應用跨樓層搬運設備建構移動式倉儲存取系統之研究

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行政院國家科學委員會專題研究計畫成果報告

應用跨樓層搬運設備建構移動式倉儲存取系統之研究(第 3

年)

研究成果報告(完整版)

計畫類別：個別型計畫編號： NSC 95-2221-E-151-035-MY3 執行期間： 97 年 08 月 01 日至 98 年 08 月 15 日執行單位：國立高雄應用科技大學資訊管理系計畫主持人：張添香共同主持人：傅新彬計畫參與人員：碩士班研究生-兼任助理人員：鄭汎原碩士班研究生-兼任助理人員：江昱潔碩士班研究生-兼任助理人員：陳乙諒碩士班研究生-兼任助理人員：陳嬌釗碩士班研究生-兼任助理人員：鍾雅娟報告附件：出席國際會議研究心得報告及發表論文處理方式：本計畫可公開查詢

中華民國 98 年 11 月 03 日

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行政院國家科學委員會補助專題研究計畫成果報告

應用跨樓層搬運設備建構移動式倉儲存取系統之研究

計畫類別：□ 個別型計畫

■ 整合型計畫

計畫編號：NSC

95-2221-E-151-035-MY3

執行期間：

95 年 08 月 01 日至 98 年 07 月 31 日

計畫主持人：

張添香

共同主持人：

傅新彬

計畫參與人員：

第一年--簡昭漢，林尚文第二年--劉智偉，高振豪，鄭秀美，曾惠苹第三年--鍾雅娟，陳嬌釗，江昱潔，鄭汎原，陳乙諒

成果報告類型(依經費核定清單規定繳交)：□精簡報告

■完整報告

本成果報告包括以下應繳交之附件：

□赴國外出差或研習心得報告一份

□赴大陸地區出差或研習心得報告一份

□出席國際學術會議心得報告及發表之論文各一份

□國際合作研究計畫國外研究報告書一份

處理方式：除產學合作研究計畫、提升產業技術及人才培育研究計畫、列

管計畫及下列情形者外，得立即公開查詢

□涉及專利或其他智慧財產權，□一年□二年後可公開查詢

執行單位：

國立高雄應用科技大學資訊管理系

中

華

民

國

98 年

10 月

8 日

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中文摘要

移動式儲存系統具有充分運用儲存空間的優點，然而目前均以人工方式作業，其缺點是存取速度慢、作業成本與錯誤率高，為了克服這些缺點，本研究將使用整合跨樓層搬運設備，從不同角度，建立三個自動揀貨模式之移動式儲存系統，以提升傳統移動式儲存系統的揀貨績效。第一個模式(第一年)，建立一個具單邊揀貨功能的自動揀貨模式之移動式儲存系統，以批次訂單揀貨為例，透過適當排序，實際模擬揀貨過程，結果顯示能有效克服人工作業問題。第二個模式(第二年)，為雙邊自動揀貨模式，透過修改揀貨機行走方式與雙邊揀貨走道設計，以提升揀貨效率，在此模式中，發展出雙邊揀貨走道指派法則，可使揀貨機在揀貨過程，所需行走走道數最少，再運用”no-skip”法則，安排揀貨走道內揀貨順序，兩個階段求解最佳揀貨順序，進行模擬實驗結果顯示，雙邊揀貨模式較單邊揀貨模式，依訂單密度不同，效率可提升 7.6％至 70.6％。第三個模式(第三年)，為中間橫向走道自動揀貨模式，透過走道佈置的改變，探討對揀貨作業之影響，模式中整合三個演算法則，以求解最佳揀貨順序，實際模擬結果顯示，中間橫向走道佈置可大量節省揀貨機在料架列中移動距離。最後以模擬實驗來驗證影響績效的因子，並且針對本研究所所建立的自動化揀貨模式，進行分析與比較，為了提供實務界應用之參考，本研究提供一些建議與未來研究之方向。 關鍵詞：移動式儲存系統、自動化移動式儲存系統、自動倉儲、整合跨樓層搬運設備

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Abstract

The mobile storage system (MSS) has the advantage of complete full use of space. The MSS operates manually now, which is characterized by slow storage and retrieval speed, high cost and frequent error. In order to overcome the disadvantage in the existing MSS, this study used the integrated multi-level conveying device (IMCD) to propose three automated picking models on mobile storage system (M-AS/RS) to enhance the performance of existing MSS.

The first (year) model is “one-side picking model”. This model is an innovative mobile automated storage/retrieval system (M-AS/RS) using an integrated multi-level conveying device (IMCD) for automated item-picking operation. Through appropriate sequencing, the model simulated the picking of items in a batch orders and presented a comparative analysis of this model with existing MSS models concluding that the former has a better performance than the latter.

To improve the performance of M-AS/RS with one-sided picking, the second (year) model is proposed so called “two-sidepicking model”.In thismodel,apicking-aisle-assignment algorithm is developed to reduce the number of picking aisles in which the IMCD is required to run. Matching with the modified IMCD movement action and a ’no-skip’ approach to arranging a picking sequence, simulations are undertaken, and the results demonstrate that the two-sided picking model improve the weaknesses of the one-sided M-AS/RS model.

The operational performance of M-AS/RS with two-sided picking model could have some improvement space if the length of racks is too long. Then, the third (year) modelso called “the crossmiddleaislepicking model”isproposed.In thismodel,theIMCD could reduce movement distance in some cases. The results of simulations demonstrated that the middle cross aisle operational model can enhance the operational efficiency of M-AS/RS with two-sided picking model

Finally, we explored factors that affect the M-AS/RS performance and also made some comparisons between models. Also, the considerations are addressed while applying to industry.

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應用跨樓層搬運設備建構移動式倉儲存取系統之研究

A Study on Automated Picking Model on MSS Using an

IMCD

計畫編號：NSC95-2221-E-151-035-MY3

執行期限：95 年 08 月 01 日至 98 年 07 月 31 日

主持人：張添香國立高雄應用科技大學資訊管理系

共同主持人：傅新彬國立高雄第一科技大學行銷與流通管理系

1. Background and Motivation

Mobile racks can be divided into two kinds: carousel system and mobile storage system (MSS). Carousel system adopts the stock-to-picker retrieval model that the racks rotate on a certain circular track, and the picking machine carries out storage and retrieval activities at a fixed position. Carousel system is mainly suitable for the storage and retrieval of small objects. As for MSS, it is a picker-to-stock retrieval model, which has, wheels placed on the bottom of all the storage equipment. Besides, parallel tracks are placed on the floor. A wheel is designed to be located at the end of each row of equipment. The mobility of each row of storage equipment is moved by turning the wheel, or by pushing the button to drive the electric motors. After separating two adjacent rows of equipment, the aisle is formed. Hence, the picker can enter the aisle to pick and placethe item atstoragerack.The aisle atany two adjacentrowsofequipmentis“mobilized.” Since only one aisle is required to be left for the whole MSS for storage and retrieval, the space of aisles can be tremendously saved, and the efficiency of storage space can be increased.

