreover, De Koster and Van der Poort (1998) found efficient order-picking routes with optimal and heuristic methods. Furthermore, Petersen (1997) examined the effects of the shape of the warehouse; a warehouse that has fewer, longer aisles results in a shorter route than a warehouse with more but shorter aisles. However, few studies have been conducted on the MSS mainly because MSS do not possess automated S/R function. Chang et al. (2000) invented an integrated multi-level conveying device (IMCD) which is an obstruction-free, cross-level, auto-access facility that provides a three-dimensional drawing movement and Chang et al. (2006a) proposed that the IMCD can solve the article transportation problem in multi-floor warehouses. Chang et al. (2006b) think that the IMCD is suitable for handling automatically the article in MSS and therefore applied it to construct an M-AS/RS of a single-sided picking model. To enhance the performance of M-AS/ RS, Chang et al. (2007) further proposed a two-sided picking model with an aisleassignment algorithm which made a modification of the movement action of the IMCD to enhance the operation performance by reducing the number of aisles required for an IMCD operation. Therefore, Chang et al. (2006b, 2007) are the only ones who applied IMCD and proposed MSS with automated S/R function (M-AS/RS). However, the problems of huge rack row movement and long travel distance have not been effectively solved, especially for heavy items. This paper proposes a MCAM to improve the problem of the existing M-AS/RS model. 3. The middle cross aisle model Before proposing the MCAM the authors first briefly describe the M-AS/RS model proposed by Chang et al. (2006b, 2007). This model integrated with the IT, IMCD and routing algorithms enable the MSS with automated S/R function. IMCD is an obstruction-free, cross-level, auto-access facility offering a three-dimensional movement (Chang et al. 2000). Furthermore, for article picking up and placement, a polar co-ordinate robotic arm (PCRA) and a container are installed on the loading platform of IMCD (figure 2). The IMCD moves along the X dimension on cross aisle and the Y dimension on the picking aisle, and the PCRA attached on IMCD moves vertically along the Z dimension and retrieves/stores articles. After the brief statement of M-AS/RS, the symbols used in the MCAM are as follows: I Number of picking aisles. J Number of stacks. K Number of layers. w Width of a unit rack, picking aisle, middle aisle. h Height of a unit rack.

4 1092 K.-Y. Hu et al. Container Loading platform Polar co-ordinate robotic arm Figure 2. The IMCD operation in warehouse. l Length of a unit rack, picking aisle, middle aisle. W Width of the warehousing centre, W ¼ (I þ 1) w. L Length of the warehousing centre, L ¼ (J þ 1) l. H Height of the warehousing centre, H ¼ K h. R i The ith rack in the MCAM. A i The ith picking aisle in the MCAM. n(x, y, z) Item n located at x row, y stack, z layer, x ¼ 1, 2,..., I; y ¼ 1, 2,..., J; z ¼ 1, 2,..., K; ify J/2 then located at block 1 else block 2. CT Cycle time of picking in a batch order. OS Set of items in a batch order. RS Set of item location racks for OS. PA Set of possible picking aisles for OS. RA Set of picking aisles for OS. P i Items picked at the ith sequence in an order batch. P i P iþ1 Distance from ith to i þ 1th picking sequence in an order batch. v x Speed of X dimension (cross aisle) movement for IMCD. v y Speed of Y dimension (horizontal) movement for IMCD. v z Speed of Z dimension (vertical) movement for IMCD. v c Speed of the movement of rack rows. t Pi P iþ1 Time of travelling from ith to i þ 1th sequence in an order batch. Time of the X dimension (cross aisle) movement for IMCD. t x

