6. Kapasitas Gudang.pptx

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II. KAPASITAS GUDANG
Manajemen Pergudangan
Oleh:
Budi Santosa ST,MT,CISCP,CLIP.
budisantosa@telkomuniversity.ac.id

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2
Versi / Revisi : 1/0
Warehouse Size
• Min = SSL + Q
• Max = SSL+T + Q

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3
Flow of Goods in Warehouse
Receiving
Holding
Picking
Shipping

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4
Flow of Goods in Warehouse
Receiving Receiving Receiving
Holding Holding Holding
Picking Picking Picking
Batch Forming
Packaging
Shipping

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5
Simple Warehouse Operation
Storage Zone
Receiving Zone
Shipping Zone

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6
Warehouse With Reserve and Forward Storage
Receiving
Zone
Reserve
Zone
Forward
Zone
Shipping
Zone

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7
Storage Media
• Physical Characteristics of Goods in Stock
• Solid Goods: Stack, Rack, Drawers
• Number of items of each product in a customer
order

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Block Stacking System

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Item Retrieval by Trolley
x
y

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10
A/R Machine
Side
aisle
Central aisle

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11
Item Storage and Retrieval By AS/RS and Belt Conveyor
Side
aisle

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S/R Machine
Side
aisle
Central aisle

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Storage/Retrieval Transport
1. Picker to Product System
• A team of human order pickers, traveling to storage
location
2. Product to Picker System
• An automated device, delivering items to stationary
order pickers
• AS/RS

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Item Storage and Retrieval By AS/RS and Belt Conveyor
Side
aisle

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Unit Load Retrieval System
• Single Cycle
• Storage and retrieval operations are performed one at a time
• Dual Cycle
• Pair of storage and retrieval operations are made in sequence in an attempt
to reduce the over all travel time
• Multi Command Cycle
• Store or pick up several loads at the same time
• Strict order picking or batch order picking

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Warehouse Design
Criteria
Services Cost

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Warehouse Cost
• Receiving Cost
• Holding Inventory Cost
• Retrieving Cost
• Assembling to customer order Cost
• Shipping Cost

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Factors To Be Considered
• Physical characteristics of products
• Number of items in stock
• Rate of storage and retrieval request

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Warehouse Design
1. Determining the capacity: length, width and height
2. Locating and sizing: receiving, shipping and storage zones (including
number of I/O port, number, length and width of the aisles of storage
zone and the orientation of stack/racks/drawers)
3. Selecting the storage medium
4. Selecting the storage/retrieval transport mechanism

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Selecting The Storage/Retrieval
• Physical Characteristics of goods
• Packaging at the arrival
• Composition of out going lots
Stack Rack Drawers

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Sizing Receiving &Shipping
The Number of Truck Dock
ND = [dt/qT]
ND : Number of Dock Truck
d : Daily demand from all order
t : Average time required to load/unload a truck
q : Truck Capacity
T : Daily time available to load/unload truck

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Example
Average daily demand is 27.000 units, outgoing shipment are performed by trucks, with
capacity equal to 850 units. Average time to load a truck is 280 minutes and 15 working
hours are available every day
Number of dock truck:
ND = [d.t/q.T]
ND = [27.000x280/850x(15x60)]
ND = 10

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A Traditional Storage Zone
Lx
Ly

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Storage Policy
1. Dedicated Storage policy:
• Product is assigned at pre-established set position
• Easy to implement but causes an under utilization
2. Random Storage policy:
• Product allocation is decided dynamically on the basis of:
• Current warehouse occupation
• Future arrival and request-forecast
• Allow a higher utilization of space but requires:
• Each item be automatically identified
• Update database of current position of all items
n
j=1
t

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Storage Policy
3. Class Based Storage policy:
• Product are divided into a number of categories according to their demand
• Each category is associated with aset of zones where the goods are stored
according to random storage policy
n
j=1
t

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Sizing of Storage Area
• Dedicated Storage policy:
MD = ∑ max Ij(t)
MD : Number of required storage location
Ij(t) : Inventory level of item j at time t
n : Number of item
• Random Storage policy:
Mr = max∑ Ij(t) ≤ MD
n
j=1
t

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Example of Storage Area
Product Lot Safety Stock
P 500 100
Q 300 60
• Dedicated Storage policy:
MD = ∑ max Ij(t)
= 600 +360 = 960
• Random Storage policy:
Mr = max∑ Ij(t) ≤ MD
= 600 + 210 = 810