The MSS has the advantage of full use of space, the storage and retrieval of the warehousing operations are now operated manually, and automated storage and retrieval function are not available. The disadvantages of manual operation are the slow storage and retrieval speed, high cost, and frequent error. The MSS is even designed to be at the height only available for manual operation, so the auxiliary tool is needed for storage and retrieval of item at taller racks, such as ladder or chair. Among the existing automated storage/retrieval systems (AS/RS) equipment, such as picking cart, tote picking, man-on-board system, various kinds of truck, etc., most of these can only enable the racks to conduct up-and-down conveyance at the fixed range of track, but cannot move to another aisle. Although the automated guided vehicle (AGV) can be applied on the transportation from one aisle to another, it cannot carry out lifting operation. So it is needed to develop a new device to automate the material handling activities.

As for the development of automated material handling with the functions of vertical lifting and horizontal moving, Chang et al. (2000) invents an integrated multi-level conveying device (IMCD) to overcome the automated material handling between two levels of a multi-story factory. Since IMCD has the design of float, it needs not depend on any floor track or conveyer when handling material on the same level, or any vertical movement equipment when handling material

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up and down. Therefore, this equipment has the self-running functions of vertical lifting and horizontal moving, Chang et al.（2006）. It is an automated material handling equipment very suitable for MSS.

The MSS possess many advantages, but very few study focus on it. The goal of this study is to construct an MSS with automated storage/retrieval functions called mobile automated storage/retrieval systems (M-AS/RS) that use IMCD so as to enhance the space utility rate and operation efficiency of MSS. In this study, three models will be proposed. First, the M-AS/RS establishes an automated one-sided picking model; that is, the stored goods can be picked on only one side. Moreover, the IMCD run with right-angled path. Second, two-sided picking model was proposed. In this model, we present a modification of the movement action of the IMCD from a right-angled path to a straight-line path. In addition, this model proposes an assignment algorithm to arrange improved picking aisles—thus reducing the number of aisles required for an IMCD operation. Finally, the ‘no-skip’ method developed by Goetschalckx and Ratliff (1988), which arranges the picking sequence inside the aisle, is integrated with the assignment algorithm and the modified IMCD movement action to produce a M-AS/RS with a two-sided picking model.

The disadvantage of M-AS/RS is that if the adjacent sequential picking location could not be picked in the same picking aisle, then tremendous equipment rows have to move in order to create a new picking aisle for picker to run. The movement of huge equipment rows increases not only the operation cost but also the risk of good damage. In the picking process, the picker has to take a long distance to travel. Therefore, the third model is proposed and presents a modification of the cross aisle layout of the warehouse from a front cross aisle to middle cross aisle layout. This model modifies the aisle assignment algorithm proposed by two-sided model to arrange improved picking aisles—thus reducing the movement distance for an IMCD run during picking operation.

This study is an innovative application to establish automated AS/RS model (M-AS/RS) for MSS. Practically, the M-AS/RS can be applied when the frequency of storage and retrieval is low, but high storage space is needed—especially in environments characterized by poor ventilation or the movement of heavy products. Finally, this study makes some comparative analyses between M-AS/RS and MSS models and addresses the advantages of the M-AS/RS model. The results can provide a solution for industry to improve the disadvantages in the current MSS model.

2. Literature Review

The issue of AS/RS always plays important role in warehousing. There are many studies enhancing the performance in different aspects. We survey and classify related studies into several areas.

With the aids of information technology, Daniels et al.(1998) tracking the inventories with computer that parts can be stored in multiple locations, simplifying replenishment of inventory and eliminating the need to reserve space for each item. Lin and Lu (1999) proposed a computer-based procedure to determine order-picking strategies and got significant effect on order picking. Several researchers have also focused on the performance of order picking using man-on-board

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carousel systems (Litvak et al. 2001; Litvak and Adan 2001).

To enhance the efficient operation of the storage/retrieval machine, Park (2001) developed an optimal dwell-point policy for AS/RS with uniformly distributed racks. Malmborg (2001) also modify a well-known rule of thumb heuristic for evaluating the storage rack configurations in AS/RS and proposed additional performance criteria for evaluation of alternative rack configurations.

Synthesizing the above studies, it is apparent that most of the studies apply various mathematical, heuristic methods, warehouse design, storage plan and information technology to enhance the operational efficiency of fixed-rack systems and carousel systems. Very few studies have been conducted on the application of MSS. Under this circumstance, this study introducing the concept which is developed in fixed rack system into MSS.

3. Design of Mobile Storage System

The IMCD is an obstruction-free, cross-level, auto-access facility that provides a three-dimensional drawing movement. The conveying mechanism includes: (i) a translation device with a base bridging the aisle and connected solidly to the horizontal guide rails; (ii) a driving device disposed on the base for driving the base along the horizontal guide rails in a first direction; (iii) a holding apparatus mounted on the base and adapted for holding an article to be conveyed; and (iv) an elevator apparatus disposed on the base for raising and lowering the holding apparatus from the base (see Figure 1). However, certain conditions of equipment and environment are required if the IMCD is to conduct up-and-down conveyancing freely, and if it is to move horizontally. Thus, before constructing an M-AS/RS operational model, it is necessary to add some sensors and controllers (attached to the transportation equipment) to both sides of each rack. The train tracks at the bottom layer not only make the conveyancing equipment row move, but also make the IMCD move. Moreover, to pick and place articles, a polar coordinate robotic arm (PCRA) and a container are installed on the loading platform of IMCD (Figure 1). The PCRA base can be rotated and robotic arms can be extended and retracted in a straight line. With such an equipment environment, an IMCD can conduct up-and-down conveyancing and horizontal transportation and pick articles and place them in the container. In M-AS/RS illustrated on Figure 2, IMCD moves along X axis on front aisle and Y axis on the picking aisle and the PCRA attached on IMCD vertically moves along Z axis and pick/place articles.

Based on above description, this study proposed three models for M-AS/RS. First (year) model is one-sided picking model. Second (year) model is two-sided picking model. Third (year) model is the middle cross aisle picking model. Three models are described respectively as follows.

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Figure 1 The IMCD operation in warehouse

Figure 2 Illustration of the M-AS/RS

Loading platform Polar coordinate robotic arm Container X Y Z

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4. One-sided Picking Model (the first year)

After the free-movement environment for IMCD is established in MSS, we start to design the mobile retrieval and storage operation model of IMCD in MSS. First of all, the symbols of operation model are defined in Table 1 before the description of IMCD operation model in MSS.

