Question

A small car dealer, who is eager to estimate his inventory cost, can hold up
to 4 cars in the showroom. The periodic demand for the cars is following a Poisson
distribution with mean 2, except for the maximum inventory level. In the case of
maximum inventory level, the dealer makes a special discount by offering a price much
below the market which results in depletion of its entire inventory. Once all the cars are
sold, the dealer immediately orders 3 or 4 cars with equally likely probabilities. Apart
from maximum and minimum inventory levels, the dealer can sell all his cars and also
seek to refill its inventory. The Inventory cost is given as; $500 per car per period.
(a) Construct the transition probability matrix, by properly defining the states and the
state space.
(b) Find the average inventory holding cost per period.

Answer 1