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Length and Width of Storage
Length: Lx = ( ax +½ wx )nx
Width : Ly = ( ay nx + wy )
Dimana:
ax : Occupation of a unit load along the direction of x
ay : Occupation of a unit load along the direction of y
wx: Width of side aisle along the direction of x
wy: Width of side aisle along the direction of y
nx: number of storage location along the direction of x
ny: number of storage location along the direction of y

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Model Formulation of Sizing The Storage zone
Minimize:
Subject to: v
w
n
v
n
w
y
y
y
x
x
x
2
2
1 










integer
0,
n
n
m
n
n
n
y
x
z
y
x



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Determining nx and ny
• Number of Storage Location Along Y Direction
• Number of Storage Location Along X Direction
 
z
y
x
x
y
n
w
m
'
n



 2
1
2
 
x
x
z
y
x
w
n
m
'
n
2
1
2 



   
y
y
x
x '
n
n
'
n
n 
 and

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Example
Warner Bross is going to build a new warehouse near Cikarang
in order to supply its sales in Jakarta. On the basis of
preliminary study, it has been decided that the facility will
accommodate at least 780x90x90 cm2 pallets. The goods will be
stored onto racks and transported by means of traditionally
trolleys. Each rack has four selves, each of which can store a
single pallet. Each pallet occupies a 1.05x1.05 m2 area. Rack are
arranged traditionally where side isles are 3.5 m wide, while the
central aisle is 4 m wide. The average speed of trolley is 5 km/h.

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Example
 
  25
32
4
05
1
05
1
780
2
05
6
05
1
4
2
05
1
780
2
5
3
2
5
3
.
.
.
x
'
n
.
.
.
x
'
n
.
.













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Example
•nx = 6 and ny = 33
•Length: Lx = ( ax + ½ wx )nx
= ( 1.05 +(3.5/2))x6
= 16.8 m
•Width : Ly = ( ay nx + wy )
= (1.05x33+4)
= 39.65 m

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Warehouse With A Reserve/Foreward Storage System
Reserve Zone Forward Zone

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Storage locations assigned to an item j; j=1,1….n

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Sizing a Forward Area
How much space must be assigned to each product ?
Performance Criteria:
Cost : Picking cost at reserve area (C1j(sj))+
Picking cost at forward area (C2j(sj)) +
Space and equipment cost (C3j(sj) )
C1j(sj) = [h(o/d)wjsj]/v
C2j(sj) = [fj(ujoj/d)mjsj] + gjujoj
C3j(sj) = kwjsj

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Sizing a Forward Area
Notation:
Sj: number of aisle position
n : number of products
o : average number of orders/period
d: average number of order in batch
oj: average number of orders/time period for product j
uj: average number of items of product j in an order
v: average speed of a picker in the forward area
h: cost of a picker /period
k: area and equipment cost per unit of lane length/period
fj: fix cost of replenishment of product j
gj: variable cost of replenishment a unit of product j
wj: length of a portion of aisle occupied by item of product j
mj: number of item of product that can be stored in an aisle position

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Model Formulation
Min Cost : ∑ c1j(sj) + c2j(sj) + c3j(sj)
Subject to : sj ≤ sj ≤ sj , j= 1,2, …. n
sj ≥ 0 , integer, j= 1,2, …. n

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Algorithma Solution
• Step 1. Determine the values s’j, j = 1, …, n, the minimizes the total cost cj(sj) = c1j(sj) + c2j(sj) + c3j(sj)
due to product j:
Set sj =[s’j] if cj([s’j])< cj([s’j]); otherwise s =[s’j], j= 1, 2….n
• Step 2. Compute the optimal solution sj*, j = 1, 2 …, n, as follows:
• The total length of the aisles wtot can than be obtained by the following relation:
 
  .
n
...,
,
j
'
kw
dv
how
m
o
u
f
'
s
.
n
...,
,
j
,
'
s
s
ds
s
dc
j
j
j
j
j
j
j
j
j
j
j
j
1
1
0






max
j
j
max
j
j
min
j
min
j
j
max
j
min
j
*
j
s
s
.
n
...,
,
j
,
s
s
s
,
s
s
s
j
s
s
s













if
1
if
if



n
j
*
j
j
tot
s
w
w
1

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Example
Wellen is firm manufacturing and distributing parts for
numerical control machinec. Its warehouse in Herstal consists of
wide reserve zone, and of forward zone. At present 10 product
are store ( see table 1). Then, o=400 order per day, d= 3 order
per lot, v= 1200 m per day, h=$75 per day, while the area and
equipment cost per unit of aisle length k is assumed to be
negligible.
•The minimum and the maximum number of position for
the various product are on table 2
•The result are in Table 3
•The total length Wtot of aisle of forward zone = 98.5 m

