2. Consider an inventory system which the sequence of events during each period is as follows. i. We observe the inventory level (call it ) at the beginning of the period. ii. If units are ordered. If 0 units are ordered. Delivery of all ordered units is immediate. iii. With probability 1/3, 0 units are demanded during the period: with probability of 1/3, 1 unit is demanded during the period; and with probability 1/3, 2 units are demanded during the period. iv. We observe the inventory level ay the beginning of the next period. a) Defines a period state to be period's beginning inventory level. Determine the transition matrix diagram that could be used to model this inventory system as a Markov chain. b) Obtain the probability of all states 3 periods from now.

MATLAB: An Introduction with Applications
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2. Consider an inventory system which the sequence of
events during each period is as follows.
i. We observe the inventory level (call it ) at the
beginning of the period.
ii. If units are ordered. If 0 units are ordered.
Delivery of all ordered units is immediate.
iii. With probability 1/3, 0 units are demanded
during the period: with probability of 1/3, 1 unit is
demanded during the period; and with probability
1/3, 2 units are demanded during the period.
iv. We observe the inventory level ay the beginning
of the next period.
a) Defines a period state to be period's beginning
inventory level. Determine the transition matrix
diagram that could be used to model this
inventory system as a Markov chain.
b) Obtain the probability of all states 3 periods
from now.
Transcribed Image Text:2. Consider an inventory system which the sequence of events during each period is as follows. i. We observe the inventory level (call it ) at the beginning of the period. ii. If units are ordered. If 0 units are ordered. Delivery of all ordered units is immediate. iii. With probability 1/3, 0 units are demanded during the period: with probability of 1/3, 1 unit is demanded during the period; and with probability 1/3, 2 units are demanded during the period. iv. We observe the inventory level ay the beginning of the next period. a) Defines a period state to be period's beginning inventory level. Determine the transition matrix diagram that could be used to model this inventory system as a Markov chain. b) Obtain the probability of all states 3 periods from now.
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