Table 1 Definitions of symbols used in M-AS/RS operation model

i

R Racks of the ithrow, i1,2,....,I

j

C Racks of the jth column, j1,2,....,J

k

L Racks of the kth layer, k 1,2,....,K

i

A Aisle no.i1,2,3,...,I1

N Total no. of item of an order

w _{Width of unit rack}

h Height of unit rack

l Length of unit rack

W Width of warehousing center

H Height of warehousing center

L Length of warehousing center



a b c



n , , Location for item n , on the athrow, bthcolumn and cthlayer.

I

a 1,2,3,...,

 , b1,2,3,...,J , c1,2,3,...,K

CT Cycle time for order picking

m

OS The set of items in the mthorder

m

RS The set of the storage racks of the items on the mthorder

m

PA The set of the possible picking aisles for themthorder

m

PS The set of the picking sequences on the #m order i

P Picking items on theithsequence of the batched orders

1  i iP P Distance fromP toi Pi1 y

v Speed of vertical movement of IMCD

x

v Speed of horizontal movement of IMCD

c

v Speed of the movement of equipment rack row

1  i iP

P

t _{Time of move from} _{P to}_i _P_i_₁

x

t Time needed for the horizontal movement of IMCD

y

t Time needed for the vertical movement of IMCD

c

t Time needed for the movement of equipment rack row

4.1 Environment of Mobile Storage System

First of all, when constructing one-sided M-AS/RS（Figure 3）, the structural design of the warehousing environment has to be changed. Besides, in the general warehousing environment

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there is one row of racks available for moving, Jcolumns for every rack, and K layers in every column. In order to make IMCD move freely, there must be a shared and changeable picking aisle and a front aisle. The author assumes the width of the aisle equal to the width of unit rack (w), so the total number of picking aisle equal toI1. Therefore, racks move inside the warehousing center, which needs to have the width, length and height as follows: (1) Width (W)＝Width



w of I units of

storage racks and width of one mobilized picking aisle ＝ (I＋1) × w. (2) Length (L)＝Length (l) of J units of storage racks and width of one front aisle ＝

 





 

Kh . The IMCD adopts one-sided picking, meaning that IMCD being at

A

_i aisle picks the item at R (during this time_i R is on the_i A_i_₁ aisle) and IMCD runs in right-angle path. We also suppose that the size of fork is limited to the length, width and height of a rack, meaning that as IMCD enters A at the lowest position, it can just pick the item ati L1

and no lifting is required. Since the width of aisle is limited to the width of an IMCD, the number of A =i I 1. With the above assumptions, we are going to explain the operation model in the

following section.

Figure 3: Initial position of one-sided M-AS/RS

4.2 Picking Model

The whole travel distance of IMCD for picking items in an order can be regarded as a well determined sequence with integration of three stages. The objective function is indicated as follows:

Min：TD OP PP P_nO n i i i   



   1 1 1 1 1

OP ：Distance between depot station and the first picking station run by IMCD.

l h P（I,J,K） w ：move direction J . 3 2 1 Front aisle A1 A2 A3…… …… AI AI+1 Depot station Mobile aisle R1 R2……….………R I Rack

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1 

i iP

P ：Distance between the ith

picking station and the (i＋1)thpicking station.

O

Pn ：Distance of return trip from the last picking station to depot station.

4.3 Operation Procedure

and P4



a4,b4,c4



, the determined sequence of the order picking, after

sequencing in advance, is PS1 



P1,P3,P2,P4



. The completion of item picking procedures can be

divided into 3 stages: a. The IMCD travels from depot station to the storage place of Item P . b.₁

The IMCD moves from the storage place of Item P to the storage place of Item1 P and IMCD3

sequentially moves to the storage place of Item P and₂ P for picking up the Item₄ P and₂ P . c.₄

After the Item P is picked, IMCD returns to depot station from the storage place of Item₄ P , and₄

the whole item picking procedures of the order are completed. The time required for these 3 stages are t ,1 t2 and t respectively.3 Therefore, the cycle time of order picking is just the total time

required for these 3 stages. After that, let us explain the detailed picking model and the calculation of t ,1 t2 and t .3

When the order contains n items of products, the picking model is listed in the objective function. The IMCD running time for completion of the whole order picking operation is:CT t1 t2 t3. Table 2 summarized. the picking cycle movement elements on M-AS/RS.

In order to apply IMCD on the automated item picking of MSS, we have to integrate computer ordering system, equipment sensor and IMCD controller so as to make IMCD pick product in MSS. This model also proposed a flowchart for the operation model of the whole M-AS/RS, as shown in figure 4.

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Table2: Summary of the picking cycle movement elements in one-sided M-AS/RS

Stage Objective

function Situation Movement of IMCD Formula

1

P is located at

row1

IMCD directly moves to P location along1

the picking aisle

 

tx ty

Sum ,

1. The rack rows automatically create (open) the new picking aisle. Simultaneously, the IMCD moves to the new picking aisle along the front aisle.

 

tx tc Max , 1 1 OP 1 P is not located at row1.

2.IMCD moves to P₁ location along the new created picking aisle

 

tx ty Sum , 1  i P and P have_i

the same picking aisle.

IMCD moves to P_i_₁ location from P_i

location along the same picking aisle

 

tx ty

Sum ,

1. The IMCD moves back to the front aisle. Sum

 

tx,ty

tx,ty

3 _P_O

n IMCD moves

back to the I/O

from Pn

location.

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Figure 4: Flowchart of operation model for one-sided M-AS/RS

4.4 Example

For instance, the orderOS₁ picking items listed in Table 3. The order contains 8 product items to be picked. Suppose IMCD has to return to the depot station after having picked all the items in one trip, and IMCD can carry 8 items of the order. These items are stored in different storage places on racks. After an appropriate sequencing is made for the picking of the 8 product

No No Yes Yes No Yes i = 1

Enter the ithorder.

k = 1

Decide the picking sequence of items (n) in the ithorder.

k = n

i=J Yes i = i+1

k = k+1

IMCD moves to the rack of

the kthitem.

IMCD moves back to the front aisle.

Moving the racks to create picking aisle.

IMCD enters the aisle and stores

the rack of the kth item.

IMCD starts to pick the kthitem in the ithorder.

Are racks of kthand

(k-1)thproduct items on

the same row?

Pick the kth item.

IMCD moves along front aisle and towards the aisle k = 1

IMCD back to depot position

No

J pieces of orders with

sequencing completed

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items of each order according to descending sequencing, IMCD starts picking. The following are the detailed description on the picking model.