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Table 1. Characteristic of Product at Wellen Warehouse
Item (j) oj uj fj ($/supply) gj ($/unit of item) wj (m) mj
1 40 4 5 0.2 0.75 12
2 60 2 5 0.2 1.00 8
3 35 5 5 0.2 0.75 12
4 45 3 5 0.2 1.00 8
5 95 2 5 0.2 1.00 8
6 65 4 5 0.2 0.75 12
7 45 2 5 0.2 0.75 12
8 50 4 5 0.2 1.00 8
9 65 3 5 0.2 1.00 8
10 45 5 5 0.2 0.75 12

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Table 2. Minimum and Maximum number of aisle position
Item (j) sj
min sj
max
1 9 14
2 5 12
3 13 15
4 8 10
5 7 20
6 9 11
7 10 13
8 8 15
9 11 16
10 14 19

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Table 3. Number of aisle positions in the forward zone
Item (j) s’j s’j cj(s’j) s’j cj(s’j) s*j
1 10.33 10 44.92 11 44.94 10 10
2 9.49 9 39.83 10 39.83 9 9
3 10.80 10 48.54 11 48.50 11 13
4 10.06 10 43.77 11 43.84 10 10
5 11.94 11 57.96 12 57.90 12 12
6 13.17 13 68.46 14 68.49 13 11
7 7.75 7 27.73 8 27.69 8 10
8 12.25 12 60.42 13 60.45 12 12
9 12.09 12 59.16 13 59.21 12 12
10 12.25 12 60.31 13 60.34 12 14

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I/O port 1
I/O port 2

45
Product Allocation
Minimasi
Subject to:

 
n
j
m
k
jk
jk
d
x
c
1 1
  ,
m
....,
,
k
,
n
...,
,
j
,
,
x
,
m
...,
,
k
,
x
,
n
...,
,
j
,
mj
x
d
jk
n
j
d
jk
m
k
jk
d
1
1
1
0
1
1
1
1
1












46
Features Of product
Item Storage Location
Number of storage and retrievals per day in the Malabar
warehouse
I/O port 1 I/O port 2
1 12 25 18
2 6 16 26
3 8 14 30
4 4 24 22
5 8 22 22

47
Distance between storage location and I/O port 1
Storage
location
Distance
Storage
location
Distance
Storage
location
Distance
Storage
location
Distance
1 2 11 2 21 14 31 14
2 4 12 4 22 16 32 16
3 6 13 6 23 18 33 18
4 8 14 8 24 20 34 20
5 10 15 10 25 22 35 22
6 3 16 3 26 15 36 15
7 5 17 5 27 17 37 17
8 7 18 7 28 19 38 19
9 9 19 9 29 21 39 21
10 11 20 11 30 23 40 23

48
Distance between storage location and I/O port 2
Storage
location
Distance
Storage
location
Distance
Storage
location
Distance
Storage
location
Distance
1 22 11 22 21 10 31 10
2 20 12 20 22 8 32 8
3 18 13 18 23 6 33 6
4 16 14 16 24 4 34 4
5 14 15 14 25 2 35 2
6 23 16 23 26 11 36 11
7 21 17 21 27 9 37 9
8 19 18 19 28 7 38 7
9 17 19 17 29 5 39 5
10 15 20 15 30 3 40 3

49
Storage
location
Distance
Storage
location
Distance
Storage
location
Distance
Storage
location
Distance
1 22 11 22 21 10 31 10
2 20 12 20 22 8 32 8
3 18 13 18 23 6 33 6
4 16 14 16 24 4 34 4
5 14 15 14 25 2 35 2
6 23 16 23 26 11 36 11
7 21 17 21 27 9 37 9
8 19 18 19 28 7 38 7
9 17 19 17 29 5 39 5
10 15 20 15 30 3 40 3