5 Improvement order picking in mobile storage systems 1093 t y t z t c Time of the Y dimension (horizontal) movement for IMCD. Time of the Z dimension (vertical) movement for IMCD. Time of the movement for rack rows. 3.1 Picking model In MCAM, the total travel distance that must be travelled by IMCD to complete batch order picking is divided into three segments and expressed with an objective function. Rather than calculating the travel distance in the horizontal dimension, the travel time required for IMCD to finish a batch order is determined by movement through three dimensions, i.e. X, Y, and Z. The objective function is expressed as follows: Min CT ¼ t P0 P 1 þ Xn 1 t pi p iþ1 þ t Pn P 0 i ¼ 1, 2, 3,..., n; n 2 integer where i¼1 t P0 P 1 P n 1 i¼1 t p i p iþ1 t Pn P 0 The time from the I/O station to the 1st picking location. The time from the ith to the (i þ 1)th picking location. The return trip time from the last picking location back to the departure station. This study makes some assumptions to simplify the calculation and analysis of MCAM: 1. The picking policy employs batch order picking. 2. The retrieval time for all stored items is constant. 3. The acceleration and deceleration of IMCD are ignored, i.e. IMCD moves at a constant speed. 4. IMCD must return to the I/O station following batch completion. 5. This study only considers picking operations and ignores storage activities such as loading and unloading operations. 6. IMCD capacity is not considered. 7. Items could be picked from both sides (so called co-picking aisle ) of the racks. 3.2 Picking elements and time calculation The MCAM movement includes two main parts; storage rack blocks and IMCD. This study analyses and arranges the movement process into five fundamental elements. Each batch order picking process involves a combination of multiple elements. The elements are 1. The IMCD moves along the middle cross aisle. 2. The racks create the new picking aisle. 3. The IMCD moves within the picking aisle. 4. The IMCD enters or leaves the block picking aisle via the middle aisle. 5. The IMCD enters or leave to another block picking aisle via the middle aisle.

6 1094 K.-Y. Hu et al. This study details the formula used to calculate the above five elements. Element 1: The IMCD moves along the middle cross aisle The movement distance is the relative distance between two entrance of picking aisle on middle aisle. The calculation formula is t 1 ¼ A iþ1 A i w ð1þ Element 2: The racks create the new picking aisle The movement time for racks to create a new picking aisle in each movement is v x t 2 ¼ w v c ð2þ Element 3: The IMCD moves within the picking aisles The movement time for the IMCD is the relative distance for consecutive location in the Y Z dimension. The time t y ¼ y iþ1 y i l and t z ¼ z iþ1 z i h v y v z respectively. Hence, the time determined is t 3 ¼ max t y, t z ð3þ Element 4: The IMCD enters or leaves the block picking aisle via the middle aisle The time t y ¼ ðj=2 þ 1Þ y i l j and t z ¼ z i 0j h v y v z respectively. The time is ðj=2 þ 1Þ y i l t 4 ¼ Max, v y jz i 0j h v z ð4þ Element 5: The IMCD enters or leaves another block picking aisle via the middle aisle The time t y ¼ y ð i J=2Þ l j and t z ¼ z i 0j h v y v z respectively. The time is t 5 ¼ Max y i J=2 l, v y jz i 0j h v z ð5þ Table 1 summarises the cycle movement scenarios involved in batch picking in MCAM. To help the reader understand the MCAM process operation in table 1, this study presents the IMCD and rack movements in figure 3a d.

