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.