Hybrid NSGA-II Algorithm on Multi-objective Inventory Management Problem - Intelligent Computing for Sustainable Energy and Environment - page 161

2 Literature Review

2.1 Inventory Models

Single-Period and Multi-period Models. Single-period model has another
name as newsvendor model. In this model, only one period is considered and
it is assumed that at the end of one period, there is always the same amount
of products left so that every period would start the same. This means that
managers would have to discard, sell at a lower price to get rid of extra products,
and they also have to bear the shortage cost if products are not enough at the
end [2]. On the contrary, multi-period model is defined on a longer time line.
This time line is segmented into many time cycles. The cycles are not the same.
At the beginning of a cycle, there will be an order so that certain inventory
would exist in the beginning. The difference in demand in every time cycle leads
to the time cycles difference. With larger demand, the inventory can only last
for a shorter period [3].

Static and Dynamic Models. In static model, the manager would order
the same amount of raw material or products at every beginning of time cycle.
While in dynamic models, ( r,Q ), ( r,nQ )or( s,S ) are strategies often accepted.
Inventory order position (IOP) is the concept we use often later in this passage.
IOP = inventory on hand + outstanding orders in transit + outstanding orders
backlogged backorders [4]. ( r,Q ) says that if IOP falls lower than r ,then the

manager would order Q units of products. ( r,nQ ) is a extended form of ( r,Q )
.Asfor( s,S ) , it means that if IOP falls below s , then order enough units of
products so that the total units can reach S .

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2.2 Risk Measurements

Two kinds of risk measurements are widely accepted and used: Value at Risk(VaR)
and Conditional Value at Risk(CVaR).

VaR. VaR answers the maximum lost a company will suffer under certain
confidence level. JP Morgan firstly applied VaR in their Risk Metrics System
[5]. Later, many assessing departments began to use VaR to measure risks.
For financial institutions, they have to be put away so that the probability
of its inability to survive an adverse market would be small. Similarly, in in-
ventory management, some products should be put away to deal with risks
generated by demand, price or other elements [6]. VaR is defined as follow-
ing, VaR α ( x )=min

. f ( x,y )isloss.Andthisequation
means the probability of loss to be lower or equal to VaR is bigger or equal to a
given parameter α .

{ u | P { f ( x,y ) ≤ u }≥ α }