At a jewelry, every month the precision of a laser cutting tool is inspected, then classified as: state 0 = as new, state 1 = low imprecision, state 2 = major imprecision, or state 3 = o ut of order. Suppose the jeweler has two operation policies to choose from and applies the first one defined as follows:
Policy 1: do nothing in states 0, 1, 2 and replace the laser cutting tool in state 3.
Suppose that the replacement process takes one month to complete with a lost profit of $16000 and a replacement cost of $32000, and that the costs of defectives are $ 0 for state 0, $8000 for state 1, and $24000 for state 2.
If the steady-state probabilities of Policy 1 are:
π0=2/9, π1=3/9, π2=2/9, π3=2/9
What is the expected average operation cost per month?