First of all, according to the coordinate numbers of storage place on racks, the computer numbers the 8 items of order OS₁ from large to small sizes based on the descending way. Since Item 7 being stored on Row 9 is the biggest in size, it is numbered as Sequence 1. Item 1 being stored on Row 7 is numbered as Sequence 2. Since Item 4 and Item 8 are stored on Row 6 at the same time, the sequencing of these two items will be according to the moving distance of IMCD. This research supposes that IMCD adopts right-angled marching. Thus, the maximum value of the sum of column and layer is just the longest of IMCD. Comparing the storage places of Item 4 and Item 8, it is found that the value of Item 4 is 3(2+1), which is bigger than the value of Item 8 being 2(1+1). Therefore, Sequence 3 is Item 4, and Sequence 4 is Item 8. Similarly, the value of Item 2 is 5, which is smaller than the value of Item 5 being 6. Therefore, Sequence 5 is Item 5, and Sequence 6 is Item 2. Sequence 7 is Item 6 on Row 3, and Sequence 8 is Item 3 on Row 2. The order OS₁ is rearranged. The picking sequence of this order according to descending sequencing is



7 1 4 8 5 2 6 3



1 n ,n ,n ,n ,n ,n ,n ,n

PS  .

Under the status of wl h1m, and v_x v_y v_c 0 m.2 /sec, the total time for picking

1

OS items take 390 sec.

Table 3: Location of picking items Location

Order 1

n n₂ n₃ n₄ n₅ n₆ n₇ n₈

1

OS (7,4,1) (5,1,4) (2,1,5) (6,2,1) (5,3,3) (3,5,4) (9,6,1) (6,1,1)

5. Two-sided Picking Model (the second year)

A one-sided picking model is that the stored goods can be picked on only one side. If the stored goods could be picked on both sides (a so-called ‘co-picking aisle’),thenumberofaisles required for an IMCD run could be reduced. Moreover, the IMCD runs at right-angle to the current M-AS/RS one-sided picking model. If the moving action of the IMCD in an M-AS/RS one-sided picking model could be modified to a straight-line path, it would possess higher performance capability.

This chapter presents a modification of the movement action of the IMCD from a right-angle path to a straight-line path（Fig 5）. In addition, an assignment algorithm has been proposed to arrange improved picking aisles—thus reducing the number of aisles required for an IMCD operation. Finally, the ‘no-skip’ method developed by Goetschalckx and Ratliff (1988), which arranges the picking sequence inside the aisle, is integrated with the assignment algorithm and the modified IMCD movement action to produce a mobile automated storage/retrieval system (M-AS/RS) with a two-sided picking model.

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The model focuses on the establishment of M-AS/RS with a two-sided picking function and IMCD running in a straight-line path to derive a better performance on movement distance; however, the proposed model can also be applied to derive the travel distance of retrieved goods if the retrieval sequence is decided. Therefore, the moving action of IMCD running in a straight-line path is modified from the right-angle path and only the picking distance is considered in this model, as described below. Min: ₀ 1 1 1 1 0P PP P P P TD _n n i i i   



   where: 1 0P

P is the distance between the depot station and the first picking station run by the IMCD;

1 

i iP

P is the distance between the ithpicking station and the (i+1)thpicking station; and

0

P

Pn is the distance of the return trip from the last picking station to the depot station.

Figure 5: Picking state of two-sided M- AS/RS

The total travel distance (TD) of the IMCD when picking items for an order in the M-AS/RS model (while running in a straight-line) can be regarded as an integration of three stages.

To describe this model, a set of OS₁ 



n₁,n₂,n₃,n₄



, with four items to be picked, can be taken as an example for further explanation. If the four items in the order are stored at n₁



a₁,b₁,c₁



,



2 2 2



2 a ,b ,c

n , n3



a3,b3,c3



, and n4



a4,b4,c4



locations respectively, the determined picking

l h P（I,J,K） w J . 3 2 1 A1 A2 A3…… …… AI AI+1 R1 R2………… ….……R I Rack Front aisle ：move direction Depot station _I/O

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sequence of the order is PS1 



n1,n3,n2,n4



, So, P1  ,n1 P2  ,n3 P3 n2 and P4  . Then4

trip can be divided into three stages and the times needed for each stage are t1, t2, and t3

respectively. In the following, the picking models and the calculation of t1, t2, and t3 are

described in detail.

Finally, Table 4 summarized the picking cycle movement elements including the movement of the rack on M-AS/RS.

In order to apply IMCD on the automated item picking of MSS, we have to integrate computer ordering system, equipment sensor and IMCD controller so as to make IMCD pick products in MSS. This model also proposed a flowchart for the operation model of the whole M-AS/RS. As shown in Figure 6.

Table 4: Summary of the picking cycle movement elements in two-sided M-AS/RS

Stage Objective

function Situation Movement of IMCD Formula

1

P is located

at row1

IMCD directly moves to P location along1

the picking aisle (Y axis)

 

tx ty

Max ,

1. The rack rows automatically create (open) the new picking aisle. Simultaneously, the IMCD moves to the new picking aisle along the front aisle (X axis).

 

tx tc Max , 1 1 OP 1 P is not located at row1.

2. IMCD (Y axis) moves to P location along₁

the new created picking aisle.

 

tx ty Max , 1  i P and P_i

have the same picking aisle.

IMCD (Y axis) moves to P_i_₁ location from

i

P location along the same picking aisle

 

tx ty

Max ,

1. The IMCD moves back to the front aisle (Y axis).

 

tx ty

Max ,

2. The rack rows automatically create (open) the new picking aisle. Simultaneously, the IMCD moves to the new picking aisle along the front aisle (X axis).

 

tx tc Max , 2



   1 1 1 n i i iP P 1  i P and Pi have the different picking aisle

3 IMCD (Y axis) simultaneously moves to P_i_₁

location from P location along the new_i

created picking aisle.

 

tx ty

Max ,

1. IMCD moves back to the front aisle (Y axis). Max

 

t_x,t_y

3 _P_O

n IMCD moves

back to the I/O from P_n

location.

2. IMCD (X axis) moves back to the depot station .

 

tx tc Max ,

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Figure 6: Flowchart of operation model for two-sided M-AS/RS Yes

The same picking aisle for item K and item K-1?

Yes

picking the kthitem. 揀取第 k 項品項

No

IMCD moves to the location of the kth

item

The IMCD back to the front aisle

Moving the equipment racks to create picking

IMCD enters the picking aisle and position to kth

item location.

