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The total power of a conglomerate depends on both the power of the holding com-
pany and the power of its subsidiary companies. But the holding company has larger
weights. This total power is defined by the weighted cost of two hierarchical companies:
power cong
n
=[ p con n ] 1 =[ f holding
n , i ] 1
f sub
+
τ
(19)
n
where p cong
< 1. Cost f sub
n , i
is the total cost of the n -th conglomerate and 0 <
τ
is the
n
geometry mean of i -th subsidiary company in n -th conglomerate. In fact,
represents
the role of the subsidiary companies in determining the total power of a conglomerate.
The market competition among conglomerates begins and all the conglomerates try
to take possession of the subsidiary companies of other conglomerates. This competi-
tion is modeled by picking some of the weakest subsidiary companies of the weakest
conglomerates and making a competition among all conglomerates to possess these
subsidiary companies. Each of the conglomerates will have a likelihood of taking pos-
session of these subsidiary companies based on its total power; therefore, powerful
conglomerates have greater chance to possess subsidiary companies. The possession
probability of each conglomerate must be found. The normalized total cost of each
conglomerate is calculated as:
P cong
n
τ
p cong
i
p cong
n
= ma i {
}−
(20)
where P con n is the normalized total cost of the n -th conglomerate.
The possession probability of each conglomerate is given by
N holding
n =1
pp cong
n
P con n /
P cong
n
=
(21)
where pp con n is the possession probability of the n -th conglomerate.
Finally, vector Dif is formed :
Dif = PP cong
1
rand N holding
rand 1 , PP cong
2
, PP cong
N holding
rand 2 ,
···
(22)
where rand 1 , rand 2 ,
, rand N holding are random numbers between 0 and 1.
The mentioned subsidiary companies will be given to an conglomerate which has the
maximum relevant index in Dif vector.
The powerless conglomerates will collapse in the market competition. Different cri-
teria can be defined for collapse mechanism. In this paper, a conglomerate is assumed
to be collapsed when it loses all of its subsidiary companies.
After the market competitions, all the conglomerates will collapse except the most
powerful one and all companies under their possession become subsidiary companies
of this conglomerate. All the subsidiary companies also have the same positions and the
same fitness. In such case, the algorithm stops.
···
4
Implementation of THMCA for UC Problem Using Expert
System
This work develops an expert system, which comprises six expert rules (ER1-ER6),
for satisfying all constraints. The expert system is applied in both the pre-scheduling
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