50
Storage location
k
Assignment Cost
Product
J = 2
Product
J = 2
Product
J = 3
Product
J = 4
Product
J = 5
21 44.17 80.67 62.00 139.00 66.00
22 45.33 77.33 58.00 140.00 66.00
23 46.50 74.00 54.00 141.00 66.00
24 47.67 70.67 50.00 142.00 66.00
25 48.83 67.33 46.00 143.00 66.00
26 47.75 87.67 67.50 150.50 71.50
27 48.92 84.33 63.50 151.50 71.50
28 50.08 81.00 59.50 152.50 71.50
29 51.25 77.67 55.50 153.50 71.50
30 52.42 74.33 51.50 154.50 71.50
31 44.17 80.67 62.00 139.00 66.00
32 45.33 77.33 58.00 140.00 66.00
33 46.50 74.00 54.00 141.00 66.00
34 47.67 70.67 50.00 142.00 66.00
35 48.83 67.33 46.00 143.00 66.00
36 47.75 87.67 67.50 150.50 71.50
37 48.92 84.33 63.50 151.50 71.50
38 50.08 81.00 59.50 152.50 71.50
39 51.25 77.67 55.50 153.50 71.50
40 52.42 74.33 51.50 154.50 71.50

51
Storage
location
Product
Storage
location
Product
Storage
location
Product
Storage
location
Product
1 1 11 1 21 5 31 5
2 4 12 4 22 2 32 2
3 4 13 4 23 2 33 2
4 5 14 5 24 2 34 2
5 5 15 5 25 3 35 3
6 1 16 1 26 - 36 5
7 1 17 1 27 - 37 5
8 1 18 1 28 3 38 3
9 1 19 1 29 3 39 3
10 1 20 1 30 3 40 3

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• Step 1. Construct a vector  of components, in which there are mj copies of each aj, j = 1, …, n. Sort the
vector  by nonincreasing values of its components. Define (i) in such away that (i) = j if i = aj, i = 1, …,
• Step 2. Let b the vector of md components coresponding to value bk, k = 1, …. ,md. Sort the vector b by
nondecreasing values of its component. Let  be the vector of
components, corresponding to the first components of the sorted vector b. Define (i) in
such away that (i) = k if i = bk, i = 1, …,
• Step 3. Determine the optimal solution of problems as :
and x*
jk= 0, for all the remaining components.
 
n
j j
m
1
 
n
r r
m
1
 
n
j j
m
1  
n
j j
m
1
 
n
r r
m
1
    


 



n
j
j
*
i
.
i m
....
,
i
,
x
1
1
1

53
Product (j) Storage location
Number of storage and retrievals
per day
aj
1 11 21 5
2 12 22 2
3 13 23 2
4 14 24 2
5 15 25 3
6 16 26 -
7 17 27 -
8 18 28 3
9 19 29 3
10 20 30 3

54
i i (i) i (i) i i (i) i (i)
1 11.50 4 2 1 20 5.50 5 11 20
2 11.50 4 2 11 21 5.50 5 14 21
3 11.50 4 3 6 22 5.50 5 14 31
4 7.00 4 3 16 23 5.50 5 15 26
5 7.00 2 4 2 24 5.50 5 15 36
6 7.00 2 4 12 25 5.50 5 16 22
7 7.00 2 5 7 26 5.50 5 16 32
8 7.00 2 5 17 27 3.58 1 17 27
9 7.00 2 6 3 28 3.58 1 17 37
10 7.00 2 6 13 29 3.58 1 18 23
11 5.50 3 7 8 30 3.58 1 18 33
12 5.50 3 7 18 31 3.58 1 19 28
13 5.50 3 8 4 32 3.58 1 19 38
14 5.50 3 8 14 33 3.58 1 20 24
15 5.50 3 9 9 34 3.58 1 20 34
16 5.50 3 9 19 35 3.58 1 21 29
17 5.50 3 10 5 36 3.58 1 21 39
18 5.50 3 10 15 37 3.58 1 22 25
19 5.50 5 11 10 38 3.58 1 22 35

55
Storage
location
Product
Storage
location
Product
Storage
location
Product
Storage
location
Product
1 4 11 4 21 5 31 5
2 2 12 2 22 5 32 5
3 2 13 2 23 1 33 1
4 3 14 3 24 1 34 1
5 3 15 3 25 1 35 1
6 4 16 4 26 5 36 5
7 2 17 2 27 1 37 1
8 3 18 3 28 1 38 1
9 3 19 3 29 1 39 1
10 5 20 5 30 - 40 -

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