The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
4. Decentralized System
In the decentralized replenishment, each entity within the supply chain focuses on minimizing its own costs. The retailer makes the replenishment decision for each item based
on the EOQ. The major component of setup cost is a fixed transportation cost, regardless of items ordered, and the minor setup costs are order-processing costs for specific items
included in the order J.-M. Chen T.-H. Chen, 2005. The total cost of n items per unit time for the retailer is:
8
The optimal time interval,
T
, that minimizes Eq. 8 with a given set of k
1
, k
2
, …, k
n
is :
9
Substituting optimal
T
into Eq. 8 gives the total cost function, which depends only on the set of
i
k
values:
n i
i i
i n
i i
i i
D h
k k
s S
k TC
1 1
2 10
The replenishment cost and inventory holding cost for item i respectively are: 11
12 Dividing Eq. 11 by Eq. 12 gives the quotient or the ratio between the two costs for
item- i: 13
Substituting
T
into
i
Q
, one has:
i i
i i
i i
i i
i i
D h
k T
s S
D h
Tk T
k s
S Q
2 2
2 2
n i
n i
i i
i i
i
D h
T k
T k
s S
TC
1 1
2 1
n i
i i
i n
i i
i i
D h
k k
s S
k T
1 1
2
T k
s S
C
i i
s i
D h
k T
C
i i
h i
2
The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
14
5. Centralized System
In the centralized policy, multi-item replenishment is coordinated using a common replenishment cycle for all items, which reduced the frequency of major setups for the retailer.
The major setup cost incurred by the retailer is reduced from n to one, due to joint replenishment among a family of items J.-M. Chen T.-H. Chen, 2005. The total cost for
the retailer per unit time is: 15
The optimal time interval,
T
, that minimizes Eq. 15 can be found after taking the derivative of TC with respect to T and equaling the result to zero, resulting in:
16 Substituting optimal
T
into Eq. 15 gives the total cost function: 17
The replenishment cost and inventory holding cost for item i respectively are: 18
19 Dividing Eq. 18 by Eq. 19 gives the quotient or the ratio between the two costs for
item- i: 20
n i
i i
i
D h
T T
s T
S TC
1
2
n i
i i
n i
i
D h
s S
TC
1 1
2
n i
i i
n i
i
D h
s S
T
1 1
2
T s
C
i s
i
2
i i
h i
D Th
C
i i
i i
i i
i
D h
T s
D Th
T s
Q
2
2 2
n i
i i
i i
i n
i i
i i
i i
D h
k k
s S
D h
k s
S Q
1 2
1
The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
Substitute
T
to
i
Q
, one has:
21
6. An Innovative Heuristic Procedure
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