UFESI6321
170202.xmcd
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17.2.2
You are a retailer considering your inventory system in which the sequence of events during
each sales period is as follows.
(1) As a retailer, you observe your inventory level
i
at the beginning of the period as one of the
following values:
i
0
4
..
:=
i
0
1
2
3
4
=
(2) You order units from your wholesaler for immediate delivery according to this formula:
o
i
if i
1
≤
4
i

,
0
,
(
)
:=
In other words, you will order and immediately receive these numbers of units depending upon
these current inventory values:
augment i o
i
,
(
)
0
4
(
)
1
3
(
)
2
0
(
)
3
0
(
)
4
0
(
)
=
(3) With conditional probability
p'
1
3
:=
retail customers will demand any one of the three discrete quantities of
r
0
2
..
:=
d
r
⟨⟩
r
:=
d
0
1
2
(
)
=
(4) You observe the inventory level at the beginning of the next period.
Define a period's state to be the period's beginning inventory level
i
.
Determine the transition matrix that could be used to model this inventory system as a Markov
chain.
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 Spring '07
 JosephGeunes
 Conditional Probability, Probability, Probability theory, Probability space, Kennedy Space Center

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