7 Improvement order picking in mobile storage systems 1095 Table 1. Summary of cyclical movements of MCAM. Stage Objective function Situation IMCD and rack rows movement steps 1 I/O point to first picking location tp0p1 (e.g. ¼ max(t tp0p1 1, t2) þ t4) 2 X n 1 i¼1 tpipiþ1 Piþ1 and Pi are at the same aisle P iþ1 and P i are not at the same aisle The same block (e.g. ¼ t tpipiþ1 3) Different block (e.g. ¼ max(t tpipiþ1 4, t 2 ) þ t 5 ) The same block (e.g. ¼ 2 t tpipiþ1 4 þ max(t 1,t 2 )) a. IMCD moves to the new picking aisle entrance along the middle aisle (X axis) (as figure 3a, 1).The rack rows create the new picking aisle (figure 3a, À) simultaneously. b. IMCD (Y Z axis) movie to P 1 location along the new created picking aisle (figure 3a, 2). IMCD moves from Pi to Piþ1 (Y Z dimension)along the same picking aisle (figure 3b, 3). a. IMCD moves from Pi to the middle aisle (Y Z dimension) along the picking aisle. (figure 3b, 4) The rack rows create a new picking aisle (figure 3b, `) simultaneously b. IMCD enter the new created picking aisle to Piþ1 (Y Z dimension) simultaneously (figure 3b, 5) a. IMCD moves from P i to the middle cross aisle (Y Z dimension) (figure 3c, 9). b. IMCD moves to the new picking aisle entrance along the middle cross aisle. (X axis) (figure 3d, 10). The rack rows create a new picking aisle (figure 3d, ˆ) simultaneously. c. IMCD moves from the middle aisle to the Piþ1 (Y Z dimension) (figure 3d, 11) Different block (e.g. ¼ max(t tpipiþ1 5, t 2 ) þ t 1 þ t 4 ) a. IMCD moves from P i back to the middle cross aisle (Y Z dimension) (figure 3c, 6) and the rack rows automatically create a new picking aisle (figure 3c, ). Time calculation max(t1, t2) t 4 t3 max(t4, t2) t5 t 4 max(t1, t2) t 4 max(t 5, t 2 ) (continued )

8 1096 K.-Y. Hu et al. Table 1. Continued. Stage Objective function Situation IMCD and rack rows movement steps b. The IMCD moves to the new picking aisle entrance along the middle cross aisle (X axis) (figure 3c, 7). c. IMCD moves from the middle aisle to Piþ1 (Y Z dimension) (figure 3c, 8). 3 t PnP0 Return to I/O point (e.g. t PnP0 ¼ t4 þ max(t1, t2)) a. IMCD moves back to the middle cross aisle (Y Z dimension) simultaneously (figure 3d, 12). b. IMCD moves back to the I/O point (X axis) (figure 3d, 13) and racks return to the initial position (figure 3d, ). Time calculation t1 t4 t4 max(t1, t2)

9 Improvement order picking in mobile storage systems 1097 A 1 A 2 A I A I +1 A 1 A 2... A I A I +1 R I R I w (a) R 1 R 2 R 1 R 2 (b) P1 3 P1 n(x,y,z) h Block 1 P5 P4 P2 P4 P5 4 P2 l I/O 1 2 I/O 5 Block 2 P3 P3 (c) P1 (d) P1 Block 1 9 P4 P5 P2 12 P5 P4 P2 I/O 8 7 I/O Block 2 6 P3 P3 IMCD movement: Figure 3. Rack movement: Illustration of travel path of MCAM. For instance, if there are five items to be picked in a batch order, each circumstance in table 1 just occurs once. Then, the CT ¼ t P0 P 1 þ t P1 P 2 þ t P2 P 3 þ t P3 P 4 þ t P4 P 5 þ t P5 P 0 ¼ðMaxðt 1, t 2 Þþt 4 Þþt 3 þðmaxðt 4, t 2 Þþt 5 Þþð2t 4 þ Maxðt 1, t 2 ÞÞ þ ðmaxðt 5, t 2 Þþ t 1 þ t 4 Þþðt 4 þ Maxðt 1, t 2 ÞÞ. 3.3 Routing algorithm All items to be picked in a batch order can be considered a sequential picking route. The routing algorithm comprises three stages used to achieve a near optimal picking route. The first stage involves obtaining the minimum picking aisles required for the IMCD to run in a batch order; the second stage determines the picking sequence among the selected picking aisles, and the third stage identifies the shortest path for IMCD movement in the picking aisle. Stage 1: Determine the picking aisles to be run in blocks by the IMCD Eight steps are performed to minimise the number of aisles traveled by IMCD during batch order picking.

