A hospital faces following blood inventory problem. There is the need for a rare blood type (AB, Rh negative) for which the demand D over any three-day period is given by
P[D=0]=0.4, P[D=1]=0.3
P[D=2]=0.2, P[D=3]=0.1
There are also three days between deliveries. Since the expected demand is one unit, the hospital proposes a policy of receiving one pint at each delivery and using the oldest blood first (a FIFO or first-in, first out policy). If more is required than on hand, an expensive emergency delivery is made. Blood is discarded if still on the shelf after 21 days. Let the state of this system be the number of pints on hand just after a regularly scheduled delivery. Model this situation as Markov chain and give the one-step state transition matrix.