The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
heuristics. An innovative heuristic procedure balances the replenishmentordersetup cost and inventory holding costs for different items in an iterative procedure Abdul-Jalbar, Segerstedt,
Sicilia, Nilsson, 2010; Nilsson et al., 2007. The objectives of this research are: 1 to derive three JRP mathematical models: classical,
centralized and decentralized models; 2 to develop innovative heuristic procedure for models with deterministic and stochastic demand. We show how the innovative heuristic approach
can minimize the total cost. The remaining parts of this paper are organized as follows. Notation and assumption is
given in section 2. The classical, decentralized, and centralized JRP models are described in section 3, 4, and 5, respectively. An innovativeheuristic procedure is presented in section 6
and stochastic demand and its implementation are given in section 7. Finally, experimental results and some conclusions are summarized in section 8 and 9, respectively.
2. Notation and Assumption
The following notations are used in this paper: T
: Time between successive replenishments years
S :
Major ordering cost associated with each replenishment order TC
: Total annual holding and ordering costs for all the products year
i :
1, 2, …, n, a product index n
: Number of products
D
i
: Annual demand for product i unitsyear
h
i
: Annual holding cost of product i unityear
s
i
: The minor ordering cost incurred if product i is ordered in a replenishment
order Q
i
: the ratio between the two costs for item- i
T
i
: Time interval between successive replenishment of product i years
k
i
: The integer number of T intervals that the replenishment quantity of item i
will last Under the Indirect Grouping Strategy IGS, the cycle time for every product is an
integer multiple k
i
of the replenishment cycle time T. Thus, the cycle time for product i is T
i
= k
i
T. In this research, strict cycle policies is used in which at least one item is ordered at every replenishment opportunity, so that k
i
1. Assumptions used in this research are: 1 consider the total cost only at the retailer site,
2 the demand rate for each item is constant, 3 the retailer replenishes the stocks from the external source on an EOQ basis, subject to a major setup cost for placing an order and a
minor setup cost for each additional item ordered.
The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
3. Classical JRP Model
The assumptions of classical JRP model are similar to the economic order quantity EOQ model. The total cost for the retailer per unit time is Khouja Goyal, 2008:
1 The optimal time interval,
T
, that minimizes Eq. 1 with a given set of k
1
, k
2
, …, k
n
is :
2 Substituting optimal
T
into Eq. 1 gives the total cost function, which depends only on the set of
i
k
values as: 3
The replenishment cost and inventory holding cost for item i: 4
5 Dividing Eq. 4 by Eq. 5 gives the quotient or the ratio between the two costs for
item- i: 6
Substitute
T
into
i
Q
, one has:
7
n i
i i
i n
i i
i i
D h
k k
s S
k TC
1 1
2
n i
i i
i n
i i
i i
D h
k k
s S
k T
1 1
2
n i
i i
i i
i
D h
T k
T k
s T
S TC
1
2
T k
s C
i i
s i
2
i i
i h
i
D h
Tk C
i i
i i
i i
i i
i i
D h
k T
s D
h Tk
T k
s Q
2 2
2 2
2 1
1 i
i i
n i
i i
n i
i i
i i
i
D h
k k
s S
D h
k s
Q
The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
4. Decentralized System