IMCD moves along front aisle and towards the picking i=1

input the ith

k=1

Decide the picking sequence for each real

IMCD starts to pick the kthitem in the ith Decide the picking aisle for Order #i, as

Form the set of picking sequences of order#i PSi 



P1,P2....Pn



No PA Yes k=1 Input J orders with sequence Yes No i=J No Yes k=n i=i+1 k=k+1 IMCD & M-AS/ RS back to initiativ En

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5.3 Operation Algorithm

After the two-sided picking model with the IMCD running in a straight-line was proposed, there are two procedures in the operation model. First, a picking-aisle-assignment algorithm is required to decide the real picking aisle for IMCD so as to reduce the number of aisles for the IMCD run. After deciding the picking aisle in which the IMCD will move, the second procedure is to discover the shortest path in the picking aisle. The two algorithms can be described as follows.

Algorithm 1: Decide the sequence of real picking aisle for IMCD run.

Step 1. Decide the set of batch order of items OSm 



n1,n2...nn



.

, j ...1,2 k,

I k 

Step 4. Expand the elements in set PA ; the possible aisle that might be used to pick the items on am

rack is given a weighted value 1, and the others are left blank. Total the weight value of each element A ini PA , as indicated in Table 5. Therefore,m A element ini PAm will have

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 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 a so-called ‘co-picking aisle’).

Table 5: The relationships of RS with PA

PA RS 1 A A₂ A₃ ………… A_i …….. A_I 1 R ₁ ₁ 2 R 1 1 i R ₁ ₁ 1  i R ₁ ₁ I R ₁ weight 1 2 1 1 2 1 1

Step 5: If the weighted value of A is larger than that ofi Ai1, then go to Step 6, if not, then go to

Step 7.

Step 6: This step is required if A can pick more items stored on racks thani Ai1, and if A isi

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the depot point, it is more efficient to enter A thani Ai1, and A is selected in the set ofi

real picking aisle RA. Then, the location of items on the racks on the two sides R ,_i R_i_₁

is deleted from the order set OS, OSOS



niniRi,Ri1



. Go to Step 8.

Step 7: This step is required if Ai1 can pick items from more racks than A . In this case, it isi

more efficient to enter Ai1 than A , andi Ai1 is selected in the set of real picking aisles

RA. Then, the locations of items on the racks on the two sides R_i_₁, R_i_₂ are deleted from the order set OS, OSOS



niniRi,Ri1



.

Step 8: Repeat Steps 1–7 until OS



.

Step 9: Descending the elements of the RA set, this is the aisle sequence in which IMCD moves when it picks the order.

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Figure 7: Flowchart for picking aisles assignment algorithm

Algorithm 2: Decide the picking sequence in picking aisles.

The‘no-skip’approach formulated by Goetschalckx and Ratliff(1988)can beused to decide the picking sequence in the real picking aisle. The approach is briefly described as follows.

Having established a network for the storage locations of the items that will be conveyed in thepicking aisle,with the‘no-skip’approach itdoesnotmatterwhethertheIMCD firstpicksthe

,qI End

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rack on the left side or the right side. However, it is forbidden to cross paths in the picking aisle (see Figure 8).

Figure 8: The picking paths of a crossed circuit

Some moving-and-picking principlesareassumed in using the‘no-skip’approach to obtain the shortest path:

（1）The location most far away from the front cross aisle is used; in other words, the column value of location, Max



n1

  

b1 ,n2 b2 ...nn

 

bn



.

（2）The smaller row value of location is the major priority. （3）The smaller layer value of location is the minor priority.

Finally, the above two algorithms can be integrated to construct the M-AS/RS two-sided picking model.

5.4 Example

An order containing 15 items (Table 6) is taken as an example. According to the proposed algorithm, the picking travel-time calculation procedure of this order is as follows.

Table 6: Location of the items

item n₁ n2 n3 n4 n5 location (10,4,7) (8,8,7) (1,2,1) (9,2,8) (5,5,6) item n₆ n₇ n₈ n₉ n₁₀ location (8,4,4) (9,3,3) (10,5,6) (4,2,10) (1,2,2) item n₁₁ n₁₂ n₁₃ n₁₄ n₁₅ location (6,7,6) (4,2,1) (6,1,9) (2,9,10) (8,5,10)

Stage1: Decide the sequence of picking aisle

The picking aisle-assignment algorithm described above is used to decide the picking

aisle in which the IMCD needs to move. The result of the assignment is that the IMCD needs to move five aisles to finish this order picking in two-sided model. The sequence of aisles in which the IMCD moves is A ,₂ A ,₅ A ,₆ A₉ and A₁₀ with three co-picking aisles, A ,₂ A , and₅ A .₉

Stage 2: Deciding the picking sequence in picking aisles

A B

D

C E

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Because more than one item might have to be picked in a given aisle, it is necessary to decide thepicking sequencein apicking aisle.The‘no-skip’approach isthen used to decidethepicking sequence in each picking aisle. The result of this arrangement is shown in Table 7. The two stages are then combined to derive the picking sequence of IMCD for this order (as shown in Table 8).

Finally, based on the assumption that v_x v_y v_c 0.5m/sec and that l wh0.5meter, the total picking travel-time calculation of this order is calculated as being 414 seconds in a one-sided model and 240 seconds in a two-sided model.

Table 7: The picking sequence in each picking aisles Model Aisles sequence The sequence in picking aisle

1 A₂ n ,₃ n ,₁₀ n₁₄ 2 A₅ n ,12 n ,9 n5 3 A₆ n ,₁₃ n₁₁ 4 A₉ n ,₄ n ,₇ n ,₆ n ,₁₅ n₂ Two-sided model 5 A₁₀ n ,1 n8

Table 8: The picking sequence for order

Model Picking sequence

Two-sided

model 1

n ,n ,₈ n ,₄ n ,₇ n ,₆ n ,₁₅ n ,₂ n ,₁₃ n ,₁₁ n ,₁₂ n ,₉ n ,₅ n ,₃ n ,₁₀ n₁₄

6.The Middle Cross Aisle Picking Model (the third year)

In M-AS/RS model whatever one-sided or two-sided picking model, when the consecutive picking location can not be picked within the same picking aisle, the IMCD has to move back to the cross aisle. If the last picked item location is far way from the cross aisle, the IMCD has to move a long distance back to the cross aisle. It is not economic for IMCD to travel through the racks with long distance movement. Further the tremendous equipment rows have to move in order to create a new picking aisle for IMCD to run. The movement of huge equipment rows not only increases the operation performance but also enhances the risk of good damage.

In order to reduce the movement distance of IMCD running for picking the batch order items, the middle cross aisle model (Figure 9) is proposed. The warehouse is divided to block A area and block B area by the middle cross aisle.

