On a two-commodity inventory problem with Markov shift in demand

The authors consider a two-commodity inventory problem with shift in demand of the commodity at each demand epoch governed by a Markov chain. At each demand epoch only one type of commodity is demanded. The quantity demanded does not depend on the type of commodity being demanded. The inventory level is continuously monitored. Lead time is assumed to be zero and shortage is not permitted. The steady state probabilities for the system state are obtained. An optimality problem is analyzed and some numerical illustrations are provided.