A warehouse uses $($s S$)$ inventory policy to satisfy uncertain demand: inventory level is checked

at the end of week, and

$$ if stock level $<$ s

$$ if s stock level S

order up to S$,$

do nothing.

Assume that s $=1,$ S $=3,$ weekly demand Dn are iid r$.$v$.$s with discrete distribution

d

$0123$

P$($Dn $=$ d$)$

$1$

$8$

$1$

$4$

and that inventory ordered on Friday arrives next Monday, model the inventory dynamics as a

Markov chain