10 1098 K.-Y. Hu et al. Table 2. Weighted value matrix. RS PA A 1 A 2 A 3... A i... A I R R i 1 R iþ1 1 R I 1 Weighted sum Step 1: Obtain the set of picking items in a batch order OS ¼ {n 1, n 2,..., n n }. Step 2: Take n i (x i, y i, z i ) location; assign x i ¼ R i ; the set of all the item storage racks is expressed as RS ¼ {R i, R iþ1,...}, i ¼ 1, 2,...I. Step 3: Item located at R i can be picked either A i or A iþ1. With the relation of R i 2 {A i, A iþ1 }, determine the set of possible picking aisles that the IMCD selected. Then PA ¼ {A i, A iþ1,...}, i ¼ 1, 2,...I. Step 4: Expand the elements in set PA; the aisle that might be used to pick rack items is assigned a weighted value 1, and the others are left blank. The total weighted value of each element A i in PA as table 2. Element A i in PA thus has two possible weighted values (1, 2). A weighted value of 1 indicates that only one rack row (on the right side or on the left side of the aisle) is stored with the items to be picked, whereas a weighted value of 2 indicates that the rack rows on both sides of the aisle are stored with items to be picked (this aisle is known as the co-picking aisle ). Step 5: If the weighted value for A i A iþ1, go to Step 6. Otherwise, go to Step 7. Step 6: In this case, if A i 4A iþ1 means that IMCD run in A i can pick both side racks than A i þ1. If the weighted value of A i equals to A iþ1, A i and A iþ1 can pick the same number of rack. As A i is closer to the departure station than A iþ1, it is more efficient to enter A i than A iþ1, and A i is chosen in the set of real picking aisle RA. The location of items on the racks on sides R i, R iþ1 is then eliminated from the order set OS, OS ¼ OS {n i jn i 2 R i, R iþ1 }. Then go to Step 8. Step 7: In this case, A iþ1 can pick more racks than A i. It is more efficient to enter A iþ1 than A i, and A iþ1 is chosen in the set of real picking aisles RA. The locations of items on the racks on the two sides R iþ1, R iþ2 are then deleted from the order set OS, OS ¼ OS {n i jn i 2 R iþ1, R iþ2 }. Step 8: Repeat Steps 1 7 until OS ¼ fg. Stage 2: Determine the picking sequence among the chosen picking aisles To determine the picking aisle sequence for IMCD run. The desending assignment rules are adopted to save energy, as follows: starting with the farthest picking aisle from the I/O point. The aisle value is determined by Max[A 1 (x 1 ), A 2 (x 2 )...A n (x n ).].

11 Improvement order picking in mobile storage systems 1099 A B C D E Figure 4. The paths in picking aisle. Stage 3: Determine the picking sequence in a picking aisle The no-skip approach developed by Goetschalckx and Ratliff (1988) is used to determine the picking sequence in the real picking aisle. This approach is briefly described as follows. After establishing a touring network for the storage locations of items conveyed in the picking aisle, when using the no-skip approach forbids the crossing of paths in the picking aisle (see figure 4). Three assignment rules are used in the no-skip approach to avoid the IMCD moving back and forth in a picking aisle. The rules are as follows: 1. The larger stack value of location; i.e. the location of stack value; i.e., Max½n 1 ðy 1 Þ, n 2 ðy 2 Þ...n n ðy j ÞŠ. 2. The larger layer value of location; i.e., Max½n 1 ðz 1 Þ, n 2 ðz 2 Þ...n n ðz j ÞŠ. 3. The larger row value of location; i.e., Max½n 1 ðx 1 Þ, n 2 ðx 2 Þ...n n ðx j ÞŠ. 4. Simulation experiment This section conducts three simulation experiments to evaluate the MCAM, including: 1. The different levels of four factors. 2. Aisle depth. 3. Warehouse shape. For order generation, a number is randomly generated to represent the item locations. All the generations are performed based on the cumulated density function. For purposes of comparison and reducing random number variance, this study adapted the common random numbers in experiments 1 and 2. Each simulation combination comprises 500 runs. The average travel time required to complete an order is selected as the performance index. 4.1 The different levels of four factors This experiment compares with traditional M-AS/RS, which was proposed by Chang et al. (2007). The experiments are performed under identical parameter and

