Transcript 6. Storage System

ระบบการจัดเก็บในคลังสิ นค้ า
Storage Systems
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Dedicated Storage Location Policy
Randomized Storage Location Policy
Class-based Dedicated Storage Location
Policy
Shared Storage Location Policy
Continuous Warehouse Layout
Determination of Space Requirement
Dedicated Storage Location Policy
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Also call “fixed slot storage”
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Specific storage location is assigned to each product
Storage system
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Part number sequence
Throughput-based dedicated storage
Throughput: Number of storages or retrievals per time
period เช่น 320 storages ต่อ 8 ชัว่ โมงการทางาน เป็ นต้น
Space Requirement
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One and only one product is assigned to a specific
location
Number of storage locations assigned must be
capable of satisfying the maximum storage
requirement of product.
Determination method
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Maximum storage location
Service level
Cost based
Space Requirement
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Maximum storage requirement
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The number of storage slots provided  max.
storage requirement
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See example (workshop)
Space Requirement
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Service Level
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Can be determined based on a probability of
having sufficient storage slots to satisfy storage
demand
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Service level = Demand Satisfied/Total Demand
Let’s
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Qj = Number of slots provided for product j
Space Requirement
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Probability of having sufficient slots for
product j is:
P[Sj  Qj]
Sj represent the slot demand for product j
The CDF of the function is:
Fj(Qj) = P[Sj  Qj]
Space Requirement
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Probability of 1 or more slot shortage
P[1 or more shortage] = 1 – P[no shortage]
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Hence, probability of no shortage for all
product j = 1, 2, …, n
P[no shortage] = (P[no shortage of product j])
P[1 or more shortage] =1-(P[no shortage of product j])
Space Requirement
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Service Level
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จากทฤษฎีความน่าจะเป็ น เมื่อกาหนดให้
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Z แทนค่ามาตรฐานของตัวแปรสุ่มที่แจกแจงแบบปกติมาตรฐาน มีค่าเฉลี่ย และค่าเบี่ยงเบน
มาตรฐาน เท่ากับ 0 และ 1 ตามลาดับ
 แทนระดับบริ การ (service level) ที่ตอ้ งการ
Space Requirement
จะได้ จานวน Slots ที่รับประกันระดับบริ การ คือ
Qj = Mj + ZSDj
เมื่อ Qj = จานวน slots ที่ตอ้ งการเพื่อรับประกันระดับบริ การ 
Mj = จานวน Slots เฉลี่ยที่ตอ้ งการต่อวัน
SDj = ค่าเบี่ยงเบนมาตรฐานของ Slots ที่ตอ้ งการต่อวัน
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See example (workshop)
Optimized Qj
Minimize Qj
(Fj(Qj))  P
Qj  0
P = minimum probability of no shortage of
storage slot
ST:
Space Requirement
Maximize (Fj(Qj))
ST:
Qj  S
Qj  0
S = Total slots available
Space Requirement
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Cost-based
Mathematical model is needed, (example)
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T
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MinimizeTCQ 1 ,...., Q n    C 0 Q j   C1 ,t min d t , j , Q j  C 2 ,t max d t , j  Q j ,0
j 1 
t 1
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n
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Conditions:
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There are fixed cost Co for “owned” storage Qj
The operating cost for owned storage is C1,t per space period
If owned storage is less than demand, the excess
requirement can be leased at an operating cost of C2,t per
space period
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Example math. Model (cont.)
Definition of parameters
- Qj : ‘owned’ storage capacity for product j
- T : length of the planning horizon in time period
- dt,j: storage space required for product j during period t
- TC(Q1,…,Qn) : Total cost function over the planning horizon as a
function of the set of storage capacities
- Co : discount present worth cost per unit storage capacity owned
during planning horizon of T time period
- C1, t: discount present worth cost per unit stored in owned space
during planning time t
- C2,t: discount present worth cost per unit stored in leased space
during planning time t
Example math. Model (cont.)
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Therefore, the Total Cost function is:
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Fixed cost + Operating cost
Example math. Model (cont.)
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min(dt,j,Qj)
= dt,j
if dt,j < Qj
= Qj
if dt,j ≥ Qj
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max(dj,t-Qj,0)
=0
= dt,j-Qj
if dt,j-Qj < Qj
if dt,j-Qj ≥ Qj
Example math. Model (cont.)
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Solution technique (one of them)
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Let’s C’ = C0/(C2-C1)
Then,
1.
2.
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Sequence in decreasing order the demand for space
Sum the demand frequencies over the sequence
When partial sum is first equal to or greater than C’, stop;
the optimum capacity equals that demand level
Example math. Model (cont.)
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Take a hand on example and see if we can…
Assigning Products Storage/Retrieval
Locations
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Given That
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s = number of storage slots or location
n = number of product to be stored
m = number of inputs/outs (I/O) points
Sj = storage requirement for product j, expressed
in number of storage slots
Tj = throughput requirement or activities level for
product j, expressed by the number of
storage/retrievals (S/R) performed per unit time
Assigning Products Storage/Retrieval
Locations
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pi,j = percent of S/R tripe for product j that are
from/to I/O point i
Ti,k = time required to travel between I/O point i
and S/R location k
Xj,k = 1 if product i is assigned to S/R location k or
0 otherwise
f(x) = expect time required to satisfies the
throughput requirement for the system
See workshop
Assigning Products Storage/Retrieval
Locations
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Mathematical model as shown can be used
(also discuss via workshop)
T
T
Minimize f(x)   p .t .x     x   p t 
S
S
m
n
s
n
i, j
i 1 j1 k 1
j ,k
j ,k
j 1
j
j k 1
ST :
n
x
j1
j,k
1 ,
k  1,...,S
j,k
 sj,
j  1,...,n
S
x
k 1
X j,k  0,1
m
where : t j,k   pi , j ti , k
i 1
s
for all j and k
m
j ,k
i 1
i , j i ,k
Assigning Products Storage/Retrieval
Locations
n
s
Minimize f(x)   c j,k x j,k
j1 k 1
ST :
n
x
j1
j,k
1 ,
k  1,...,S
j,k
 sj,
j  1,...,n
S
x
k 1
X j,k  0,1
m
where : t j,k   pi , j ti ,k , c j ,k
i 1
 Tj

s
 j
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t j ,k
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for all j and k
Randomized Storage Location Policy
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Also known as “Floating Slot Storage”
Each open storage slot has equal chance of
being assigned when a load arrive
In practice, when the load arrive, it is placed
in the “closest” open feasible location
Retrieval occurs on a FIFO basis
Space Requirement
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Storage space requirement equal the
maximum of the aggregate storage
requirements for products.
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See example (workshop)
Dedicated (D) VS Randomized (R)
Storage Location Policy
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R requires less space than D
It is more difficult to determine the exact
location of R than that of D
D requires less travel time (on average) in
storages and retrievals of products
Class-based Dedicated Storage
Location Policy
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A compromise between dedicated and
randomized storage location policies
Products are classified into classes
according to their S/R ratios
Dedicated policy applies between classes
while Randomized policy applies within each
class.
See example (workshop)
Shared Storage Location Policy
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Shared storage recognizes and takes
advantage of the inherent differences in
lengths of time that individual pallet loads
remain in storage