The whole travel distance of IMCD for picking items of an order can be divided two stages. It is assumed that the picking times of various stored items are fixed. The constructed objective function therefore does not consider the retrieval time; rather, it calculates the travel distance of the IMCD for order picking is calculated. The objective function is described as follows:

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Min: ₀ 1 0 1 PP P P TD _n n i i i  



   where: 1  i iP

P is the distance between the ith picking station and the (i+1)th picking station; and depot station can be set asp .0

0

P

Pn is the distance of the return trip from the last picking station to the depot station.

Figure 9： Initial position of M-AS/RS with middle cross aisle

There are two movement scenarios in the trip for IMCD movement among racks. One is that

1 

i

p and p can be picked in the same picking aisle; another is thati pi1 and p can not bei

picked in the same picking aisle. In the first scenario, there is no movement for equipment rows. The movement distance between two consecutive picking locations is the relative distance in X-Y dimension. The second scenario is much more complicated than the first one. Actually, the model can be decomposed into three steps. (1)The IMCD must move back to middle cross aisle from pi

location. (2) The rack rows automatically create the new picking aisle and the IMCD moves to the new picking aisle along the middle cross aisle simultaneously. (3) The IMCD enters new created picking aisle from middle cross aisle to pi1 location.

In the following section, we describe the picking models and the calculation of picking time in detail. Mobile R1 R2… .. RI Rack B1 B2…….. BI BI+1 Aisle Block A I/O Block B



I J K



P_B , 2 ,



I J K



P_A , 2 , A1 A2 A3……… AI AI+1 Middle aisle

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Finally, Table 9 summarized the picking cycle movement elements on M-AS/RS with a middle cross aisle picking model.

Table 9: Summary of the picking cycle movement elements in middle cross aisle M-AS/RS

Stage Objective

function Situation IMCD and rack rows movements Formula

1 

i

P and P can_i

be picked within the same picking aisle.

IMCD moves to P_i_₁ location from P with_i

Y-Z dimension along the same picking aisle simultaneously

 

tx ty

Max ,

1. The IMCD moves back fromP to the middle_i

cross aisle (Y-Z axis simultaneously).

 

tx ty

Max ,

2. The rack rows automatically create (open) the new picking aisle. Simultaneously, the IMCD moves to the new picking aisle along the middle cross aisle (X axis).

 

i=1

Input the ithorder.

k=1

Decide the picking sequence among real picking aisle Decide the picking aisle for Order #i

Form the set of picking sequences of order #i Decide the picking sequence for each real picking aisle

The IMCD moves back to the middle cross aisle

Moving the equipment racks to create picking aisle.

IMCD enters the picking aisle and position to kthitem

location.

IMCD moves along middle aisle and towards the picking aisle entrance No

No

PA

Yes

Yes IMCD moves to the location of the kthitem The same picking aisle for item K and item K-1?

Picking the kthitem. k=1 Input J orders with sequence i=i+1 i=J No Yes k=n k=k+1 IMCD & M-AS/RS back to initial position End No

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6.3 Operation Algorithm

There are three algorithms to be applied to achieve the optimal picking sequence in the operation model. First, a picking-aisle-assignment algorithm is required to decide the real picking aisle for IMCD so as to reduce the number of aisles for the IMCD run in the warehouse blocks. The second procedure is to decide the sequence among real picking aisles. The third procedure is to discover the shortest path in the picking aisle. We integrated the above three algorithms and then form the whole batch order picking sequence. The three algorithms were described in details as follows:

Algorithm 1: Deciding the real picking aisle for IMCD run in blocks separately

Using the following 9 steps, we can decide the real picking aisle in the warehouse block A, and achieve the minimum number of picking aisles. The same steps also can be applied to get the picking aisles in block B.

Step 1. Deciding the set of batch order of items OSm 



n1,n2...nn



.

,

k

j  ...1,2  , k I.

Step 4. Expanding the elements in set PA ; the possible aisle that might be used to pick the itemsm

on a rack is given a weighted value 1, and the others are left blank. Total the weighted value of each element A ini PA , is shown on Table 10. Therefore,m A element ini PAm will

have 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) stores with items to be picked, whereas a weighted value of 2 indicates that the rack rows on both sides of the aisle store with items to be picked (this aisle is a so-called ‘co-picking aisle’).

Table 10: The relationships of RS with PA

PA RS 1 A A₂ A₃ ………… A_i …….. A_I 1 R ₁ ₁ 2 R 1 1 i R ₁ ₁ 1  i R ₁ ₁ I R ₁ weight 1 2 1 1 2 1 1

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Step 5: If the weighted value of Ai is larger than that of Ai1, then go to Step 6, if not, then go to

Step 7.

Step 6: This step is required if A can pick more items stored on racks thani Ai1, and if A isi

included in the set of real picking aisles RA. If the weighted value of A is equal toi Ai1,

i

A and Ai1 aisles can pick items stored on the same rack rows, but aisle A is closer toi

the depot point, it is more efficient to enter A thani Ai1, and A is selected in the set ofi

real picking aisle RA. Then, the location of items on the racks on the two sides R ,_i R_i_₁

is deleted from the order set OS, OSOS



niniRi,Ri1



. Go to Step 8.

Step 7: This step is required if Ai1 can pick items from more racks than A . In this case, it isi

more efficient to enter Ai1 than A , andi Ai1 is selected in the set of real picking aisles

RA. Then, the locations of items on the racks on the two sides R_i_₁, R_i_₂ are deleted from the order set OS, OSOS



niniRi,Ri1



.

Step 8: Repeat Steps 1–7 until OS



.

Step 9: Descending the elements of the RA set, this is the aisle sequence in which IMCD moves when it picks the order.

Algorithm 2: Deciding the picking sequence among picking aisles

To decide the sequence of picking aisle for IMCD to move, this study proposes the assignment algorithm as follows:

（1）The picking aisle most far away from the I/O point is used; that is, the aisle value of location is

 



A1 a1 ,.An(an)..B1 a1 ,..Bn(an).



Max .

（2）The block A is the major priority.

Algorithm 3: Deciding the picking sequence in picking aisles

The‘no-skip’approach formulated by Goetschalckx and Ratliff(1988)can beused to decide the picking sequence in the real picking aisle. The approach is briefly described as follows.

Some moving-and-picking principlesareassumed in using the‘no-skip’approach to obtain the shortest path:

（1）The location most far away from the middle cross aisle is used; That is, the column value of location is Max



n1

  

b1 ,n2 b2 ...nn

 

bn



.

（2）The smaller row value of location is the major priority. （3）The smaller layer value of location is the minor priority.

Finally, the above three algorithms can be integrated to construct the middle picking model of an M-AS/RS.

6.4 Example

An order containing 15 items (Table 11) is taken as an example. According to the proposed procedures, the picking travel-time calculation procedure of this order is as follows.