12 1100 K.-Y. Hu et al. warehouse size conditions. A warehouse with 10 rows, 10 stacks, 10 layers, and l ¼ w ¼ h ¼ 1m. The four factors of order size, warehouse size (the number of equipment rows), v x and v y, were set at three levels (table 3). Based on the L 9 (3 4 ) orthogonal array (table 4), there were a total of nine combinations. Table 5 lists the results of each combination. Table 3. Experiment factor level. Level Factor Order size No. of equipment row x (m/sec) x (m/sec) Table 4. L 9 (3 4 ) orthogonal array. Factor Combination Table 5. The simulation results of nine combinations. Average travel time (sec) Combination M-AS/RS MCAM Reduction Percentage

13 Improvement order picking in mobile storage systems 1101 The results (table 5) demonstrate that the MCAM outperforms M-AS/RS in all combinations. Thus the MCAM clearly outperforms the M-AS/RS model. Furthermore, the factor effects of order size for three levels were 5.6%, 6.6%, and 6.9% respectively. Demonstrating that larger order size achieves greater time savings than smaller order size. Regarding the warehouse size factor, the reduction percentages were 5.2, 6.5, 7.6 for the warehouse size three levels. This result indicates that order density reduces with certain order quantities,exerting a significant impact on performance. In contrast, a smaller warehouse size has high-order density with certain order quantities, demonstrating that performance is not significantly affected. 4.2 Aisle depth To examine the effects of aisle depth on MCAM, a warehouse comprising 10 rows, 10 layers, and different stacks with l ¼ w ¼ h ¼ 1m, v x ¼ v y ¼ v z ¼ v c ¼ 1 m/sec is made the subject of a simulation. Different aisle depths are set at five levels (see table 6). Similarly, results demonstrate that the average travel time is considerably reduced with MCAM for all settings, particularly for the cases involving longer aisle depth and low order density. 4.3 Warehouse shape The experiments attempt to justify MCAM based on the effects of warehouse shapes given constant warehouse capacity. With the same warehouse dimension as above and ratio of warehouse shape l/w set to range between 0.1 and 5.0 with increments of 0.1 in each simulation run, i.e. a total of 50 shapes are presented. The results indicate that the average travel time increases markedly, exceeding 1 for all order sizes (as shown in figures 5 and 6). However, a small ratio of l/w is impractical for warehouses because the rack length is too small to store goods. This study thus argues that the optimal ratio range of l/w is roughly from 0.6 to 1.0. The results support the findings of Petersen (1997) that the shape of the warehouse can affect the picking efficiency. Table 6. The simulation results of five different aisle depth. Travel time Situation I J K M-AS/RS MCAM Performance improvement (%)

14 1102 K.-Y. Hu et al. Average travel time(sec) Ratio of l/w with w=1m n=5 n=25 n=50 n=75 n=100 Figure 5. The average travel times with different ratios of l/w (w ¼ 1m). Average travel time(sec) Ratio of l/w with w=2m n=5 n=25 n=50 n=75 n=100 Figure 6. The average travel times with different ratios of l/w (w ¼ 2m). 5. Conclusion Without reducing the storage capacity, this study redesigned the cross aisle layout in M-AS/RS from front to middle. The MCAM downsizes the large rack rows and thus enables not only the generation of shorter picking tours but also makes equipment row movement easier and more economical and reduces the risk of goods being damaged. Comparing the M-AS/RS under simulation experiment the MCAM offers higher performance. Furthermore, the experiment results demonstrate that MCAM is suitable for cases with large pick lists, low order density, and optimal rack shape ratio range of from 0.6 to 1.0. Table 7 compares MCAM with the traditional M-AS/RS. In practical applications, the MCAM can be applied to such settings as storage of documents in offices, storage of books in libraries, and the storage of maintenance, repair, and operational materials for manufacturing. However, pragmatic issues require consideration in determining whether the system is suitable for specific circumstances. Issues requiring consideration include high investment

