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
The innovative heuristic procedure balances the replenishmentorder cost and inventory holding costs for different items in an iterative procedure. The JRP has the same
concept as the traditional EOQ for an individual item. The ratio between the replenishment cost and the inventory holding cost without any safety stock is equal to one. The smaller the
ratio, the higher the cost. The closer the individual ratio to one, the better the solution. In order to adjust the ratio closest to one, two-steps of heuristic is needed. In the
heuristic step, the step starts by setting the k
i
values to one all items are replenished every time interval. Then, check the ratios and track how the total cost changes as the
replenishment frequencies k
i
values are updated Nilsson et al., 2007. The detail of the innovative heuristic procedure is presented in Figure 1. The steps
are given below: 1. Set all values of k
i
to 1, and compute the total cost for the initial solution. 2. Compute Q
i
and increase the values of k
i
by one for all items with ratios higher than 1.4. 3. Calculate the total cost. Repeat until all ratios are below 1.4 or the total cost start to
increase. 4. If all ratios are below 1.4, then we have derived the best solution for the total cost.
5. If the total cost start to increase, the best solution is the previous iteration. 6. Choose the highest Q
i
. Then increase k
i
value one by one for i
th
item. 7. Calculate the total cost and ratios. Repeat this until all quotients are below 1.4.. If there is
k
i
=1, then it must be skipped. 8. If all ratios are below 1.4 excluding the exception, then we got the best solution for the
total cost. The value 1.4 is chosen because it produces the lowest error Nilsson et al., 2007.
Nilsson already tested for 48,000 simulated test problems with the value of ratios ranging from 1.0 to 2.0.
7. Stochastic demand
There is significant uncertainty when retailer has to forecast or estimate customer demand
. In
most business activities, it is too complex to solve planning and processing using analytical solution. Recently, several coordinated replenishment policies for stochastic
1 1
i i
n i
i n
i i
i i
i
D h
s S
D h
s Q
The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
demands are suggested in the literature Kiesmuller, 2009. Monte Carlo can be used for
stochastic demand with random variables. The flow chart diagram to implement the innovative heuristic using random variates is generated by Monte Carlo simulation for
Poisson and Negative Exponential distribution. It is given in Figure 2.
Start
k
i
=1, for i = 1,..,n
k = k
1,...,
k
n
TC =TCk
Qk
i
for i = 1,..,n
Qk
i
1.4?
k
i
=k
i
+1 for i = 1,..,n
TCk
Qk
i
Yes
TCkTC and
Qk
i
1.4? Yes
TCk TC and
Qk
i
1.4? No
Yes TC is the
best solution
No
No k
i
=k
i
-1 for i = 1,..,n
TCk
Qk
i
back to best solution so far
k
i
= k
i
+1 i = max Q
i
TCk
Qk
i
TCkTC and
Qk
i
1.4 and k
i
≠ 1 Yes
No
End
Figure 1 . Flow Chart of Heuristic Procedure
The 2010 International Conference on Innovation and Management, Penang, Malaysia, July 7- 10, 2010.
Define an input domain Poisson Exponential and number of forecasting
periods N d = 0
Generate Inputs randomly for several items by Monte Carlo Simulation
Set d= d + 1
1. Set the k
i
values are to one 2. Compute quotient Q
d
i
and the Total Cost TC
d
using the innovative heuristic procedure
d =N?
Yes
Sum = TC
d
for d = 1, …, N
No
Figure 2 . A new heuristic implementation in Monte Carlo simulation
8. Result Discussion