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Table 11: Location of the items item n₁ n2 n3 n4 n5 location (10,4,7) (8,8,7) (1,2,1) (9,2,8) (5,5,6) block A B A A A item n₆ n7 n8 n9 n10 location (8,4,4) (9,3,3) (10,5,6) (4,2,3) (1,2,2) block A A A A A item n₁₁ n₁₂ n₁₃ n₁₄ n₁₅ location (6,7,6) (4,3,1) (6,1,9) (2,9,1) (8,5,1) block B A A B A

Stage1: Decide the picking aisle in the blocks separately

The picking aisle-assignment algorithm described above is used to decide the picking aisle in which the IMCD needs to move. The result of the block A is that the IMCD needs to move six aisles to finish this order picking. The picking aisles in which the IMCD moves areA ,1 A ,5 A ,6

9

A and A . In block B, it only needs three aisles to finish this order picking. The picking aisles in10

which the IMCD moves are B ,2 B , and6 B .8

Stage 2: Decide the picking sequence among the picking aisles

Because IMCD might run more than one aisle, it is necessary to decide the sequence among picking aisles. The block A picking aisles areA ,1 A ,5 A ,6 A9 and A . In block B, the picking10

aisles areB ,2 B , and6 B . According to descending block algorithms, the total sequence of picking8

aisle are A ,10 A ,9 B ,8 B ,6 A ,6 A ,5 B and2 A .1

Stage3 Decide the sequence in each picking aisles

The‘no-skip’approach isused to decidethepicking sequencein each picking aisle.Theresult of this arrangement is shown in Table 12.

After integrating the separated picking aisle of different blocks (Table 12), the final picking aisle sequence of the whole batch order is shown in Table 13

Table 12: The picking sequence in each picking aisles Block Picking Aisles The item picked

in picking aisle

Picking sequence in the picking aisle

1 A₁ n ,₃ n₁₀ n ,₃ n₁₀ 2 A₅ n ,₅ n ,₉ n₁₂ n ,₅ n ,₁₂ n₉ 3 A₆ n₁₃ n₁₃ 4 A₉ n ,4 n ,6 n ,7 n15 n ,15 n ,6 n ,7 n4 A 5 A₁₀ n ,₁ n₈ n ,₈ n₁ 1 B₂ n₁₄ n₁₄ 2 B₆ n₁₁ n₁₁ B 3 B₈ n₂ n₂

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Table 13: The picking sequence for this order

Model Picking aisle sequence

middle model n ,₈ n ,1 n ,15 n ,6 n ,7 n ,4 n ,2 n ,13 n ,11 n ,5 n ,12 n ,9 n ,14 n ,3 n10

The three stages are combined to derive the picking aisle sequence of IMCD for this order (as

shown in Table 13). Finally, based on the status that vx vy vc 0.5 m/sec and that 5 . 0   w h

l meter, the total picking travel-time calculation of this order is calculated as being 115 seconds in middle cross aisle model.

7. Simulation and Analysis

7.1 One-sided Model

Taking a cubic warehousing center with 10 rows, 5 columns and 5 layers (I = 10, J = 5 and K = 5) as an example, as shown in the Figure 11 below:

To simulate the picking situations of M-AS/RS under different conditions, the parameters of 4 storage environments are preset as shown in Table 14 below.

Figure 11: Mobile storage system (MSS)

Table 14: Different parameters for different picking environments Situation Width of a storage place on Rackw (m) Length of a storage place on Rack l(m) Height of a storage place on Rack h(m) Moving Speed of IMCD (m/sec) vi Moving Speed of Equipment Row (m/sec)vc 1 1.0 1.0 1.0 0.2 0.2 2 1.0 1.0 1.0 0.2 0.5 3 1.0 1.0 1.0 0.5 0.2 4 1.0 1.0 1.0 0.5 0.5 9 10 5 4 3 2 1 5 4 3 2 1 5 6 3 2 1 7 8 DEPOT station Moveable aisle Front aisle

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For instance, the sequence of order picking of this lot of items listed in 3 orders (Table 15) is

1

OS , OS2 and OS . After an appropriate sequencing is made for the picking of the 8 product3

items of each order according to descending sequencing, IMCD starts picking.

Table 15: Coordinates of racks with product items of orders Location Order 1 n n₂ n₃ n₄ n₅ n₆ n₇ n₈ 1 OS (7,4,1) (5,1,4) (2,1,5) (6,2,1) (5,3,3) (3,5,4) (9,6,1) (6,1,1) 2 OS (6,5,5) (2,2,2) (6,5,1) (9,4,4) (8,4,2) (9,5,5) (6,3,2) (3,3,1) 3 OS (7,3,1) (6,2,3) (6,3,2) (8,3,1) (7,5,3) (4,2,1) (8,1,5) (4,2,4)

After the picking sequence is arranged, the control center commands the controller to complete the picking of all items of the order in right sequence. The picking sequences obtained from the Table 16 are matched with some parameters of warehousing environment and the picking time required for the 3 orders are shown in Table 17.

Table 16: Picking sequence of orders

Descending Sequencing Picking

Integrated Sequence Picking 1 2 3 4 5 6 7 8

1 PS n₇ n₁ n₄ n₈ n₅ n₂ n₆ n₃ 2 PS n6 n₄ n₅ n₁ n₃ n₇ n₈ n₂ 3 PS n₇ n₄ n₅ n₁ n₃ n₂ n₈ n₆

Table 17: Picking results of orders Picking Time

Situation

Order A Order B Order C

1 390 440 360

2 390 440 360

3 170 183 151

4 156 172 144

Unit of time: seconds

7.2 Two-sided Model

Having calculated the total picking travel time of an exemplar order, three kinds of simulation were executed to validate the proposed model: (1) with different levels of four factors (order size,

warehouse size, v_x and v ); (2) with different ratios of X–_y Y dimension speed (v_y v_x); and (3) with different rack shapes (h l). The first simulation is performed to compare the performance of the one-sided model with the two-sided model. The second and third simulations are used to

identify the optimal ratio of X–Y dimension speed (v_y v_x ) and rack shape (h l) to produce optimal performance. The three simulations are described below.

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7.2.1 The different levels of four factors

Assume a warehouse with 10 rows, 10 columns, 10 layers, and l wh1m. The order size and warehouse size (the number of equipment rows), v_x and v , were set at three levels_y

(Table 18). According to the L₉(34) orthogonal array (Table 19), there were, in total, nine combinations. Each combination runs 150 orders generated by computer, and the simulation results of each combination are shown in Table 20.

