Information Technology Reference
In-Depth Information
CVaR.
VaR has been widely used. However, according to Atzner, VaR is not
a consistent measurement and this may cause problems in calculating. CVaR
was brought up as Optimization of Conditional Value-at-Risk [7] as a better
substitute for VaR. CVaR is defined as
CVaR
=
E
[
f
(
x,y
)
>VaR
]. VaR has
the disadvantage of not being convex, thus conceptually and numerically being
problematic [8]. CVaR, on the other hand, can be written in the form of a convex
optimizing problem.
CVaR
α
(
x
)=min
{
η
α
(
x,u
)
|
u
∈
R
}
1
u
]
+
and [
t
]
+
:= max
where
η
α
(
x,u
):=
u
+
α
E
[
f
(
x,y
)
−
{
0
,t
}
.With better
1
−
attributes, we use CVaR for our model.
KeeH. Chung(1990)[9]analyzedsingle-stageinventorymodel withrisk.Charles
S. Tapiero(2003)[10] examined the use of VaR, which is not consistent, in supply
chain management. Xin Chen, Melvyn Sim(2007)[11] studied multi-stage inven-
tory model with risk using expected utility function, which cannot show the risk
a company is facing directly. So in this passage, we use CVaR as the risk measure-
ment to build a bi-objective model combing risk and inventory.
Genetic Algorithm and NSGA-II.
Genetic Algorithm (GA) was first brought
about by Holland and his colleagues [12]. The basic idea originates from the na-
tures evolution. In the evolution process, the more adaptable individuals tend to
have a bigger chance of surviving, thus the next generation is with less weak genes.
Applying this to GA, it means that individuals with lowercosttend to be combined
and produce offspring more often.
In multi-objective problems, parents cannot be chose just based on one single
value. Therefore, the concept of Pareto front is used to compare the individu-
als with several objectives. Multi-objective problems differ from single-objective
problems in comparison and selection parts. In comparison, we use the concept
of Pareto dominance to measure two solutions. In selection, we need to choose
individuals to be parents according to Pareto rule. Abdullah Konak[13] sum-
marized the genetic methods used in multi-objective problem, among which are
NSGA[14] and more effective NSGA-II(non-dominated-sort-algorithm)[15]. We
here use NSGA-II for our problem.
3Mod lFormu on
3.1 Problem Description
There are
K
suppliers and in every single stage, they each have independent
demand. And in every stage they make decisions as following
1) To meet the demand according to inventory at hand and instantaneous
demand.
2) If demand can be fully satisfied, then order using policy after the demand
is fulfilled.
Search WWH ::
Custom Search