We focus on the ABC storage (class-based storage) and COL policy since they are basic policies for developing continuous cluster method. Per mention at section 1.2.1, ABC storage policy is a combination of dedicated and randomized policy (see Fig. 2.4).
Randomized policy is used for sorting SKU (stock keeping unit) within a class, and dedicated policy is used among different classes. Under COL policy, SKU is sorted into storage location where is closest to the I/O point [2, 3, 4].
Under ABC storage policy, warehouse space is divided into three classes (see Fig.
2.4). Each class contain goods with the same parameters (same good type or same travel distance). In storage and retrieval process, goods will be sorted on each class with priorities in turn are A, B and C. In each class, goods are arranged randomly into a certain location.
All storage locations of class A are considered to have the same distance and they have same priority in storage process, although the actual distance of each storage
Fig. 2.4 ABC storage policy
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location to I/O point is different from the others. So if goods is stored in the same class, the travel distance is not really optimal. This argument is correct when the number of pallets is smaller than the number of available storage location in class A.
To increase the efficiency of the algorithm, the ABC storage and COL policy are combined together. That mean each class is divided into several smaller classes, each of which is called a cluster (see Fig 2.5). The radius of cluster is the travel distance from storage location on racking to I/O point. In storage and retrieval process, SKUs are priority arranged into the cluster which has smallest radius. By this method, the storage location is found always has travel distance less than the ABC class method. If the number of clusters in each class is greater, the algorithm is more efficient. To see the effectiveness of the algorithm, a warehouse system is simulated and analyzed in the following section 3. Continuous cluster method is a combination of ABC storage (class- based storage) and Closest Open Location policy – COL. [2, 3, 4]
In detail, each class of ABC policy is divided into several smaller classes, each of which is called a cluster. In Fig. 2.5, Fig. 2.6, each cluster is represented by a different color, the cells with the same color have same valuedij. The radius of cluster is the travel distance from storage location on racking to I/O point. In storage and retrieval process, SKUs are priority arranged into the cluster which has smallest radius. By this method, the storage location is found always has travel distance less than the ABC class method.
If the number of clusters in each class is greater, the algorithm is more efficient.
Fig 2.5. Continuous cluster concept
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In storage process, pallets are transferred from I/O point to storage location in turn by 3 axes in space as Line (x axis), Bay (y axis) and Tier (z axis) [7]. The travel distance of pallet in each circle can be computed as follows:
ij ij ij ij
d x y z
(2.16) Fig 2.6. Storage location under Continuous cluster policy
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Where, xij xj xi yij yj yi zij zj zi (2.17)
xi, yi, zi,xj, yj, zjare coordinates of I/O point and storage location.
Total travel distance for an order of n SKUs:
1 n
ij k
D d
(2.18) However, above arguments only in the ideal case, in fact the forklift cannot move at three sides of the space that always has a rotation angle (Turning Radius) between the two axes x and y. Therefore the actual distance forklift to move is constructed as follows:
t: Total time
tR: Total running time tl: Total lifting time des: Expected distance
1
vr u : Running speed in straight line
2
vrc u : Running speed in curve line 𝑅: Turning radius
nr: Number of turning radius in actual rout
/
vl u: Average loading speed/unloading speed
i, i
x y : X and y coordinates of the Node
zi: Height of storage locations (i = 1, 2, 3, 4, 5) n Number of picking product
k : Number of Node on forklift truck route
Expected distance are determined from the IN terminal to the center of each slot in 2D warehouse layout (see Fig. 2.7). The expected distance can be estimated by Euclidian distance.
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1
2 2
1 1
1
( ) ( )
k
es i i i i
i
d x x y y
(2.19)
In practice, it is faster that the forklift follows a continuous path rather than making a rigid 900 turn so turning radius is essential. Each node is presented by 3 coordinates
x y zi, i, i and the turning angle can be calculated:
1 1
( i i , i i )
u x x y y (2.20)
1 1
( i i, yi i)
v x x y (2.21)
cos .
. u v u v
(2.22)
|𝛳| = { 0, forklift truck continue to go straight 1: forklift truck begin to turn at Node (i − 1) From Eq. (2.19) and Eq. (2.22),
2 0.5
es r r
r
r rc
d Rn n R
t v v
(2.23)
Estimate total loading and unloading time base on the height of storage racks.
/
2. i
l l u
t z
v (2.24)
The total time is needed to transfer from I/O point to all storage locations can be calculated. The total time after calculated are stored in 5x6 matrix. During storage process, system using this matrix to find which location has lowest time index to sort pallet.
(2.25) So travel distance are used in this article can be computed by the formulas below:
ij ij ij ij
d x y z offset (2.26)
/
2 0.5 2
es r r i
r l
r rc l u
d Rn n R z
t t t
v v v
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Fig 2.8. Travel distance index for rack S-III Fig. 2.7 The mapping model in simulation
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ij j i
x x x
, yij yj yi , zij zj zi
Where,x y zi, i, i, x y zj, j, j are coordinates of I/O point and storage location. Offset is the distance need to be added to suitable with layout in section 2.1.