Table 18: Experiment factor level Level

factor

1 2 3

1.Order size 5 15 25

2.No of equipment row 10 50 100

3.v （m/sec）_x 0.2 0.5 1

4.v_y（m/sec） 0.2 0.5 1

Table 19: L₉(34)orthogonal array factor combination 1 2 3 4 1 1 1 1 1 2 1 2 2 2 3 1 3 3 3 4 2 1 2 3 5 2 2 3 1 6 2 3 1 2 7 3 1 3 2 8 3 2 1 3 9 3 3 2 1

Table 20: The simulation results of nine combinations Number of picking aisles Number of equipment

row movement

Average travel time（sec） combination One-sided Two-s ided Reducti on (％) One-sided Two-s ided Reducti on (％) One-sided Two-sided Reducti on (％) 1 4.2 3.5 20.0 3.8 3.2 18.8 578.1 338.8 70.6 2 4.9 4.4 11.6 4.8 4.2 13.1 373.5 281.5 32.7 3 5.0 4.8 3.2 4.9 4.7 3.2 268.9 215.1 25.0 4 8.2 4.7 74.5 7.3 4.4 65.9 327.5 228.0 43.6 5 13.1 10.5 24.8 12.8 9.4 36.2 937.3 824.3 13.7 6 14.1 12.4 14.2 13.9 12.1 14.9 1782.8 1657.0 7.6 7 9.5 4.8 97.1 8.6 4.4 94.3 417.5 252.3 65.5 8 19.8 14.1 40.4 19.4 13.4 44.8 1879.5 1297.8 44.8 9 22.5 17.6 27.8 22.2 17.2 29.1 1880.8 1584.0 18.7

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The results (Table 20) show that, in the two-sided model, the number of picking aisles in the IMCD run, the number of equipment-row movements, and the average travel time are all obviously smaller than is the case in the one-sided model for each combination. It is thus apparent that the two-sided model has better performance than the one-sided model.

With regard to the number of aisles in the IMCD run and the number of equipment-row movements, the smallest and largest proportional reductions of performance were found in combination three and in combination 7 (the number of aisles :3.2% and 97.1%; the number of equipment-row movements :3.2% and 94.3%). This means that the number of aisles in the IMCD run and the number of equipment-row movements are in direct proportion. With respect to average travel time, the average reduction in terms of three levels of warehouse size were 59.5%, 30.4%, and 17.1%; demonstrating that larger warehouse size has lower-order density with certain order quantities, and that the number of co-picking aisles therefore affects performance significantly. In contrast, a smaller warehouse size has higher-order density with certain order quantities, demonstrating that the number of co-picking aisles does not affect the performance significantly—because the number of picking aisles of the IMCD does not differ significantly between the one-sided model and the two-sided model runs.

7.2.2 X–Y dimension speed ratio (v_y v_x)

Assume a warehouse with 10 rows, 10 columns, 10 layers, and l wh1m. The v_x

values were set at 0.5, 1, and 2m/sec, and the ratios of X–Y dimension speeds, v_y v_x , were set

from 0.1 to 5.0 in increments of 0.1. In all, there were therefore fifty experiments. According to the above value settings, each experiment runs 150 orders generated by computer under order sizes of 5, 15, 25, 35, and 50 respectively. The average time of each experiment is shown in Figures 12, 13 and 14. 0 300 600 900 1200 1500 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 av er ag e tr av el ti m e _n=5 n=15 n=25 n=35 n=50

Figure 12: Simulation results of average travel time on v 0 m.5 /sec

x y v

(34)

0 200 400 600 800 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 av er ag e tr av el ti m e( se c) n=5 n=15 n=25 n=35 n=50

Figure 13: Simulation results of average travel time on vx 1m/sec

0 200 400 600 800 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 av er ag e tr av el ti m e( se c) n=5 n=15 n=25 n=35 n=50

Figure 14: Simulation results of average travel time on vx 2m/sec

The simulation results indicate that the average travel time rapidly decreased in response to the ratio increasing. However, it assumed a steady rate of decrease after the ratio passed through a ‘turning-point’ofabout0.6 to1.0. In general, it displayed a stable average travel time when the ratio of v_y v_x was greater than 1. Therefore, it can be argued that the optimal range of ratio for

x y v

v is from about 0.6 to 1.0.

7.2.3 Different rack shape (h l)

Assume a warehouse with 10 rows, 10 columns, 10 layers, w1m, v_x v_y 1m/sec, and sec

/ 5 . 0 m

vc  . The l values were set at 0.5, 1, and 2m/sec, and the ratios of X–Y dimension

speeds h l were set from 0.1 to 5.0 in increment of 0.1. In all, there were therefore fifty experiments.

Based on an order size of 5, 15, 25, 35, and 50 items, the simulations produced average travel times as shown in Figures 15, 16, and 17. The results indicate that the average travel time increased

x y v v x y v v

(35)

rapidly when the ratio was greater than about 1. In practice, a very small ratio of h l is not used in warehouses because the height of the rack is too small to store goods.

Therefore, it can be argued that the optimal ratio range for h l is from about 0.6 to 1.0. This result is similar to the research result of Amit and Rosenblatt (1994).

0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 av er ag e tr av el ti m e( se c) n=5 n=15 n=25 n=35 n=50

Figure 15: Average travel time with the ratio of h l (l1m)

Figure 16: Average travel time with the ratio of h l (l 0.5m)

Figure 17: Average travel time with the ratio of h l (l 2m)

Although the two-sided model of M-AS/RS has some advantages, some practical considerations have to be taken into account. These include the establishment costs, operational costs, the physical environment of the storage area, the frequency of storage and retrieval, and

l h l h l h

應用跨樓層搬運設備建構移動式倉儲存取系統之研究

行政院國家科學委員會專題研究計畫 成果報告

應用跨樓層搬運設備建構移動式倉儲存取系統之研究(第 3

年)

研究成果報告(完整版)

中 華 民 國 98 年 11 月 03 日

行政院國家科學委員會補助專題研究計畫成果報告

應用跨樓層搬運設備建構移動式倉儲存取系統之研究

計畫類別：□ 個別型計畫

■ 整合型計畫

計畫編號：NSC

95-2221-E-151-035-MY3

執行期間：

95 年 08 月 01 日至 98 年 07 月 31 日

計畫主持人：

張添香

共同主持人：

傅新彬

計畫參與人員：

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■完整報告

本成果報告包括以下應繳交之附件：

□赴國外出差或研習心得報告一份

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執行單位：

國立高雄應用科技大學資訊管理系

中

華

民

國

98

年

10

月

8

日

中文摘要

Abstract

目錄

應用跨樓層搬運設備建構移動式倉儲存取系統之研究

A Study on Automated Picking Model on MSS Using an

IMCD

1. Background and Motivation

2.

Literature Review

3. Design of Mobile Storage System

4. One-sided Picking Model (the first year)

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行政院國家科學委員會專題研究計畫成果報告

中華民國 98 年 11 月 03 日