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Consider an inventory system in which the sequence of events during each period is as follows. (1) We observe the inventory level (call it i) at the...

Consider an inventory system in which the sequence of
events during each period is as follows. (1) We observe the
inventory level (call it i) at the beginning of the period.
(2) If i  1, 4  i units are ordered. If i 2, 0 units are
ordered. Delivery of all ordered units is immediate. (3) With
probability 1
3
, 0 units are demanded during the period; with
probability 1
3
, 1 unit is demanded during the period; and
with probability 1
3
, 2 units are demanded during the period.
(4) We observe the inventory level at the beginning of the
next period.
Define a period’s state to be the period’s beginning
inventory level. Determine the transition matrix that could
be used to model this inventory system as a Markov chain.

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