Consider an inventory system in which the sequence of events during each period is as follows: (1)
Question:
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.
(3) With probability 1/3, 0 units are demanded during the period;
a. With probability 1/3, 1 unit is demanded during the period; and
b. 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.
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman