Analysis of two commodity Markovian inventory system with lead time

A two commodity continuous review inventory system with independent Poisson processes for the demands is considered in this paper. The maximum inventory level for the ith commodity is fixed as Si, i = 1,2. The net inventory level at time t for the ith commodity is denoted by Ii(t), i = 1,2. If the total net inventory level I(t) = I1(t) + I2(t) drops to a prefixed level s [≤ (S1 − 2)/2 or (S2 − 2)/2], an order will be placed for (Si − s) units of the ith commodity (i = 1,2). The probability distribution for inventory level and mean reorders and shortage rates in the steady state are computed. Numerical illustrations of the results are also provided.