Question: Consider an inventory system in which the sequence of events during each period is asfollows. ( 1 ) We observe the inventory level ( call

Consider an inventory system in which the sequence of events during each period is asfollows.

(1)

We observe the inventory level

(

call it i

)

at the beginning of the period.

(2)

1, 4 -

i units are ordered. If

2, 0

units are ordered. Delivery of all ordered unitsis immediate.

(3)

With probability

1 / 4, 0

units are demanded during the period; withprobability

2 / 4, 1

unit is demanded during the period; and with probability

1 / 4, 2

unitsare demanded during the period.

(4)

We observe the inventory level at the beginning ofthe next period. Define a periods state to be the periods beginning inventory level.Determine the transition matrix that could be used to model this inventory system as aMarkov chain.

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