15 Improvement order picking in mobile storage systems 1103 Table 7. Comparisons of MCAM with the original M-AS/RS. Items M-AS/RS MCAM Rack size Smaller Mobility for racks Faster Travel distance Shorter Risk of heavy Lower goods damage Energy saving Better costs, limitations on the type of items that can be stored, storage environment, and frequency of storage and retrieval. According to Roodbergen and De Koster s research (2001), they found that to add too many or less cross aisles is not good for a picking tour. If the rack is very deep, then this study can consider the optimisation of warehouse shape. MCAM can be extended to add two or more cross aisles for performance enhancement. Finally, several factors that may enhance the performance of the proposed MCAM model still need to be explored. These include storage planning, application of other algorithms, and dual cycling of goods retrieval and picking. This study acknowledges a deliberate focus on the warehouse layout alone, without consideration of these other factors, which are likely to provide abundant avenues for future study. Acknowledgment The authors would like to thank the National Science Council of the Republic of China, Taiwan for financially supporting this research under Contract No. NSC E MY3. References Castillo, I. and Peters, B.A., Unit load and material-handling considerations in facility layout design. Int. J. Prod. Res., 2002, 40(13), Chang, T.-S., Fu, H.-P. and Hsu, L.-C., The innovative picking device application for transferring articles between two-levels of a multi-story building. Int. J. Adv. Manuf. Tech., 2006a, 28(1/2), Chang, T.-H., Fu, H.-P. and Hu, K.-Y., Innovative application of an integrated multi-level conveying device to a mobile storage system. Int. J. Adv. Manuf. Tech., 2006b, 29(9/10), Chang, T.-H., Fu, H.-P. and Hu, K.-Y., A two-sided picking model of M-AS/RS with an aisle-assignment algorithm. Int. J. Prod. Res., 2007, 45(17), Chang, T.-S., Hsieh, Y.-A., and Yang, C.-H., Warehousing system having a picking device For transferring articles between two levels of a multistory building. US Patent No , Daniels, R.L., Rummel, J.L. and Schantz, R., A model for warehouse order picking. Eur. J. Oper. Res., 1998, 105(1), De Koster, R. and Van Der Poort, E., Routing order pickers in a warehouse: a comparison between optimal and heuristic solutions. IIE Trans., 1998, 30(5),

16 1104 K.-Y. Hu et al. De Koster, R., Le-Duc, T. and Roodbergen, K.J., Design and control of warehouse order picking: a literature review. Eur. J. Oper. Res., 2007, 182(2), Hwang, H. and Song, J.Y., Sequencing picking operations and travel time models for man-on-board storage and retrieval warehousing system. Int. J. Prod. Econ., 1993, 29(1), MMH, Mobile-rack system optimises use of cube. Modern Materials Handling, 2000, October, 75. Petersen, C.G., An evaluation of order picking routeing policies. Int. J. Oper. Prod. Manag., 1997, 17(11), Roodbergen, K.J. and de Koster, R., Routing order pickers in a warehouse with a middle aisle. Eur. J. Oper. Res., 2001, 133(1), Yang, T.H., Su, C.T. and Hsu, Y.R., Systematic layout planning: a study on semiconductor wafer fabrication facilities. Int. J. Oper. Prod. Manag., 2000, 20(11),

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