Consider the blood-inventory problem presented in Prob. 16.6-5. Suppose now that the number of pints of blood delivered (on a regular delivery) can be specified at the time of delivery (instead of using the old policy of receiving 1 pint at each delivery). Thus, the number of pints delivered can be 0, 1, 2, or 3 (more than 3 pints can never be used). The cost of regular delivery is $50 per pint, while the cost of an emergency delivery is $100 per pint. Starting with the proposed policy given in Prob. 16.6-5, perform two iterations of the policy improvement algorithm.

Prob. 16.6-5

A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of four possible states:

(a) Find the steady-state probabilities.

(b) If the costs of being in states 0, 1, 2, 3, are 0, $1,000, $3,000, and $6,000, respectively, what is the long-run expected average cost per day?

(c) Find the expected recurrence time for state 0 (i.e., the expected length of time a machine can be used before it must be replaced)